Octo62000 0S7-/ Proceedings of The

REcE1kq=D OCTo62000 0s7-/ Proceedings of the

EIGHTEENTH SYMPOSIUM ON ENERGY ENGINEERING SCIENCES

May 15-16,2000

ARGONNE NATIONAL LABORATORY

Argonne, Illinois

Cosponsored by

Office of Basic Energy Sciences U.S. DEPARTMENT OF ENERGY

and

Energy Technology Division ARGONNE NATIONAL LABORATORY

Coordinated by

Argonne National Laboratory 9700 South Cass Avenue Argonne, Illinois 60439

DISCLAIMER

This repo~ was.prepared as an account of work sponsored bjan agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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Portions of this document may be illegible in electronic image products.. Images are produced from the best available original document. EIGHTEENTH SYMPOSIUM ON ENERGY ENGINEERING SCIENCES

FOREWORD

This Proceedings Volume includes the technical papers that were presented during the Eighteenth Symposium on Energy Engineering Sciences on May 15-16, 2000, at Argonne National Laboratory, Argonne, Illinois. The Symposium was structured into seven technical sessions, which included 30 individual presentations followed by discussion and interaction with the audience. A list of participants is appended to this volume.

The DOE Office of Basic Energy Sciences (BES), of which Engineering Sciences is a component of the MateriaIs Sciences and Engineering Division, is responsible for the long-term, mission-oriented research in the Department. The Office has prime responsibility for establishing the basic scientific foundation upon which the Nation’s future energy options will be identified, developed, and built. BES is committed to the generation of new knowledge necessary to solve present and fiture problems regarding energy exploration, production, conversion, and utilization, while maintaining respect for the environment.

Consistent with DOE/BES mission, the Engineering Sciences Program is charged with the identification, initiation, and management of fundamental research on broad, generic topics addressing energy-related engineering problems. Its stated goals are to improve and extend the body of knowledge underlying current engineering practice so as to create new options for enhancing energy savings and production, prolonging the usefid life of energy-related structures and equipment, and developing advanced technologies and materials processing. The program emphasis is on reducing costs through improved industrial production and performance and expanding the nation’s store of fundamental knowledge for solving anticipated and unforeseen engineering problems in energy technologies.

To achieve these goals, the Engineering Sciences Program supports approximately 100 research projects covering a broad spectrum of engineering topics. The Eighteenth Symposium involved approximately one-third of the research projects currently sponsored by DOE/BES Engineering Sciences Program.

The Eighteenth Symposium was held under the joint sponsorship of the DOE Office of Basic Energy Sciences and Argonne National Laboratory (ANL). Ms. Marianne Adair and Ms. Judy Benigno of ANL Conference Services handled local arrangements. Ms. Gloria Griparis of ANL’s Information and Publishing Division, Technical Communication Services was responsible for assembling these proceedings and attending to their publication.

I am grateful to all that contributed to the success of the program, particularly to the participants for their excellent presentations and active involvement in discussions. The resulting interactions made the symposium a most stimulating and enjoyable experience.

BassemF.ArmaIy,SC-131 Division of Materials Sciences and Engineering Office of Basic Energy Sciences.

... 111 -. <

. Proceedingsofthe

EIGHTEENTH SYMPOSIUM ON ENERGY ENGINEERING SCIENCES

May 15-16,2000

Argonne National Laboratory

Argonne, Illinois

TABLE OF CONTENTS

Technical Session I — Fracture Mechanics

AN OVERVIEW OF HIGH TEMPERATURE TIME DEPENDENT DAMAGE DEVELOPMENT ...... l F.W. Brust (Battelle) J. Oh and N. Katsube (Ohio State Universi~) R. Mohan (Rouge Steel)

CRACK PATTERNS DUE TO RESIDUAL STRESS IN THIN FILMS ...... 9 L.B. Freund (Brown Universi~) V.B. Shenoy (Indian Institute of Technology)

OBSERVATION OF CLEAVAGE FRACTURE AFTER SUBSTANTIAL DIMPLE RUPTURE IN ASTM A71OSTEEL ...... 17 W.G. Reuter and W.R. Lloyd (Idaho National Engineering and Environmental Laboratory)

Technical Session II — Optical Diamostics

CAVITY RING-DOWN SPECTROSCOPY AS A PLASMA DIAGNOSTIC: APPLICATIONS TO DIAMOND MLMGROWTH ...... 25 U. Lommatzsch, E.H. Wahl, C.H. Kruger, and R.N. Zare (Stanford University)

LIGHT SCATTERING MEASUREMENTS OF THERMAL DIFFUSIVITY FOR REFERENC!E STANDARDS ...... -31 C. Muzny and R. Perkins (National Institute of Standards and Technology)

COHERENCE AND SYNCHRONIZATION IN ARRAYS OF CLASS B LASERS . . ...39 Y. Braiman, G. Bitton, H.K. Liu, V. Protopopescu, L. Zhang, and J. Barhen (Oak Ridge National Laboratory)

v EXPERIMENTAL TESTS OF RADIATIVE TRANSFER INCORPORATING STATISTICAL OPTICS USING BLACKBODY SOURCES ...... 49 Y. Sun, R. Winston, and J.J. O’Gallagher (Enrico Fermi Institute, UniversiQ of Chicago) K.A. Snail (Naval Research Laboratory)

Technical Session III — Thermofluid Transuort Processes I

LUBRICATED TRANSPORT ...... ,.. ,57 D.D. Joseph (Universi~ of Minnesota)

INTERFACIAL WAVE TRANSITIONS IN LIQUID-LIQUID FLOWS AND INSIGHT INTO FLOW REGIME TRANSITION...... 65 M.J. McCready, B.D. Woods, and M.R. King (University of Notre Dame)

SIMULATING COMPLEX DYNAMICS IN INTERMEDIATE AND LARGE-ASPECT- RATIO CONVECTION SYSTEMS ...... 73 M.-C. Lai (Chung Cheng University) K.-H. Chiam and M.C. Cross (California Institute of Technology) H. Greenside (Duke University)

ENTRAINMENT IN HIGH-VELOCITY, HIGH-TEMPERATURE PLASMA JETS . ..81 J.R. Fincke, D.M. Crawford, S,C. Snyder, W.D. Swank, D.C. Haggard, and R.L. Williamson (Idaho National Engineering and Environmental Laboratory)

FILM COOLING IN A PULSATING STREAM: RECENT RESULTS FOR LAMINAR AND TURBULENT WALL JET .,...... , .,89 H. Fasel, A. Ortega, and I.J. Wygnanski (The University ofArizona)

Technical Session IV— Thermotluid Transport Processes II

OPTIMIZATION OF HEAT TRANSFER EFFECTIVENESS IN HETEROGENEOUS MEDIA ...... 101 V.S. Travkin, 1.Catton, and K. Hu (UniversiQ of Cal~ornia, Los Angeles) .

USE OF HOT-FILM ANEMOMETRY TECHNIQUE IN HORIZONTAL BUBBLY TWO-PHASE FLOW ...... 109 A. Iskandrani and G. Kojasoy (University of Wisconsin-Milwaukee)

MICRO FOUR-SENSOR PROBE METHOD FOR INTERFACIAL AREA MEASUREMENT AND AREA TRANSPORT EQUATION ...... 117 M. Ishiiand S. Kim (Purdue University)

THEORY OF SUBCOOLEDBOILING ...... 125 S.G. Bankoff and S.H. Davis (Northwestern University)

vi COMPLEX DYNAMICS IN LARGE ARRAYS OF FLUID-ELASTIC OSC~LATOW ...... 130 F.C. Moon (Cornell University) M. Kuroda (Mechanical Engineering Laboratory)

Technical Session V — Nonlinear Systems

ROBUST FOREWARNING OF DYNAMICAL CHANGE FROM SINGLE-CHANNEL SCALP EEGDATA ...... 137 V. Protopopescu, L.M. Hively, and P.C. Gailey (Oak Ridge National Luboratoiy)

ENERGY LOCALIZATION, ENERGY PROPAGATION, AND THERMAL RESONANCE IN NONLINEAR ARRAYS ...... 146 K, Lindenberg, R. Reigada, and A. Sarmiento (UniversiU of Calijomia, San Diego,

NATURAL ENERGY AND STRESS FOCUSING PHENOMENA ...... 154 S. Putterman and R. Budakian (Universi~ of Calijomia, Los Angeles)

INSTABILITIES AND DEFECT CHAOS IN MODELS FOR ROTATING NON-BOUSSINESQ CONVECTION ...... 161 H. Riecke, B. Echebarria, V. Moroz, and F. Sain (Northwestern University)

Technical Session VI — Intelligent Machines

COMPLEX INTELLIGENT MACHINES ...... 169 H.B. Smartt, C.R. Tone, and K,L. Kenney (Idaho National Engineering and Environmental Laborato~)

LEARNING AND ADAPTATION IN MULTI-ROBOT TEAMS ...... 177 L.E. Parker, C. Touzet, and D. Jung (Oak Ridge National Laboratory)

INFORMATION FUSION IN PHYSICAL SYSTEMS USING PHYSICAL LAWS . ...186 N.S.V. Rae, D.B. Reister, and J. Barhen (Oak Ridge National Laboratory)

Technical Session VII — Micro and Nano Scale Processes

INTEGRATION OF NANOSENSORS IN MICROSTRUCTURES ...... 194 L. Shi, G. Wu, and A, Majumdar (University of California, Berkeley)

GENERATION OF HIGH CONCENTRATION NANOPARTICLES FOR FILTRATION STUDIES ...... 202 D.R. Chen and D.Y.H. Pui (University ofillinnesota)

vii

,. ::,, ,.,~,$~,.,.,:,./,,.,,,,.:,- ;T:j$.,, .,. ,..:.-?/,,”.+<)/,,-.,$1.,.:5-.f ,<..>..l:+y~,?,,+..,~>.,*>>{/.+,,,,.Q-,.,;,..,..: ,.;,...Jay’:;::;,.”;,.. .:.$8.;!::;.: ,:,;>.::‘ .;,>=l’,.~:..>; ; .“. - ‘y’. ,,;- “--- BIOPHYSICAL DIRECTED ASSEMBLY OF NANOSTRUCTURES FOR NEUROCOMPUTING ...... 212 J.C. Wells, L. Maya, K. Stevenson, T.G. Thundat, J. Barhen, Y. Braiman, and V. Protopopescu (Oak Ridge National Laboratory)

EXPERIMENTAL AND THEORETICAL ASPECTS OF QUANTUM TELEPORTATION ...... ,. .220 L. Zhang, J. Barhen, and H.K. Liu (Oak Ridge National Laboratory)

ENZYME ADSORPTION AND FUNCTION AT INTERFACES ...... 229 L.G. Casc50-Pereira, C.J, Radke, and H.W. Blanch (University of California, Berkeley)

METABOLIC ENGINEERING OF BIODEGRADABLE PLASTIC PRODUCTION BY CYANOBACTERIA: MODEL STUDIES IN Synechocystis sp. PCC6803 ...... 239 G.Taroncher-Oldenburg and G. Stephanopoulos (Massachusetts Institute of Technology)

FINAL LIST OF PARTICIPANTS ...... 247

... VIII AN OVERVIEW OF HIGH TEMPERATURE TIME DEPENDENT DAMAGE DEVELOPMENT

F. W. Brustl, J. Oh*, N. Katsube2, and R. Mohan3

lBattelle, Columbus, Ohio, 43214, U. S. A. 20hio State University, Columbus, Ohio, 43214, U. S. A. 3Rouge Steel, Dearborn, Michigan, 48121, U. S. A.

ABSTRACT

Damage nucleation, growth, and failures of metallic structural components that operate at high temperature are overviewed. Damage nucleation usually begins with the development of small voids at a size level at the high end of the nanoscale (50 to 500 rim). These voids begin to grow via diffusion mechanisms along the grain boundaries along with dislocation creep within the grains. Voids eventually link-up to produce micro-cracks (size 2 to 20 pm). Micro-cracks then link-up to produce macro-cracks, which eventually leads to component failure. Here we overview the high temperature damage development process, especially with regard to cyclic loading, which has received little attention to date. It is seen that damage development under cyclic loading develops in a fashion quite different from the constant load situation.

INTRODUCTION

From recent studies and field experience it is now known that current engineering methods to predict the life and prevent failures of components that operate in severe high temperature environments are ineffective. Hence, an understanding of the high temperature cyclic response of these components, as well as a predictive life methodology, is very important to the DOE goal of providing safe and cheap energy to the USA. On the nanoscale level, cavitation along grain boundaries leads to isolated voids, which eventually link up and lead to a macro crack. The macro . .

crack then grows until it reaches a size where ultimate failure occurs. On both the micro- and macro-mechanics levels, the response under severe history dependent loading had received little attention to date. Prior work mainly focused on simple thermal and load environments. More importantly, the link between the nanoscale level where damage nucleates and the macro level, where predictions must be rndde has not been adequately established, especially under cyclic loading. Thk link is another research goal. Finally, the effect of residual stresses and porosity caused by wekling on structures that operate at high temperature has not been well understood. Since failures frequently occur in the field in and near welds, it is important to extend the understanding and models to account for weld residual stress, strain, and damage effects. By learning how to manage the high temperature structural environment the goal of providing safe, cheap, and efficient energy will be improved.

HIGH TEMPERATURE DAMAGE PROGRESSION

Damage nucleation, growth, damage link-up, crack growth, and breakage is the typical progression of failure for components that operate at high temperature. Damage nucleation begins with the nucleation of a cavity at a size scale at the higher end of the nanoscale level (-50 to 300

HHI (-20 to 200 pm) (-50 to 500 nm) :% .it$’. -. $ OTENTIALCRACKPATHS

~J. $v -o (-2 to 20 pm)

Figure 1. Scales of Creep Damage Development and Failure.

nm, depending on the material). Early in the process, such nucleation and growth phenomenon is explained by diffusion of atomic flux from the cavities to the grain boundaries, along with grain boundary sliding (to a lesser extent). As time proceeds, nonlinear viscous flow (creep) occurs, and, depending on the local stress state, eventually overrides the diffusion growth process, especially as the neighboring voids approach each other. As voids link, micro-cracks develop, link-up, and lead toamacro-crack. Depending ontieoperating conditions, themacro+rack cmslowlygrowdting component operation, or fail quickly. Often failures are catastrophic with release of large amounts of energy. In addition, as we move forward in the new millennium, higher temperature chemical processes are clearly required to hicrease efilciencies and reduce pollution levels In earlier work [1-4] we focused on the understanding, control, and development of predictive methodologies to manage this type of growth under severe history dependent conditions. However, the current efforts are focused on understanding the cavitation process at the high end of the nanoscale through the grain boundary scale. Indeed, control of creep faihm.s can only be accomplished by chemical solutions at this scale, or clever ‘mechanical’ solutions such as control of ‘residual stresses’ at this level. Since few analytical efforts have focused on cyclic time dependent cavity growth at this scale, it is the main focus of our effort. A complimentary, related effort involves the development of predictive models that can be used to control failures at the macro- scale by clever control of weld residual stresses. It is now realized that weld induced residual stresses can be a major factor in life extension.

CAVITY GROWTH BY DIFFUSION

From matter conservation and the kinetic relation between difisive flux and chemical potential (respectively):

QV”JGB.+$=O QJGB= -(DGB6B/k?’)v(Kbn) a constitutive law for the relation between diffusive creep and field variables was developed and implemented within a finite element framework [5]. In the above, Q is atomic volume, J is atomic flux measured in units of atoms crossing unit length per unit time, 5 is the grain boundary opening (due to matter addition) with the over-riding ‘.’ representing rate, and the rest are constants, A periodic grain boundary model was developed and the effect of elastic accommodation on grain boundary diffusion creep was studied, Figure 2 illustrates results. In Figure 2, ‘a’ represents void size and ‘b’ represents void spacing. The solution was normalized by a classical closed form expression [6], which was derived neglecting elastic effects. It is seen that, during the early transient time, transients significantly increase void growth rates. This has extremely important ramifications for cyclic loading [3]. Additional key results show that stresses change markedly ahead of the void during the transients, again having important ramifications for cyclic creep conditions. This had been suspected before but had not been proven.

CAVITY GROWTH BY VISCOUS FLOW

A model was also developed to permit the analysis of flow-induced creep of isolated and interacting voids [6]. In contrast to the observations regarding elasticity effects of diffusion II ,\*l=Jq ... .. U II .J1 K + “ ‘“

1.OE-06 1.OE-05 1. OE-04 1. OE-03 1,OE-02 1.OE-01 1.OE+OO 1.OE+O1

tl~

Figure 2. Effect of Elastic Accommodation On Void Growth

controlled cavity growth, creep controlled growth rates were found, somewhat surprisingly, to be only mildly influenced by elasticity, except for high initial void fractions experiencing large triaxial stress states, even under cyclic loading. However, cavity growth rates and cavity aspect ratio growth rates are strongly influenced by inclusion of large geometry effects, Though the void growth rates are somewhat higher for the large initial void volume fraction in a creeping solid exposed to very high triaxialities when elasticity is included, it is unlikely to impact the total time to failure because the growth rates are very high. Additionally, the elastic transient time during void growth is found to be quite negligible for all the cases considered.

fa%- 51r.ain-finitcgcm

1.2 I I I 1 I I

Cycles ‘

Figure 3. Void Growth Under Balanced Strain-Controlled Cyclic Creep.

4 #.,

Of particular interest is the fact that certain metrds experience intergranular cavitation under a balanced cyclic loading condition [7]. Several attempts have been made to explain the phenomenon of intergranular void growth under balanced cyclic loading. A good discussion on these various attempts can be found in Reidel [8]. Some of our recent results are shown in Figure 3. That elastic transient effects after reversal of loading maybe an important consideration in understanding this phenomenon was advocated by several investigators (see for instance the overview in [8]) in the past. The present results unequivocally demonstrate that material elasticity does not play any significant role in void growth under balanced cyclic loading if viscous flow dominates. Rather nonlinear shape changes that occur during the balanced cycling process are an important consideration in explaining this phenomenon. This is not surprising since nonlinear shape changes significantly affect the void growth and interaction even under constant stress conditions. The present calculations reveal that the cavity growth rate under balanced cycle loading is constant over the number of cycles performed. Interestingly, this observation is consistent with the experimental findings of Baker and Weertman [7], who show that cavity growth rate is constant in copper experiencing balanced cyclic loading at 678 K. Recently, Van der Geissen and Tvergaard [9] have performed detailed numerical calculations of void growth under cyclic creep conditions using a plane strain multi-grain model. Their model accounts for interaction of creep and diffusion mechanisms as well as other complex mechanisms such as continuous cavity nucleation, grain boundary sliding, and creep constrained cavitation. In addition to considering balanced cyclic creep, they consider asymmetric cycling as well. Our discussions of these results are confined only to the balanced cycling loading under creep dominated conditions. When creep dominates cavity growth, Reference [9] shows that the damage level steadily oscillates in time around its initial level even in regions where free grain boundary sliding occurs. While this observation is clearly in contrast to our result, it is not surprising that this should be so. One obvious reason is that Van der Geissen and Tvergaard [9] use the BHS modeI to account for the volumetric growth rate of the cavities under creep dominated conditions. It wm shown in [10] that this solution does not assume nonlinear shape changes of cavities. It is emphasized that cavity growth under balanced loading is predicted to be zero for many current models in the literature that were developed neglecting large geometry effects. Under balanced cyclic loading, for high stress triaxialities, we find that the cavities grow in an oblate fashion, favoring void interaction and link-up, in contrast to low stress triaxiality conditions. Again, this is consistent with experimental observations, which show that high constraint greatly reduces creep fatigue life. Finally, it was shown that the failure mode will depend on load type (stress versus strain control). In general, our results are in contrmt to those found in the literature, which neglect large geometry effects, especially for cyclic loading at high temperature conditions. Correct trends in void growth predictions are critical for understanding the high temperature failure process and developing solutions to increase life.

COMBINED DIFFUSION AND VISCOUS FLOW

Multi-void, Multi-Grain Model Studies. The next area of study involves the consideration of multiple void growth along a grain boundary. This reduces the effect of periodic boundary assumptions used in the above work since each void along a grain boundary can grow

5 tttttcd ‘\\ mton .“ ‘\ ‘\ .- --(: \ ,/ > /’ -L- --- ‘\ // -< --- 4’ 4 4 4 --o1-5- ----4 \ ‘\ &----- “x. \ ‘>------f, ..” +22-lii__J’” -, 16/2 .)+--W::. + .-”’; + J ~ ~+ 111110 n

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Figure 4. Multiple Void Grain Boundary Model.

independently. This work represents the link in the 2 to 20 pm scale shown in Figure 1. Figure 4 illustrates this concept. The combined effect of diffusion and viscous flow effects of a periodic array of voids within a periodic array of grains can be studied with such a model. This model represents a ‘link’ between the isolated void at the nanoscale discussed above and the full macro- crack studies, which were investigated in a prior phase of the program. In Figure 4,

● ✎☛ v=v/)+vc represents the diffusion and creep contributions to void growth for each void along the grain boundary (see [11] for details). This model represents an extension of a very recently proposed model by Tvergaard. We have extended this model to permit proper consideration of cyclic load effects. This is done by incorporating a correct cyclic creep constitutive law (Murakami-Ohno (M-O - see [12]) rather than Norton power law creep (N)) and the inclusion of large geometry change effects [11] (which we know are important from our isolated cavity growth studies). One key result is illustrated in Figure 5 where void growth is shown as a function of time for the load spectrum shown. Important differences are clearly observed between the use of different constitutive laws. Moreover, use of small geometry changes, not shown here, shows a very low void growth rate. It is clear that the Norton creep law should be abandoned for investigations of creep fatigue growth. The evolution of cavity growth under strain controlled cycling likewise

6 produces similar results. Other studies of load frequency effects and the importance of shear n~c1 M-OJT-0) I co~inue-to be studied. - Welds and Residual Stress E#ects. A new constitutive law that is appropriate for weld modeling has been developed (see [4]). This new law accounts for weld and base metal melting, Ratio “ N (T-C) 0.2 softening, and history annihilation, among many If other effects that are critical for proper weld 0.15 modeling. The constitutive law makes weld analyses very rapid. The effects of residual 0.1 stresses, as may occur from a weld is shown to

0,05 have an important effect on cyclic creep void I growth rates. It is important to note that a 1 hr o compressive residual stress state can greatly 0 0.1 02 0.3 0.4 0.s 0.6 0.7 reduce void growth rates. The possibility of NormalizedTime macro-scale improvement of history dependent Figure 5. Cyclic Creep Growth Rates. creep lives by controlling residual stresses near welds, or from post fabrication heat treatments, is being considered. This model was used to investigate creep life extension procedures for aging power plants by using hot compression. Similar ideas will be studied in relation to nanoscale void growth reduction. Details maybe found in [3], [4], and references cited therein. Future Work. Further investigation of void nucleation and growth using a combined diffusion/creep law under both cyclic and constant loading is ongoing. Cavity growth in the presence of weld residual stresses must be studied as well. Properly including the effects of weld damage has not been performed to date. Finally, and perhaps most important, we plan to link the micro approach, which considers cavity growth at the nanoscale to crack nucleation, and the macro approach, which is used to predict final fracture. This last, difficult step is very important to permit the long-term goal of improving the safety of advanced and aging power generating equipment and other applications discussed above to be achieved. Improvement of the weld process models will continue.

ACKNOWLEDGEMENT

This work was supported by Department of Energy, OffIce of Basic Sciences under Grant No. DE-FG02-90ER14135. The authors thank Dr. R. Price and B. Armaly for their support.

REFERENCES

7 1. G. NEWAZ, B. MAJUMDAR, AND F. W. BRUST, “Thermo-Cycling Response of Quasi- Isotropic Metal Matrix Composites,”, Journal of EnginerinE Materials and TechnoloEy,VoI. 114, pp 156-161, April, 1992.

2. BRUST, F. W., “Investigations Of High Temperature Damage And Crack Growth Under Variable Load Histories,” International Journal Of Solids And Structure, Vol. 32, No. 15, pp. 2191-2218, 1995.

3. BRUST, F.W., 1999, “Classical and Emerging Fracture Mechanics Parameters for History Dependent Fracture with Application to Weld Fracture”, PVP-VO1.393, Fracture, Fatigue and Weld Residual Stress ASME.

4. F. W. BRUST, P. DONG, 2000, “Welding Residual Stresses and Effects on Fracture on Pressure Vessel and Piping Components: A Millennium Review and Beyond”, To Appear in the ASME Journal of Pressure Vessel and Piping, Special Millennium Edition, 2000.

5. MOHAN, R., AND BRUST, F. W., “Effect of Elastic Accommodation on Diffusion Controlled Cavity Growth in Metals” to appear in Journal of Pressure Vessel Technology, June 2000 Special Issue.

6. MOHAN, R., AND BRUST, F. W., “An Analytical Study of Void Growth in Viscoplastic Solids”, Fatime and Fracture of En~ineerin~ Materials & Structures, Vol. 21, pp. 569-581, 1998.

7. BAKER AND WEERTMAN, J. R, 1990, Scripts Metallurgic et Materialia, 24, pp. 221- 234.

8. RIEDEL, H. 1987, “Mechanisms of Creep Rupture,” Elsevier Applied Science, London.

9. VAN DER GEISSEN, E., AND TVERGAARD, V., 1995, Micromechanics of Intergranular Creep Failure under Cyclic Loading, Acts Metallurgic et Materialia, 44, pp. 2697-2710.

10. MOHAN, R., AND BRUST, F. W., “On Void Growth in Elastic-Nonlinear Viscous SolidsUnder Creep and Cyclic Creep Conditions”, to appear in Journal of Pressure Vessel Technology, June 2000 Special Issue.

11. OH, J., KATSUBE, N., AND BRUST, F. W., “Unresolved Issues With Regard to Creep and Creep Fatigue Life Prediction”, ICES’2K, Proceedings of the International Conference on Engineering Sciences, August, 2000, Ed. S. N. Atluri, et al.

12. MURAKAMI, S. AND OHNO, N. (1982): “A Consitutive Equation of Creep Based on the Concept of a Creep-Hardening Surface”, ht. .T.Solids Structures, Vol. 18, No.7, pp.597-609 CRACK PATTERNS DUE TO RESIDUAL STRESS IN THIN FILMS

L. B. Freund Divisionof Engineering,BrownUniversity,Providence,RI 02912USA

V. B. Shenoy Departmentof MechanicalEngineering,Indian Institute of Technology,UP 208016 Kanpur, lndla

ABSTRACT The physicalsystemstudiedis a brittle elasticfilmbondedto an elasticsubstrate with different properties;a residual tensilestress is presumedto exist in the film. The focusof the study is the influenceof the mismatchin elasticpropertieson patterna of crackformationin the film. The stress intensity factor and crack drivingforcefor growthof a periodicarray of cracksin the directionnormalto the interfaceunder two-dimensionalconditionsare determinedforany crack depth and any mismatchin elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor as a function of crack depth *lbIts a local maximum. The driving forcefor crack extensionin the dhection parallel to the interfaceis then determined,and the equilibriumspacingof crack arrays is estimated for givenresidual stress. The results of the calculations are used as a basis for understanding the crack patterns which have been observed in GaN films on Si substrates.

INTRODUCTION

A range of developing technologies rely upon the deposition of thin films of one material on substrates of another materia~ examples include thermal barrier coatings, microelectronic devices and functionally graded materials. In many cases, deposition results in significant residual stress in the film, Microelectronic device technology relies heavily on the ability to fabricate devices that are made of thin films bonded epitaxially to lattice mismatched substrates. The mismatch in the lattice parameter causes the film to be severely stressed and induces several stress relaxation mechanisms which can affect the performance and structural integrity of the device. Cracking of the film is a common mode of stress relaxation when the mismatch stress is tensile and the film material is brittle. Examples of such systems include GaN and AIN films on Si substrates. The crack patterns that form in these films usually involve an array of cracks which is roughly periodic, Thouless [1] derived an expression for the crack spacing based on an energy release argument. This argument was later modified to account for the sequential formation of cracks [2]. A slightly different argument, put forth by Hutchinson and Suo [3],gives a spacing between the earlier estimates [1] and [2]. These analyses assumed identical elastic properties for the film Figure 1: Crack patterns observed in GaN films on a Si substrate. The film is about 5pm thick and the shortest distance between cracks is about two to five times the film thickness. and substrate. Beuth [4] obtained stress intensity factors for a single crack in a film as a function of the crack depth and the Dundurs [5] parameters which characterize the differences in elastic properties between film and substrate. The present study is motivated by experimental work conducted at Brown University [6]. Films of (0001) GaN were grown on (111) Si substrates in which the triangular nets between the close-packed planes are coincident. These 5pm thick films developed cracks as shown in Figure 1. The cracks tend to form on preferred (li’00) prismatic cleavage planes which are oriented at 120° with respect to each other due to the anisotropic nature of the surface energy in GaN. Furthermore, there are several “generations” of cracks. The first generation appears to be the deepest and they are spaced at intervals of more than ten to fifteen times the film thickness; these are seen as the thickest lines in the micrographs. Subsequent generations which form are less deep and are spaced at much smaller intervals, typically from two to five times the film thickness. The latter feature is due to the elastic interaction between members of various generations of cracks. The assumption of like elastic properties may be too drastic in the case of GaN/Si system where the elastic modulus of the film is about three times that of the substrate, The aim of this report is to extend the work of [1] and [2] to account for the mismatch in elastic constants between the film and the substrate.

THE MODEL

The film considered has thickness h and is bonded to a relatively thick substrate, The film and substrate have elastic parameters pl, U1and p2, V2,respectively, where p represents the shear modulus and v the Poisson ratio, The Dundurs parameters [5] which characterize the difference in elastic properties between the film and the substrate are r(E2+l)–(~1 +1) ~=r(~2–1)–(~1–1) (1) a=r(~2+l)+(~1+ l)’ r(~2 + 1) + (~1+1)’ where 17= pl/pz and K = 3 – 4v. The film is assumed to have a lattice mismatch with respect to the substrate with mismatch strain CO.This mismatch strain induces a stress 00 = Ec. in a uniform film, where ~ = 2p1/(1 – V1) is the plane strain modulus of the film. In the untracked configuration, the strain energy density in the film is a~/2E.

10 “:<,., ,

,.,.. .. . : r ,.. * . ““%.. 1 1 .... 2’

Figure 2: Geometryof a periodicarray of cracksin a film bonded to a substrate (left). Inset on right showsa schematicof a channelingcrack.

The strain energy developed in the film due lattice mismatch is relieved by means of crack formation. Crack patterna in the film are modeled using a periodic array of cracks. A generic configuration of the cracked film is shown in Figure 2. In such a configuration, the crack depth is a and the crack spacing is p. The task is to determine a and p, given the parameters a, e, ao and h. As long as the crack depth a is less than the film thickness h, the stress field at the crack tips is described by the well known square root singularity, the strength of which is called the stress intensity factor -K. When the crack touches the interface, the singularity is a more complicated type. This work does not take this complication into account and attention is restricted to the case when a < h. The calculation of energy release rate right up to a = h is not afFected by this restriction. When the film is cracked to a depth a, the amount of elastic energy released through formation of one of the cracks is given by

(2) where y is a coordinate along the crack face with the crack tip as the origin and 6(v) is the crack opening profile over O < y < a. On the other hand, some energy goes into creation of new surfaces and this can be expressed as

(3) for one crack, where ~ is the fracture energy per unit area. Thus, the total change in energy due to formation of a single crack is

ms~ha AE = –AEe + AEj = -@y” - G*), (4)

The total free energy of the system per unit interface area in the cracked configuration is

(5)

The objective is to determine a and p for a given ~“. Several ideas have been proposed to obtain p as a function of -y”. Thouless [I] obtained this spacing for a = h using the criterion that AE S O, that is, the crack spacing is determined by the greatest lower bound on the value of p for which there is a reduction in the free energy. This criterion assumes that all cracks nucleate and propagate simultaneously. Thouless et al. [2] modified thk argument to account for the sequential formation of cracks. In this case, the crack

11 1.5 ‘ I [1= 0.99

1.0

x“ Y

0.6

0.0------0.O 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 alh alh Figure 3: Stress intensity factor normalized by Ko = aofi as a function of crack depth a/h for various values of crack spacing p/h and Dundurs parameter a = 0.99 and 0.50. spacing is taken to be that which minimizes the free energy U. This gives a spacing larger than the former case and is in better agreement with experiments. Hutchinson and Suo [3] used a different argument in that they consider the lateral propagation or channeling of cracks across the film and suggest that the driving force for self-similar lateral propagation or channeling determines the crack spacing. The driving force for channeling can be written as

(6)

Thus, the quantity G* represents the nondimensional driving force for crack channeling. The channeling argument gives a spacing intermediate to the two criteria of [1] and [2]. The objective here is to report results of calculation of G*(a/h, p/h, a, @ which implies values of driving force for channeling as well. The equilibrium crack spacing is obtained by finding the value which minimizes the free energy U. G* has been determined using a singular integral equation formulation based on the concept of a continuous distributions of dislocations, each of infinitesimal strength [7].

REPRESENTATIVE RESULTS

In this section, the results for stress intensity factor, driving force for channeling, and equilibrium crack spacing are summarized. It is found that the results are relatively insensitive to changes in the value of@ and, therefore, results are presented for various values of a but only for p = cY/4.

Stress intensity factors Figure 3 shows representative plots with a = 0.50 and 0.99 of the normalized stress intensity factor under two-dimensional conditions as a function of the crack depth a/h, for various values of crack spacing. The most significant feature to note in these graphs, as well as others included in [9], is the existence of a local maximum in the stress intensity factor as a function of crack depth when a >0. As the crack approaches the interface, however, the stress intensity factor

12 - -——— 1.25 1.00 al al ~ 0 (f= 0,99 —- ... ..—. — .— .—. —— .— z 0.= 0.50 J? 1.00 ‘-— -----T ...... -—. --- ~ [I=U14 plh=lo m 0.75 — l\=lL14 —– -.— ,- .-c > .=> g 0,75 u u ---- .-.— __ al ~ 0+50------.—- . —.— = : 0.50 — g E E o = 0.26 70.26 “— ‘— — 2 --- ——. “u ‘4 .

0.00 0.00 0.0 0.2 0.4 0.6 0,8 1.0 0.0 0.2 0.4 0.6 0.6 1.0 alh alh

Figure4: Normfllzed driving force forchanneting ma function ofcrakdepth a/h forvmious values of crack spacing p/h and Dundurs parameter a = 0.99 and 0.50. invariably increases and it becomes indefinitely large as a ~ h. As the crack spacing increases, the local maximum in the stress intensity factor vanishes. Also, the crack depth at which the local maximum occurs increases with increasing crack spacing until the maximum dkappears. No such maxima are observed for an isolated crack, that is, when p/h ~ co. When the substrate is stiffer than the film (a < O), the stress intensity factor exhibits a local maximum, and it then approaches zero as the crack edges approach the interface. This is similar to the result of [4] for a single crack.

Driving force for channeling Figure 4 shows representative plots with a = 0.50 and 0.99 of the normalized driving force for channeling as a function of the crack depth a/h for various values of crack spacing The most important feature in these results is that, as the crack spacing p/h decreases, the driving force decreases. For crack spacing p/h between 1 and 3 the driving force initially increases with crack depth, and subsequently attains an almost constant value for larger crack depths. In cases where the substrate is stiffer than the film, the driving force has a shallow maximum as the crack approaches the interface. This effect is also observed by Beuth [4]for a single crack.

Equilibrium crack spacing The equilibrium crack spacing is obtained by finding the crack spacing that minimizes the free energy. In fact, both the crack depth and spacing are to be determined by the minimization of free energy. It turns out from the calculations that the free energy is always minimized when the crack approaches the interface, and therefore the crack spacing p/h that minimizes U as defined in (5) is determined with a/h set equal to 0.99. The results of the calculation shown in Figure 5 provide equilibrium crack spacing as a function of a*, the normalized measure of mismatch stress. For a given value of a“, the crack spacing for a relatively stiff film is larger than that for a relatively compliant film. It is noted that the equilibrium curves for a = —0.75 and –0.99 end abruptly at about O* = 1,8, This is due to the fact that, in this case, the minimum value of energy of the cracked film is larger than for an untracked film for normalized stress less than rY*.In other words, cracking is not possible for smaller values of a*. It is also clear that this critical value of stress, below which fracture cannot occur, decreases with increasing a. ..— -.

41 ————–——— --- -,

+Yl—-–—1-%-+. .__,

-0.99 0.75 1 I 1 2 3 4 5 u’ - normalized residual stress

Figure 5: Equilibrium crack spacing versus normalized mismatch stress (7* — “’-’m

Crack opening In plan view photographs of cracked films, cracks are seen as dark lines, as illustrated in Figure 1, It seems reasonable to associate the thickness of these lines with the amount of crack opening on the film surface. This opening can be calculated from the solution of the integral equation for dislocation density. Figure 6 shows plots of ~6(a)/aoh versus a/h. The most interesting feature to be observed in this figure is that, when CYis positive and very close to 1, normalized displacement has a local maximum at some value of crack depth a/h. Thus, for very stiff films, thicker lines on the micrograph do not necessarily imply deeper cracks! This feature, although present, is not significant at lower a.

DISCUSSION

The foregoing results indicate that the elastic mismatch between the film and the substrate can significantly influence behavior such as that of the stress intensity factor as a function of crack depth for a fully formed crack array. The local maximum which arises in the stress intensity factor as a function of crack depth may be understood by the following arguments. The stress intensity at the tip of each crack is affected by the presence of all other cracks in the array. The presence of all other cracks except the one of interest may be taken into account by considering their influence on the film. The main effect of the presence of the cracks is that the film effective modulus is lowered. The reduced effective modulus ~.ff can be estimated to be

27ra &f=l –TG*(;,;,LYJ3). (7) E

It is noted that this approximate formula [2, 3] neglects the effect of the substrate. It is clear that, as the crack depth increases, the effective modulus falls. Furthermore, the fall is larger for a larger G*. It is clear from Figure 4 that, for a given geometry of cracks, G* is larger for larger a and, therefore, this effect must be greater for stiffer films. These approximate arguments are in

14 ~––– ...... -i -.. --- - . — .- ——-— —.. - ..-. 14 [—-l—— $8 – \ I g 12 II= 0.99 u = 0.50 In / [i=u/4 %($ --- .-[%= CL14 . .. plh=10. 10 @h=10 -- “-—- g 7 c 5/ – 8 ‘-——-- ——””— m ~>4 54 x 6 c) m ,...... ------... . 4 -

I I I 1 n e -6.0 0.2 0.4 0.6 0.8 1.0 -&o 0.2 0.4 0.6 0.8 1.0 alh alh

Figure 6: Normalized crack opening ~6(a)/a& versus crack depth a/h for various values of crac!~spacing p/h and Dundurs parameter a = 0.99 and 0.50. agreement with the calculations. It is, however, to be noted that as the crack depth approaches the film thickness, the assumption used to derive (7) breaks down in that the role of the substrate becomes increasingly significant. Turning now to equilibrium crack spacing, it is clear that very stiff films will have cracks spaced further apart. Also, the least normalized stress a“ for which fracture is possible decreases with increasing stiffness of the film. Thus, cracks are more easily (in nondimensional terms) nucleated in stiff films but their density is smaller. On the other hand, more compliant films require larger a* for the formation of cracks. After this stress is attained, the crack density is higher than for stifler films. The features observed in the experimental photograph in ~lgure 1 may be explained as follows, The threefold symmetry occurs due to the fact that the surface energies of these three crystallographically equivalent planes is the lowest, so they are the preferred fracture planes. The stresses in this system are generated by a combination of lattice mismatch and mismatch in thermal expansion coefficient. As the sample is cooled from its growth temperature, the tensile stress in the film increases. When the critical stress for the formation of cracks is attained, the first generation of cracks forms; these are more than ten to fifteen film thicknesses apart and they are as deep as the film thickness. As the film cools further, select new generations of cracks channel across the film in the gaps between individual cracks in the previous generation, in an attempt to attain the equilibrium crack density. When the crack spacing reaches about two or five times the film thickness, the driving force for channeling does not increase significantly with crack depth, and in addition, the stress intensity factor falls with increasing crack depth. Thus, the last generation of cracks that forms is not as deep as the film thickness. These arguments are meant to provide only a qualitative understanding of the cracking patterns. The quantitative details of these patterns are obviously afFectedby the biaxial state of stress in the film and by the three dimensional nature of the cracks which is not taken into account in the present analysis.

CONCLUSIONS

This report is aimed at extending previous work on crack patterns in brittle thin films to account for the mismatch in elastic properties between the film and substrate. The main conclusions

15 of this investigation are:

– The stress intensity factors at the edges of a periodic array of cracks under two-dimensional plane strain conditions shows a local maximum for small enough values of the periodic spacing of cracks. This effect is stronger when the film is stiff relative to the substrate. – The driving force for channeling cracks falls with increasing crack density. For small crack spacing, the driving force for channeling increases initially with crack depth, but attains an almost constant value for greater depth. – The equilibrium crack spacing is larger for a relatively stiffer film at a given value of the nondimensional mismatch stress. It is easier to nucleate craclcs in a more stiff film (in nondimensional terms) than in a more compliant film. More compliant films allow for cracks only at larger values of the nondimensional mismatch stress, with a larger crack density.

REFERENCES

1. THOULESS, M. D., “Crack spacing in brittle films on elastic substrates,” Journal of the Amer- ican Ceramic Society 73, 2144 (1990).

2. THOULESS, hL D., OLSSON, E. and GUPTA, A., “Cracking of brittle films on elsstic sub strates,” Acts Metallurgic et Materialia 40, 1287 (1992) .

3. HUTCHINSON, J. W. and SUO, Z., “Mixed mode cracking in layered materials,” Advances in Applied Mechanics 29, 63 (1992).

4. BEUTH, J. R., “Cracking of thin bonded films in residual tension,” International Journal oj Solids and Structures 29, 1657 (1992).

5. DUNDURS, .J., “Edge-bonded orthogonal elastic wedges,” Journal of Applied Mechanics 36, 650 (1969).

6. STEVENS, K. S., OHTANI, A., SCHWARTZMAN, A. F. and BERESFORD, R,, “Growth of group III nitrides on Si(lll) by plasma-assisted molecular beam epitaxy,” Journal of Vacuum Science and Technology 812, 1186 (1994) .

7. FREUND, L. B. and KIM, K. S., “Spiral cracking around a strained cylindrical inclusion in a brittle material and implications for vias in integrated circuits, Materials Research Society Symposium Proceedings 226, 291 (1991).

8. SUO, Z., “Singularities interacting with interfaces and cracks,” International Journal of Solids and Structures 25, 1133 (1989).

9. SHENOY, V. B., SCHWARTZMAN, A. F. and FREUND, L. B., “Crack Patterns in Brittle Thin Films,” International Journal of Fracture, to appear.

16 OBSERVATION OF CLEAVAGE FRACTURE AFTER SUBSTANTIALDIMPLE RUPTURE IN ASTM A71OSTEEL

W. G. Reuter and W. R. Lloyd

Idaho National Engineering and Environmental Laboratory P.O. BOX 1625, MS 2218 Idaho Falls, ID 83415-2218

ABSTRACT

A major-concern often arising in structural integrity predictions is the possibility that low-energy brittle fracture could result as a consequence of cleavage either under normal operating or design accident conditions. This can be especially troublesome when the leak-before-break (LBB) approach shows an additional safety margin of the design. For LBB to be applicable, the fracture process must remain ductile (dimpIe rupture), and not change to cleavage. The American Society for Mechanical Engineers Boiler and Pressure Vessel Code (Code) provides guidelines for avoiding cleavage fracture for Code-accepted materials. Experimental results for anon-Code steel are provided, and show that cleavage may occur for a thickness under16 mm (where the code suggests it will not) after stable crack growth (As) of up to 20 mm. This work is still in progress; test results are provided along with possible reasons for the mode transition, but complete explanations are still being developed.

INTRODUCTION

Cleavage fracture during crack growth initiation generally results in sudden, catastrophic structural failure, and must be avoided! Cleavage fracture after stable ductile crack growth is also a concern, but this transition has only been observed in limited cases where crack growth was less than 2 mm~(lJ) How- ever, the possibility of a sudden fracture after stable crack growth has significant practical concerns. Steel structures, including pressure vessels, should certainly incorporate a fracture-resistant design. If cracks should appear and grow, the mechanism should be hole growth (ductile) rather than cleavage (brittle) to limit crack velocities and fragmentation. The need to reduce chances of cleavage fracture led to development of design procedures to revent unexpected, sudden failure of structural components. Welding Research Council Bulletin 175(3Fprovides these procedures, based on the requirement that the minimum operating temperature will exceed the material’s “transition temperature.” This corresponds to a fracture mechanism change from cleavage (low absorbed energy) to ductile hole growth (high absorbed energy). The approach requires drop weight tests (per ASTM E208-69), when geometrically possible, to obtain the transition temperature (TDT), and Charpy V-notch (CVN) impact tests when the material thickness exceeds 16 mm.

NB-2332 of the Code(4)provides guidelines for the minimum operating temperature relative to CVN impact results. Minimum specified CVN values are required at test temperatures less than or equal to the lowest desired material service temperature. Thin materials(46 mm) have no requirement, and

17 I intermediatethicknesshave a minimumCVN lateral expansionrequirement. Plates thicker than 63.5 mm have a minimum absoluteoperatingtemperature(RTmT+ 56”C)specified. Thus, the ability to design structural components to prevent non-ductile fracture appears to be established simply by following these requirements.

The Leak-Before-Break (LBB) approach to fracture-resistant design was originally developed by Irwin(s)to establish the required fracture toughness to prevent crack growth when a material was loaded to the yield strength. In the late 1970s, LBB was extended (required fracture toughness such that a through- thickness crack, twice as long as the material thickness, will not extend unstably- corrosion-enhanced growth excluded). This suggested that, if a crack penetrated the wall thickness of a vessel pressurized with a fluid, and the crack length was less than twice the wall thickness, then the vessel would simply leak, hence, “leak-before-break.” Further, such a vessel would not experience catastrophic failure until additional crack growth occurred. During the time that the crack leaks, it is assumed that the leak will be detected and remedial measures performed before the crack reaches a critical size. Therefore, by following this hypothesis, it would be possible to predict conditions where LBB would apply. In those cases, LBB can be a safety mechanism of last resort to detect a significant crack before unstable fracture occurs. The LBB concept of pressure vessel safety is now used throughout the world.

This paper provides experimental results from surface crack test specimens (simulating the fracture behavior of structural components). Cleavage fracture occurred in the experiments when the Code sugests it will not. Through careful examination and critical analysis of these results, we hope to better understand factors controlling cleavage fracture following stable ductile tearing. This will help provide solutions to practical problems associated with applying LBB concepts to structural safety.

MATERIAL CHARACTERIZATION

The A710 steel used in this study is not explicitly qualified by the Code. But, the A71Osteel showed the unexpected cleavage transition behavior of interest, and a large database of material properties and experimental data already exist that will aid in analyzing the phenomenon, Therefore, for purposes of comparison and analysis, the intent of the Code relating to material properties was applied.

The thickness of theA710 steel plate was 31.8 mm. The specimens containing surface cracks were either 6.4 or 12.7 mm thick, and they were removed from the central plate thickness. The chemistry of the A71Osteel is: 0.05 C, 0.47 Mn, 0.010 P, 0.004 S, 0.25 Si, 0.74 Cr, 0.85 Ni, 0.21 Mo, 1.20 Cu, and 0.038 Cb with an ASTM grain size of 8. ASTM E208,(G)P-3 NDT tests were performed on the 31.8 mm thick steel plate. The results showed that TNDTis - 18°C (O”F)for plateCl2188. CVN impact tests were petiormed per ASTM E23(7)with the specimens oriented in the transverse (T) direction.

A number of specimens containing surface cracks with a/t ranging from 0,15 to 0.85 and a/2c ranging from 0.1 to 0.5 were tested. Data collection included: stop-action photographs at the front and back surfaces; acoustic emission; applied force, crosshead displacement, and crack mouth opening displacement (CMOD); and the applied force when the growing crack penetrated the opposite surface. (penetration was identified using a rubber air bulb held to the back surface by vacuum; it fell off when air passed through the opening at crack penetration, releasing the vacuum.)

TEST RESULTS FOR SURFACE CR4CKED SPECIMENS

We have observed that surface cracks grow predominantly through the thickness direction, with little or no growth in the plate width (2c) direction. Once the crack penetrates the back surface, it then

18 grows until the length at the back sutiace is 400 # 1 I 4 1 “’’1’’’’!’’’’!’’’’!” “ the same as the length at the front surface. , The crack growth to this point is essentially , , dimple rupture occurring in the plane of the original fatigue precrack. Asthe testpro- 300 ...... gresses, the specimen configuration is analogous to a middle crack M(T)] specimen, The crack growth then transforms to a single- or double-slant fracture. Stable crack growth continues until either the crack tip reaches the --—— specimen edge, or sudden cleavage fracture results in catastrophic specimen failure. Fig- ure 1 shows force vs. crosshead records for Specimen 32 (experienced cleavage fracture at both crack tips) and for Specimen B-11 (did 100 ....------.-&------not experience cleavage). Figure 2 shows the fracture surfaces of specimens (#15, #B-42) that experienced cleavage fracture. It is apparent that the amount of stable crack growth 0 preceding catastrophic failure varied consid- 0 3 5 8 10.13”15 erably (ranging from a few mm, up to CrossheadDisplacement(mm) 20 mm), and that the transition from ductile fracture to cIeavage was abrupt. The fi-acture Figure 2. Test record for two surface crack specimens, surfaces of these specimens were examined by light microscopy, and with SEM, and only a few islands of cleavage were detected behind the main ductile/cleavage boundary. These isolated islands were smalI (-30 pm) and occurred infrequently. Figure 2 suggests that there is almost a straight line of transition separating dimple rupture from cleavage.

Recently, another series of specimens (B-24, B-29, B-43, C-6, C-23, and E-14) were tested. Of the six specimens, four experienced cleavage (B-29, B-43, C-23, and E-14). Figure 3 shows the fracture surface for Specimens B-29 and B-43.

Figure 1. Fracture surfaces of specimens #B-42 (above, 12.7 mm thick) and #15 (below, 6.4 mm thick) tested in mid-1980s. Transition from ductile (darker) to cleavage (brighter) fracture is visible. Note chevron shape of transition boundary at left on #15.

19 Figure 3. Specimen B-43 (above) and B-29 (below). Darker, crescent-shaped region extending to back surface on B-43 is ductile fracture region. Cleavage on B-29 is isolated to far left and right.

DISCUSSION CVNResults:TNDTis-18°C(O”F)for plate C12188of A71Osteel. The steel’s 0.89 mm lateral expansionat 24°C easily exceedsthe Coderequirementof 0.64 mm for materials up to 38,1 mm thick. Therefore, the test results at 24°C determined the minimum “operating” temperature. At 24°C the CVN impact energy results for the transverse-oriented (L-T’)specimens were 62, 62, and 87 J with corresponding lateral expansion of 0.94, 0.94, and 1.24 mm. Therefore, applying the “intent” of the Code, the minimum operating temperature was set to be 24°C. Reference 3 notes that energy absorption (higher measured CVN energy) maybe increased by increasing material yield strength or ductility. Of these, ductility (associated with CVN lateral expansion) is a better indicator of fracture toughness change. For this material, the measured lateral expansion of 0.94 mm exceeds the Code-required values, and is a positive indicator that the material meets the minimum Code-inferred fracture toughness. Another item of possible concern is that the CVN specimens had only 10% shear fracture area at 24”C. However, this parameter is not considered in the ASME Code.

Surface Cracked Specimens: Figures 2 and 3 clearly show that cleavage did not occur until after the surface cracks had penetrated the back surface and were growing in the plate width (2c) direction, In many instances, the cleavage fracture initiated from 45 deg ductile, slant fracture, e.g. #B-29. In one of the fracture surfaces studied extensively in the SEM (Figure 2, B-42), there is a distinct, uninterrupted boundary separating ductile and cleavage fracture zones. There are only a few islands of cleavage in the dominantly ductile region, and they are located close to the transition boundary. It is commonly accepted that the probability of cleavage fracture initiation is modeled by a Weibull-type continuous probability fimction. The model uses a critical cleavage stress and a representative material length as its governing parameters for a particular material, The probability of cleavage fracture initiation, at any location in the

20 volume being considered,for a given crackboundaryand stressstate in that same volume, is calculated through volume integrationof principalstressesnear the crack boundary. For a given material, a longer crack bounda~ (specimen/cracksize effect) or higher principalstresses(material strength/hardening influence and applied loading)can increasethe probabilityof cleavagefracture initiation. This model is limitedto predictingthe probabilitythat cleavage fracturewill initiate at any instant at some point within the volume of material considered. The so-calledweakest link model of macroscopiccleavage fracture assumesthat an individual initiationwill alwaysprogressto a macroscopicfracture event. However, if cleavage fracture does initiate,whetheror not it will continue beyondthe grain in which it initiates is not an explicit model output since the material stress state has changed. In addition,the model does not explicitly predict the likelihoodthat cleavage fracturewill initiate simultaneouslyat multiple locations in the” volume under consideration.

Gerberichet al~8)extendthis probabilisticcleavage initiationconceptto macroscopic cleavage crack growth. They suggestthat sustainedcleavagecrack growth(followinginitiation) may very likely be the result of multiple cleavage initiationevents occurringalmost simultaneously.The various distinct cleavage islandsthen growtogether to sustainthe macroscopiccleavagefracture process, In effecg they acknowledgethe validity of the Weibullmodel for cleavage initiation,but reject the weakest-link as- sumptionfor continuingmacroscopicfracture.Gerberich’ssuggestedcrack growthprocesswas strongly supportedby INEEL’ssurfacecracktest results. For example,extensiveexaminationof the fracture surface of specimenB-42 showed“river patterns”(chevron-shapedfeatures)on the cleavage region pointing backto numerous initiation sites along the ductile/cleavagefracture boundary. Other specimens show isolated islandsof cleavagefracture embeddedwithin the ductile fractureregion. These are sites where cleavage initiated, but most likely arresteddue to insufficientdrivingenergy. Certainly,the weakest link assumptionprovidesa useful boundaryto applicationof the WeibullPDFwhere cleavage fracture is to be avoided. However,it is a rather severerestrictionwhen it comesto fractureprocess modeling. The real crack growth process observed in experiments is not allowed by the “weakest link” stipulation,

It maybe possible to extend the Weibull probability model to estimate the likelihood of a macroscopic cleavage fracture event arising from essentially simultaneous multiple initiations. BUGthe complexities of the process make the job enormous. The fracture process volume must be discretized to small volume elements, and the associated stresses determined using FEM. Then, an iterative probability simulation considering all possible outcomes must be performed. We hope that the INEEL microtopography fracture process analysis system will provide additional information on crack boundary locations at various points in the fracture process, This will eliminate a very tedious and still very difficult 3-D plastic crack growth modeling process, and reduce some uncertainty in the model associated with predicting crack growth. Rather than calculating crack growth increments based on some estimated criteria (which may not match the actual specimen behavior), incremental crack boundary positions can be specified based on experimental data. We also hope to establish at what point (crack boundary position, applied remote load) some of the isolated cleavage islands were generated. This will be accomplished through the correlation of engineering test data (force, displacement, COD, etc.), acoustic emission monitoring data, electric potential crack growth monitoring data, and microtopography-determ ined crack boundary locations.

At the present time, test data exists from a variety of A71Osteel surface crack specimen geometries. Some specimens exhibited sudden catastrophic failure after little ductile crack growth, others afler a large amount of ductile growth, while others experienced plastic instability with no cleavage at all. Various test parameters, such as test machine and specimen compliance, crack growth rate, specimen thickness, and initial surface flaw configurations were examined for correlation with the crack growth behavior. No correlation with observed crack growth behavior was found.

Specimen E-14 (a recent surface crack test) exhibited a double 45 deg slant fracture with a central flat region that was nominally triangular in shape, with mostly ductile fracture appearance. Point sources of specular Iight reflection from small cleavage facets were observed in this flat region, However, considerable ductile crack growth occurred before the transition to cleavage. Specimen B-24, also tested recently, exhibited a single 45 deg slant fracture. Light reflection from a section that went completely through the thickness (see Figure 4) shows that cleavage fracture occurred in this region. These types of cleavage regions were not observed in the first series of surface crack tests performed in the mid- 1980s. We presently have no guess why these regions of cleavage did not cause catastrophic failure of the test specimens. We also do not have a qualified explanation for the difference in fracture behavior of recent tests compared to those performed some 15 years ago.

Our best hypothesis at present includes two inter-related factors for the surface crack specimens. First, crack tip constraint varies significantly during the fracture process. Second, plastic deformation of the material far ahead of the original crack (pre-straining) creates an effective yield strength increase before the fracture process zone reaches those locations (also assisting in elevation of local constraint). Reuter et al.(g)show that differences in constraint exist between specimens containing surface cracks and SE(B) specimens. In all surface crack specimens (that had some cleavage) that have been examined, the cleavage events initiated in the central portion of the specimen thickness. Constraint is known to be higher there than nearer the specimen surface. Further, the maximum local stress intensity, K (or local J-integral), obtained from FEM analysis methods for surface cracks, does not occur at a corresponding location. Crack initiation studies indicate that local maximum driving force, K(9)(or J(2)),alone do not dictate the crack initiation location, but that some (yet to be defined) critical combination of crack driving parameter and constraint measure (e.g. K and T or J and Q)(912)control the fracture initiation process.

We also noted that cleavage fracture did not occur until the surface crack penetrates the opposing surface. Reduced constraint on the crack perimeter due to plastic flow to the opposing surface is a likely cause. The critical stress level required to initiate cleavage cannot, therefore, be reached. Once the crack penetrates the thickness and is growing parallel to the plate surface, the local constraint probably increases due to several factors(’)until the critical condition for cleavage initiation can be reached. Green and Hundy(lO)note that pre-straining a material increases its yield strength, causing the ductile-

Hxwx Figure 4. (a) Specimen B-24 fracture surface (inch scale). (b) Inset, magnified, showing band of cleavage traversing the specimen thickness,

22 ; “. 4; .1,),, . N;; ,,~ ...

brittle transition temperatureto increase, At a given temperature,this will increasethe probability of brittle cleavagefracture occurring. M(T) plate specimensof the same A71Osteel (tested in the mid- 1980s)do not undergoas much material pre-strainingas the surkce crack specimens,and they never had a cleavage fracture, This infersthat the level of material pre-straining(in the surfacecrack specimens) plays some role in the ductile-to-cleavagefracturemode change, Doddset alj2)also note that crack tip meandering(out of the nominal crack plane) associatedwith ductile crack growthhas a substantial effect on the s~ressfields at the crack tip.

The differencein behavior(observedcleavageregions)betweenspecimenstested recently and those tested about 15years ago maybe explainedby a change in the material’s sensitivityto constraint. The percentageof cleavage flactures experiencedin the recent test series appearsto be about twice that of the earlier tests. This differencemay be real which would mean that embrittlement occurred while the test specimenshave been in storage at nominally24°C. This maybe due to a room temperature aging phenomenon,which we feel is unlikely, but that is yet unproven. To evaluatethis possibility,the grip section (only elastically strained) of some of the recentlytested specimenswere machined into CVN specimens. Theywere impact tested, and lateral expansionexceeded 1.6mm at 24”C. Comparisonof recent CVNtest resultswith original material certificationdata (1981)suggeststhat T~DTis unchanged; the transition region slope is now steeper (narrowertemperaturerange);and flacture energy (CVN) is elevated. These results, obtainedjust a few days ago, are contraryto what was expected based on the recent surfacecracktests. Becauseof these conflictingresults,we have no explanationfor the change in observedbehaviorof the surfacecrack specimens. We are planningadditionaltests and analysesto un- ravel the mysteryof this apparentmaterial change.

At this time, we can draw the following conclusions:

(1) Catastrophic cleavage fracture can occur after a surface crack has penetrated the opposing surface when the plate thickness is less than 16 mm, even after ductile crack growth (by hole growtlddimple rupture) has progressed over 20 mm;

(2) Catastrophic cleavage fracture can occur even when the test temperature equals a temperature where the Code requirement for minimum lateral expansion in a CVN test is exceeded

(3) Comparison of Charpy impact (CVN) test results, from the same heat of material but measured 18 years apa~ show substantial differences. The more recent results suggest cleavage fracture should not occur, while the surface crack tests result in more observed cleavage;

(4) We cannot explain the sudden transition from ductile fracture to cleavage that occurs in the surface crack specimens, but recommendations for future work to study the phenomenon are as follows:

RECOMMENDED ACTIONS

(1) Calculate (via FEM) the stress fields, and corresponding constraint, at the front of the growing cracks for C(T), SE(B), and surface cracked (SC) specimens. Experimental methods will be used to establish incremental crack front positions, CTOD, and CTOA for input to the FEM;

(2) Test additional surface crack specimens (crack geometries and plate sizes) to replicate all configurations that were tested in the mid-1980s for comparative purposes;

(3) Tests of middle crack plate [M(T)] specimens for comparison with recent surface crack test results, and with earlier M(T) and surface crack results;

23 .,

(4) Perform tensile tests of the A71O steel over a range of temperatures for comparison with original tensile data (1981);

(5) Use tensile or notched bend specimens to measure the critical cleavage stress of the A710 in its present condition; and

(6) Continue SEM studies to identify structure features responsible for initiation of cleavage fractures.

These tests and analyses will help us understand the substantial differences between the earlier (1981) and recent (2000) CVN test results, and the role these differences play in the sudden transition from ductile fracture to cleavage fracture.

ACKNOWLEDGEMENTS

This work was supportedby the U.S. Departmentof Energy,OffIceof Science,Office of Basic En- ergy Sciences, Engineering Research, Under DOE Idaho Operations OffIce Contract DE-AC07-991D13727.

REFEllENCES

(1) Faleskog, J. (1995), Effect of Local Constraint Along Three-Dimensional Crack Fronts – A Numeri- cal And Experimental Investigation, J. Mech. Phys. Solids, 43(3),pp. 447-493. (2) Dodds,R. H., Jr., M. Tang, and T. L. Anderson(1993),Eflects of Prior Ductile Tearing on Cleavage Fracture Toughness in the Transition Region, UILU-ENG-93-2014, Department of Civil Engineer- ing, University of Illinois, Urbana, Illinois, November 1993. (3) PVRC Ad Hoc Group on Toughness Requirements (1972), PVRC Recommendations on Toughness Requirements for Ferritic Materials, WRC Bulletin 175, August 1972. . (4) NB-2330, Section III, Division 1-NB (1998), ASME Boiler and Pressure Vessel Code, 1998 Ed. (5) Irwin, G.R.(1964), Structural Aspects of Brittle Fracture, Applied Mat’Is Res, 3, April 1964,p. 65. (6) ASTME208-91(1993),Standard Test Method for Conducting Drop-Weight Test to Determine Nil- Ductability Transition Temperatures of Ferrite Steels, 1993 Annual Book of ASTM Standards, Volume 03.01, American Society for Testing Materials, Philadelphia, PA, pp. 374-385. (7) ASTM E23-93 (1993), Standard Test Methods for Notched Bar Impact Testing of Metallic Materi- als, ibid., pp. 206-226, (8) Gerberich, W. W., S.-H, Chen, C.-S, Lee, and T. Levine (1987), Brittle Fracture: Weakest Link or Process Zone Controlled?, Metallurgical Transactions A, 18A, November 1987, pp. 1861-1875. (9) Reuter, W. G., J. C. Newman, Jr., J. Skinner, and M. Mear (2000), Use of K1.and Constraint to Pre- diet Location and Load Corresponding to Initiation of Crack Growth for Specimens Containing Surface Cracks, 32n~National Symposium on Fatigue and Fracture (accepted for publication), West Conshohocken, PA, June 2000. (10) Green, A. P. and B. B. Hundy (1956), Initial Plastic Yielding in Notch Bend Tests, J. Mech. Phys. Solids, 4, pp. 128-144.

24 CAVITY RING-DOWN SPECTROSCOPY AS A PLASMA DIAGNOSTIC: APPLICATIONS TO DIAMOND FILM GROWTH

U. Lommatzsch 1,E.H. Wahl 2, C.H. Kruger 2,R.N. Zare i

] Department of Chemist~, Stanford University, Stanford CA 94305, USA 2 Department of MechanicalEngineering, Stanford University, Stanford CA 94305, USA

ABSTRACT

Cavity ring-down spectroscopy is a highly sensitive technique for absorption measurements and is used here for concentration and temperature measurements in a CVD reactor. Results are reported for the CH and the CH3 radical in a hot-filainent reactor for the synthesis of diamond thin films. The spatially resolved concentration measurements indicate different formation mechanisms for both radicals. The temperature measurements show a large temperature drop as the distance increases from the filament. The large gradients of concentration and temperature are typical for a system f~ from equilibrium and seem to be an important condition for achieving diamond growth under thermodynamically unfavorable conditions.

INTRODUCTION

The extreme hardness, the very high thermal conductivity and the high chemical resistance of diamond have led to large interest in diamond thin films for technological applications [1, 2]. The outstanding physical properties of diamond are the consequence of its structure and the strength of the bonding between the carbon atoms. Diamond thin films are used in such different areas as wear-resistant coatings for drilling tools, as thermal management devices in microelectronics, as sensors in harsh environments, and as optical materials. Synthetic diamond was first made by a high-pressure synthesis under conditions for which diamond is the thermodynamically stable modification of carbon. Diamond synthesis at low pressures and temperatures for which diamond is metastable with respect to graphite was first achieved in 1953. Based on this work several groups developed in the early 1980s the synthesis of thin film diamond by chemical vapor deposition (CVD). Diamond synthesis by CVD is accomplished in three steps: (1) activation of a mix of reactant gases to create reactive species in the gas phase; (2) transport of those species to the substrate coupled with additional gas-phase reactions; and (3) deposition of carbon-containing species on the substrate surface and additional stiace reactions resulting in diamond formation.

Activation is achieved thermally with a hot filament (HFCVD), by microwave plasmas, by RF plasmas or in flames. In a HFCVD system methane and hydrogen flow over a hot wire at . a typical temperature of 2500 K. The activation includes the dissociation of the molecular hydrogen and the subsequent formation of various CXHYspecies. Diamond formation occurs on a substrate located about 1 cm from the filament. The main precursor(s) in the diamond growth is (are) still not identified, but CHg and CZHZseem to be the most likely candidates [1, 2]. Despite much effo~ widespread applications of diamond thin films are still limited owing to its high production cost. A rational attempt to improve film quality and growth rates requires the understanding of the reaction mechanisms and the identification of the precursor(s) in the diamond growth. An identification of the precursor would allow for a specific optimization of the growth conditions. Further scientific interest in diamond CVD synthesis is stimulated from the need to explain the growth of a material under metastable conditions.

In this study, cavity ring-down spectroscopy (CRDS) [3, 4] is used as a gas-phase diagnostic in a diamond HFCVD reactor. CRDS is a novel method for laser-based absorption measurements of species that either weakly absorb or exist at low concentration. The high sensitivity (~1~ = 10-9cm-l), the simplicity of quantification without the need of a calibration procedure, the applicability to harsh environments and the spatial resolution make this technique especially usefid for this purpose. In CRDS the intensity of a light pulse circulating in an optical cavity containing the absorber(s) is measured. In its simplest implementation a short light pulse from a pulsed laser is injected into a high-finesse linear resonator built from two highly reflective mirrors. Owing to mirror losses and sample absorption an exponential decay of the light intensit y I with a characteristic time constant z, the ring-down time constant, is observed.

I(t) =10 exp(-th) (1)

The ring-down time constant is inversely proportional to losses of the empty resonator including mirror losses and scattering and also to the absorption of gaseous species present within the resonator. By measuring the decay constants z and Tofor a cavity with and without a sample present, respectively, the sample absorbance A is determined (see eq. 2, for t~= 21/c where c is the speed of light and 1is the distance between both mirrors).

(2)

The number density N can then be extracted with the help of Beer’s law (eq. 3) from the sample absorbance A when the absorption cross section o and the path length/ are known.

A=o. N”l (3)

26 The high sensitivity of CRDS results from the insensitivity to shot-to-shot fluctuations in laser intensity and the long absorption path length.

In this report it is demonstrated how CRDS can be used to determine the concentrations of short-lived radicals and their spatial dktributions in a HFCVD reactor. From the line intensities in the absorption spectra of those radicals the gas temperature in the reactor is derived.

EXPERIMENTAL

Experimental details can be found in Refs. [5, 6]. For completeness a short description is given here. The CVD reactor is maintained at a pressure of 20 Torr and is filled with a mixture of 1% methane in hydrogen at a flow rate of 100 seem. A resistively heated filament made out of tungsten with a length of 20 mm and a diameter of 0.2 mm is used. The molybdenum substrate is positioned at a filament distance of 7 mm. The optical cavity consists out of two mirrors with a maximum reflectivity R = 99.993 YO at 430 nm that are separated by 65 cm. They are attached to the reactor by means of flexible bellows, allowing the CVD reactor to be moved independently with respect to the light path in the resonator. Thus spatially resolved measurement become possible. An optical parametric oscillator (OPO) pumped by a NdYAG laser with a repetition rate of 10 Hz is used as the light source. Before introducing the light into the optical cavity some optics are used to match the laser beam profile to the TEMOOmode of the cavity. The light exiting the cavity is detected by a photomultiplier (PMT) whose output is processed by a digital oscilloscope and a personal computer to extract the ring-down time constants.

Nd:YAG OPO :<,.- ..... ,;”; ~:;.. , “..355 n“ ,jtj.. $<:,. ,, ~@&. ~m~; ,:5$:.” ;.:”yzrnm.Wsi4qf$ Iik ,- .“, beam shaping : optics B Ifilament I ““ L----J, ‘ ,. ‘::@#j‘, { —-” ..+-.. .’!, ., .. . .. w. “-t?

P ‘--%-Wmirrors I Digital oscilloscope

Figure 1. Schematic of the experimental setup. The CVD reactor with the filament and substrate inside can be translated to measure the ring-down signal at different distances from the filament.

27 RESULTS and DISCUSSION

CH Absorption Spectrum

The absorption spectrum of a molecule can be measured by CRDS when the change in ring-down time versus wavelength is recorded. As an example Fig. 2 shows the Q-branch members of the CH A-X band around 430 nm. Also shown in Fig. 2 is a simulated spectrum that is in excellent agreement with the experimental data. The A-type doubling and spin-orbit coupling can be clearIy resolved owing to the small bandwidth of the OPO.

Q g ~2 .-c

430.4 430.6 4S0,8 431.0 4s1.2 431.4

L [rim] Figure 2. Experimental (top) and simulated (bottom) part of the absorption spectrum of CH A-X (0,0) band. The line marked with an asterisk is used to evaluate concentrations.

Spatial Distribution of Radical Species

Fig. 3 compares the concentration distributions of the CH3 and the CH radical in our HFCVD reactor. The concentration profiles differ in two ways. First, the CH3 concentration on the order of 10’3 molecules/cm3 is two orders of magnitude larger than the CH concentration. Secondly, both profiles differ also in their qualitative trend. While for CH3 a concentration maximum occurs at a distance of 2 mm from the filament, the CH concentration declines steadily with increasing distance from the filament. Two conclusions can be drawn from those results related to diamond growth. The absolute concentration values for both radicals make it unlikely that CH is important in the diamond growth and confirm the view that CH3 could be an important precursor in diamond growth. The differences in spatial distribution indicate different formation mechanisms for both radicals. While the maximum of the CH3 concentration excludes a filament production mechanism, the CH profile resembles those of the H radical, a species that is formed heterogeneously at the filament [7],

28 I

8 - -. -’7 - % <6 - n 25 - . ~4 - 1’ “g ‘j : 8 gz -t u 1 01 t I I t * 1 J 0 -6-4-202468 -8-6-4-20246 8 Distance fromFilament[mm] DistancefromFilament[mm]

Figure 3. Concentration of CH3 (left) and CH (right) at a filament temperature of 2500 K and a substrate temperature of- 1200 K.

Gas temperature in the CVD reactor

From the line intensities in the absorption spectrum the rotational temperature of a species can be derived horn a Boltzmann plot. Fig. 4 displays the temperature of the CH radical at different locations in our reactor. Remarkable is the large temperature difference of -1000 K between the filament and the gas phase. This behavior was already observed by L.angmuir [8] in 1927 and can be related to the breakdown in the continuum energy conduction theory at low pressures. The comparison of the CH temperature profile with published profiles for the H atom [7] reveals a high correspondence. It can be thus concluded that most gas-phase species in the reactor have the same temperature, which is a behavior that is expected from the large number of collisions in the gas phase at a pressure of 20 Torr. Therefore the temperature profile in Fig. 4 can be used to represent the temperature in the reactor in theoretical simulations.

~ooo~ 01234567 DktancefromFilament[mm]

Figure 4. The temperature of the CH radical. Transitions withN=5-15 were included in the E301tzmannPlot. Filament temperature is 2500 K. From the Iarge gradients in concentration and temperature it follows that the whole CVD system is fhr from a thermodynamic equilibrium state. This non-equilibrium state is an important prerequisite for achieving diamond growth under thermodynamically unstable conditions.

ACKNOWLEDGMENTS

Uwe Lommatzsch gratefully acknowledges support from the Deutsche Forschungsgemeinschaft. This work was supported by the Engineering Research Program of the OffIce of Basic Energy Sciences at the Department of Energy.

REFERENCES

1. M. N. R. Ashfold, P. W. May, C. A. Rego, and N. M. Everitt, “Thin-Film Diamond By Chemical-Vapor-Deposition Methods”, Chenz.Sot. Rev. 23,21 (1994).

2. D.G. Goodwin and J.E. Butler, in M.A. Prelas, G. Popovici, L.K. Bigelow (Eds.), Handbook of industrial diamonds and diamond films, Marcel Dekker, New York, p. 527 (1998).

3. A. O’Keefe and D.A.G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources”, Rev. Sci. Jnstr. 5!J, 2544 (1988).

4. K.W. Busch and M.A. Busch (Eds.), Cavity-Ringdown Spectroscopy, American Chemical Society, Washington (1999). ,

5. E.H. Wahl, T.G. Owano, C.H. Kruger, U. Lommatzsch, D. Aderhold and R.N. Zare in: J.C. Angus, W.D. Brown, J.P. Dismukes, M.D. Drory, A. Gicquel, A. Grill, R.H. Hauge, H. Kawarada C.P. Klages, R.L. Opil~ A. Paoletti, Y. Sate, K.E. Spear, and B.V. Spitsyn (Eds.) Diamond Materials VI, l%oc. Elelectrochem. Sot. PV99-32 (1999), “Spatially resolved measurements of CH concentration and temperature in a hot filament CVD reactor” The Electrochemical Society, Pennington (in press).

6. U. Lommatzsch, E.H. Wahl, T.G. Owano, C.H. Kruger and R.N. Zare, “Spatial Concentration and Temperature Distribution of CH Radicals Formed in a Diamond Thin Film Hot-Filament Reactor”, Chem. Phys. Lett. ~ (2000) 339.

7. S. A. Redman, C. Chung, K. N. Rosser, and M. N. R. Ashfold, “Resonance enhanced multiphoton ionisation probing of H atoms in a hot filament chemical vapour deposition reactor”, Phys. Chem. C%em. Phys. ~ (1999) 1415.

8. I. Langmuir, “The dissociation of hydrogen into atoms”, J. Am. Chem. Sot. 37,417 (1915).

30 LIGHT SCATTERINGMEASUREMENTSOF THERMALIXFFUSIVITY FOR REFERENCESTANDARDS

Chris Muzny and Richard Perkins

Chemical Science and TechnologyLaboratory National Instituteof Standardsand Technology Boulder, Colorado80303

ABSTRACT

Measurementsof the thermal diffusivity of l,l,l,2-tetrafluoroethane (R134a) are reported for the saturatedliquid and vapor at temperaturesfrom 293 to 374 K. These data were obtained by dynamic light scatteringexperimentson a verypure sampleof R134a. This sample has been well characterizedand was used previously for international round-robin measurements of the thermal conductivity and viscosity organizedby the IUPACSubcommitteeon TransportProperties. The thermaldiffusivitydata can be used to calculate values for the thermal conductivity with values for the density and specific heat from the equation of state recommended by the International Energy Agency Annex 18 for R134a. Good agreement is found between thermal conductivity data obtained directly by transient hot-wire measurementson thk same round-robinsample.

INTRODUCTION

Accurate knowledgeof the thermophysicalproperties of fluids is required to optimally design gas transmission pipelines, thermomechanical systems such as power plants and refrigeration units, and chemical process plants. Internationally accepted values for the thermophysicalproperties of fluids are required to calibrate and use mass flow meters in pipelines as a bask for custody transfer agreementsand to calibrate instruments used to measure thermophysical properties. The thermal dKfusivity is a key thermophysical property that characterizes transient heat transfer through a medium. The thermal diffusivity a is defined as

A a— (1) = pcp ‘

31 .. ‘, ‘, .’

where A is the thermal conductivity, p is the density, and CP is the isobaric specific heat. The thermal diffusivity characterizes the ratio of energy transport to the volumetric energy storage of a medium. Eq. (1) shows that the thermal diffusivity is related to three thermophysical properties that can be independently measured. NIST has a unique capability to measure all of these properties with low uncertainty over a wide range of conditions (30 K to over 700 K, at pressures to 70 MPa) due to long- term support from the U.S. Department of Energy. Comparison of independent measurements of each of these properties through Eq. (1) provides a verification of the consistency of all of the measurements.

Both CPand A are divergent at the gas-liquid critical point. This divergence can be characterized by critical exponents, with CP diverging about twice as quickly as A so that the thermal diffusivity approaches zero at the critical point. Direct measurements of thermal conductivity require a temperature gradient that has the potential to drive convection of the fluid, making the measured heat flux higher than that due to pure conduction. Since the fluid is very compressible in the critical region, convection can be driven by extremely small temperature gradients making accurate thermal conductivity measurements nearly impossible. Additional] y, a temperature gradient introduces heat transfer by thermal radiation. The thermal radiation contribution to the measured heat flux increases in proportion to the absolute temperature cubed. Most fluids are not transparent to infrared radiation but instead have complex absorption and emission spectra that are a function of both temperature and density, so that analysis of the contribution of thermal radiation during a thermal conductivity measurement becomes extremely difficult. Dynamic light scattering does not require a macroscopic temperature gradient to measure thermal diffusivity so it has significant advantages over other techniques used to measure thermal conductivity and thermal diffusivity in the critical region (fluid convection) and at elevated temperatures (thermal radiation).

The refrigerant 1,1,1,2-tetrafluoroethane (R134a) was selected for the present measurements of thermal diffusivity by dynamic light scattering. The gas-liquid critical point of R134a is located at a temperature of 374.21 K and a density of 511.9 kg”m-3. R134a is the most widely studied and the best characterized of the new alternative refrigerants. It is used as the reference fluid in corresponding states models that allow the prediction of the thermophysical properties of mixtures of alternative refrigerants. For this reason, it is necessary to know the properties of R134a with the lowest uncertainty possible. However, early measurements of the viscosity, thermal conductivity, and thermal diffusivity of alternative refrigerants, such as R134a, were found to have inconsistencies of as much as 30 to 40 YO [1]. These large discrepancies were observed between laboratories that historically provided reliable data for nonpolar fluids, R134a is a relatively polar fluid with very good solvent properties. It easily picks up water and ionic solutes if not handled properly. Moderate electrical conductivity is observed in some samples that increases as a function of the water concentration. In 1992, the IUPAC Subcommittee on Transport Properties organized a round-robin study of these transport properties to try to resolve these discrepancies [1,2].

EXPERIMENTAL

The sample of 1,1,1,2-tetrafluoroethane (R134a) used in the present study was prepared for the IUPAC round robin on transport properties. It is from one of nine cylinders that were filled from a single high-purity sample, using procedures for pharmaceutical materials to insure the cleanliness of the cylinders before use. The purity of the sample was verified by gas chronmtography for organic compounds and by the Karl-Fischer test for water. The purity of the batch was greater than 99.9 ~o, and the principal impurity was R 134 at a concentration of 850 ppm. Water was present at a concentration of 6 ppm. NIST has made extensive measurements of the thermal conductivity of this round-robin sample

32 with two transient hot-wire instruments [1-3]. All the laboratories that participated in the IUPAC study agreed to analyze their data using the equation of state recommended by Annex 18 of the International Energy Agency for R134a [4,5]. This equation of state is also used to calculate the fluid density and specific heat as a function of the measured temperature and pressure in the present analysis.

The dynamic light scattering technique (DLS) is used to probe the microscopic entropy fluctuations of a transparent sample of pure fluid that remains in macroscopic equilibrium, For the thermal diffusivity, the broadening of the central RayIeigh line of the scattering spectrum is probed. At conditions away from the critical point, the scattering signal is a homodyne composite of the scattering from the sample containment windows and the fluid. As the fluid scattering becomes more intense near the critical point, the composite scattering signal is dominated by scattering from the fluid and may be treated as a self-beating correlation function. For the homodyne case, the intensity correlation function is of the form

(2) where A, B, and r~are experimental parameters determined from a fit of the correlation function. The thermal diffusivitya is calculated using 1 a=z. (3)

For scattering of coherent laser light of wavelength &at low scattering angles in the fluid 0,, fhl e 27cn6, 2zQe —sin~ Z— — (4) ‘=ao [) 2 A, ‘a,’ so the refractive index n of the fluid of interest is not required since it is the scattering angle Q, external to the vessel window, that is measured. The error associated with the low angle approximation is of the order of Q3.

The sample of interest is contained in a cylindrical pressure vessel with highly polished quartz windows on each end. The quartz windows are sealed with polyimide o-rings that are compressed with threaded closures. The entire vessel is made from black anodized aluminum to minimized surface reflections and is designed for pressures to 35 MPa at 600 K. The fluid enters the cell from the bottom to minimize convection in the critical region at elevated temperatures. The fluid vessel is held tightly in an aluminum thermostat block with temperatures controlled with either circulating fluid or electrical heaters. The entire thermostat is well insulated to minimize temperature gradients and isolated from the optical bench with a temperature controlled shield plate. The temperature of the cell is measured with a reference platinum resistance thermometer (PRT) with an uncertainty of 5 rnK. The calibration of the PRT is verified periodically with a water triple point cell. The pressure of the sample is measured with a quartz pressure transducer with a range from Oto 21 NIPa with an uncertainty of 0.01 % full scale (0.002 MPa). The calibration of the pressure transducer is verified periodically relative to a gas dead-weight gauge.

A schematic of the opticaI cell is shown in Fig. 1. The light source is a 1 W argon ion laser operating at a wavelength &of 514.5 nm. This laser is locked to a single longitudinal mode and the beam intensity is externally stabilized and focused prior to entering the scattering cell. The cell is maintained at a fixed angle 0~relative to the incident laser beam. This angle is determined accurately by the distance between the incident beam and its reflection from the vessel window at a known distance from the window. The scattered light passes through two apertures to minimize scattered light from the windows and detected by 2 cross-correlated photomultiplier detectors located normal to the cell windows. The use of two photomultiplier detectors eliminates errors due to afterpulsing. The signals from the photomultiplier detectors are collected and analyzed with a log-time correlator with a minimum time resolution 25 ns with up to 400 channels. From 4 to 20 replications with a duration of 5 minutes were obtained for each data point reported here.

Mirror 1

Argon Ion Laser -514.5 nm Intensity Stabilizer [ t I

Mirror 2 Beam Stop

Lens Beam Splitter Scattering Aperture 1 Cell Apetture 2

IYY

BI-9000 Conelator

Figure 1. Schematic of the dynamic light scattering apparatus to measure the thermal diffusivity of fluids. The scattering cell operates at temperatures from 273 K to 500 K with pressures to 35 MPa.

The measurement vessel and its associated pressure system were evacuated and filled from the vapor phase of the round-robin sample of R 134a. Three filling cycles were made prior to measurements to purge adsorbed compounds. The volume of the pressure system was varied with a hand piston pump to adjust the position of the liquid-vapor interface relative to the laser beam in the optical cell. The measured thermal diffusivity is provided in Table 1 and shown in Fig. 2 for saturated liquid and vapor at temperatures from 294 to 374 K. All temperatures are reported based on the ITS90 temperature scale.

DISCUSSION

The reference correlation of Krauss et al. [6] is selected as the basis for comparing the present measurements with other data obtained on this same round-robin sample of R134a [3,7-10]. This correlation is valid at temperatures from 240 to 410 K with densities to 1500 kg”m-3. The estimated uncertainty of this correlation is 5 %, increasing to 10 % in the near critical region. The critical point is located at a temperature of 374.274 K (ITS90) and a density of 515.25 kg”m-3.This correlation includes a crossover equation of state and is currently the best representtttion of the therrndl diffusivity of R134a. Evidence of residual particle scattering (Stokes-Einstein diffusion) was observed in the liquid phase R134a at the lower temperatures where the scattering intensity was very low. Good agreement is found between the present measurements and the DLS measurements of Kraft and Leipertz [7] on the same round-robin sample of R134a.

34 Table 1

Thermal diffusivity of the round robin sample of R134a in the liquid (1)and vapor (v) phases.

T (K) al (mzs-i) T. (K) ~“ (m2s-1)

294.478 4.72E-08 297.927 4.94E-08 306.750 4.69E-08 316.558 4.60E-08 326.589 4.41E-08 336.279 4.34E-08 346.130 2.97E-08 346.042 1.07E-07 355.894 2.86E-08 365.726 1.59E-08 365.719 2.86E-08 372.712 5. 14E-09 372.696 5.82E-09 373.174 3.88E-09 373.230 3.96E-09

l.l E-7 , I 1 I 1 I I , I t I 1 [ , 1

~~~ JEE?E! ‘ ; 8.OE-8 ~- 7.OE-8 ‘m A ~ 6.OE-8- E A ; 5.OE-8- A 080sO00 ● 4.OE-8- 0..O A 0 0 0.O 3.OE-8- 0.O 4 OOA - 2.OE-8- ●O 6 1.OE-8- O.OEO 290 300 310 320 330 340 350 360 370 380 T (K)

Figure 2, Thermal diffusivity of the round-robin sample of R134a near saturation as a function of temperature. ——_—..-. — .,, ......

Saturated Vapor

The thermal diffusivity data were used to obtain estimates for thermal conductivity using Eq. (1) with density and specific heat values calculated using the Krauss et al. [6] correlation. These thermal conductivity estimates can then be compared with direct measurements of the thermal conductivity that were made on the vapor phase of the same sample of R 134a. Deviations of these results from the Krauss et al. [6] correlation are shown in Fig. 3 for the saturated vapor phase. Good agreement is found between the present results and the results of the Kraft et al. [7] measurements of thermal diffusivity as well as the direct thermal conductivity measurements on the same sample. There are no systematic trends in the present data. The relatively large scattering in the present measurements is attributed to light scattering associated with the Stokes-Einstein diffusion of small particles that were observed in the sample. Good measurements were obtained at lower temperatures (lower intensity of scattered light) than those reported by Kraft et al. [7]. This demonstrates the high quality of the present optical setup.

10 I o I I I 1 I i I i I 0 I 1 I ✞I ● 8

6 ✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✎✎✎✎✎✎✎✎✎✎✎✎✎✎✎✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍✍ 4 ● *A- 2

0 1 .%-

-2 A?- 0 0 +f@ r- +++++ -4 ----X------~ . #---?&-g... X x p-$+-.4.---z...*...... -6 * -8 1 1 -10 I I ! I I I , I 1 I I I 9 I , I 240 260 280 300 320 340 360 380 T, K

Figure 3. Deviations of the measurements of the thermal conductivity of vapor R134a along the saturation line from the correlation of Krauss et al. [6]. Round-robin sample: +, Assael et al. [8]; X, Perkins [3] (Tr-Pt); +-,Perkins [3] (Tr-Ta); A, Kraft and Leipertz [7]; ●, present results.

Saturated Liquid

Deviations of these results from the Krauss et al. [6] correlation are shown in Fig. 4 for the saturated liquid phase. Good agreement is found between the present results and the results of the Kraft et al. [7] measurements of thermal diffusivity as well as the direct thermal conductivity measurements on

36 the same sample. There are no systematic trends in the present data. The relatively large scatter in the present measurementsis again attributedto the presence of particles in the sample and the transitionfrom the homodyneto the self-beatingscatteringsignal at temperaturesfrom 320 to 340 K.

10 I 1 I t I I I 1 I I I 1 I i I I 1 , I o 1 A 8 - ● + +A - 6 - ...... - ...... ------..-.------...... & .-1 4 - + ?+ . k !J & : 2 - ■ 48 A , A ?!!-+;- - ?! m % t8 + -i A, A

w ------.... o 1- I 0 -1 L . . -8 -

-lo I I t I I I ! I I I I I I I I I a, I I 180 200 220 240 260 280 300 320 340 360 380 T, K

Figure 4. Deviations of the measurements of the thermal conductivity of liquid R134a along the saturation line from the correlation of Krauss et al. [2]. Round-robin sample: ●, Assael et al. [8]; X, Perkins [3] (Tr-Pt); +, Perkins [3] (Tr-Ta); 1, Gurova et al. [9]; O, Nagasaka [10]; A, Kraft and Leipertz [7]; ●, present results.

FUTURE WORK

The uncertainty of future thermal diffusivity measurements will be reduced by careful cleaning of the optical cell and improved filtration of all samples. Measurements will be made at multiple scattering angles to eliminate uncertainties in the transition of the scattering signal from homodyne to self beating. The measurements will be validated over an extended range of temperature with both R134a and toluene. Thermal diffusivity measurements will be made on toluene over a wide range of temperatures (178 to 592.8 K) in conjunction with an international round robin on density calibration standards.

Since the dynamic light scattering technique does not require a temperature gradient, the thermal diffusivity measurements allow verification that independent measurements of thermal conductivity, density, and specific heat are consistent with each other at high temperatures where thermal radiation effects become very significant. The dynamic light scattering technique will be extended to simultaneous measurements of the thermal dlffusivity and mass diffusivity of key mixture systems that are common in the chemical and energy industries. Selected measurements will be made on well-defined mixtures to develop and validate predictive models for these mixture properties. These validated models will allow the design of highly optimized chemical and energy processes and the assessment of the environmental fate of chemical waste.

ACKNOWLEDGEMENT

The financial support of the United States Department of Energy, Division of Engineering and Geosciences, Office of Energy Sciences, is gratefully acknowledged.

REFERENCES

1. M.J. ASSAEL, Y. NAGASAKA, C.A. NIETO DE CASTRO, R.A. PERKINS, K. STROM, E. VOGEL, and W.A. WAKEHAM, “Transport Property Measurements on the IUPAC Sample of l,l,l,2-Tetrafluoroethane (R134a),” Int. J. Thermophys. ~, 1 (2000).

2. M.J. ASSAEL, Y. NAGASAKA, C.A. NLETO DE CASTRO, R.A. PERKINS, K. STR~M, E. VOGEL, and W.A. WAKEHAM, “Status of the Round Robin on the Transport Properties of R134a~’ Int. J. Thermophys. IG, 63 (1995).

3. R.A. PERKINS, J. HOWLEY, M.L,V. RAMIRES, A.N. GUROVA, and L. CUSCO, “Experimental Thermal Conductivity Values for the IUPAC Round-Robin Sample of 1,1,l,2-Tetrafluoroethane (R134a)/’ National Institute of Standards and Technology, NISTIR, 2000, in press.

4. R. TILLNER-ROTH and H.D. BAEHR, “An International Standard Formulation for the Thermodynamic Properties of 1,1,l,2-Tetrafluoroethane (HFC-134a) for Temperatures from 170 K to 455 K and Pressures up to 70 M’Pa/’J. Phys Chein Rej Data 23,657 (1994).

5. S.G. PENONCELLO, R.T. JACOBSEN, K.M. DE REUCK, A.E. ELHASSAN, R.C. WILLIAMS, and E.W. LEMMON, ‘The Selection of International Standards for the Thermodynamic Properties of HFC-134a and HCFC-123,” ht. J. Thermophys. l&5,781 (1995).

6. R. KRAUSS, J. LUETTMER-STRATHMANN, J.V. SENGERS, and K. STEPHAN, “Transport Properties of R134a~’ ht. J. ‘i%ermophys.14,951 (1993).

7. K. KRAFT and A. LEIPERTZ, “Thermal Conductivity and Sound Velocity of Round-Robin R134a;’ Fluid Phase Equil. ~, 245 (1996).

8. M.J. ASSAEL, N.A. MALAMATARIS, and L. KARAGIANNIDIS, “Measurements of the Thermal Conductivity of Refrigerants in the Vapor Phase,” lnt. J. Therwzophys.18,341 (1997).

9. A.N. GUROVA, U.V. MARDOLCAR, and C.A. NIETO DE CASTRO, “The Thermal Conductivity of Liquid 1,1,l,2-Tetrafluoroethane (HFC 134a),” ht. J. Thermophys. ~, 1077 (1997).

10 Y. NAGASAKA, Personal Communication, Keio University, Yokohama, Japan.

38 COHERENCE AND SYNCHRONIZATION IN ARRAYS OF CLASS B LASERS

Y. Braiman, G. Bitto~ H. K. Liu, V. Protopopescu, L, Zhang, and J. Barhen

Center for Engineering Science Advanced Research Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6355

ABSTRACT

Wc report preliminary results on the feasibility of a compact source of high power and high intensitycoherent radiation emitted from an array of semiconductordiode lasers via the injection of a controlledelectromagneticfield into the cavity of each laser. The new source is expectedto generate coherent radiation of the order of magnitude of 10 Watts and to spawn a new laser technology of compacthigh power devices.

INTRODUCTION

In recent years there has been a dramatic increase in demands for high power, high intensity diffraction limited beams. High power compact coherent sources are extremely usefil in many engineering applications. For this reason, phase-locked arrays of diode lasers have been studied extensively over the last 15 years [1,2]. Such devices have been built to achieve high coherent radiationfor applicationssuch as space communication,blue-light generationvia frequencydoubling, optical interconnects,parallel optical signalprocessing,high-speed,high-resolutionlaser printing, and end-pumping solid-state lasers. Conventional,narrow-stripe (< 3 -4 pm wide), single-mode lasers provide, at most, 100mW reliably [1], since they are limited by the optical power density at the laser facet. For reliable operation at watt ranges, broad-area laser (13AL)arrays with large-aperture(2 100 pm in width)are necessary.However,suchBAL arrays usually exhibit multi-lateral-spatialmodes and the output beams are mutually incoherent. Thus, the challenge has been to obtain single-mode operationfrom large-aperturedevices,and maintainstable, coherentbehaviorto high power levels.

Laser arrays provide an intriguing class of nonlinear dynamical systems with many degrees of freedom. Of particular interest is the cmergencc of mutual synchronized behavior where all the . .

elements execute in-phase oscillations. This phenomena is very important in a variety of engineering, physical, and biological systems, yet our current theoretical understanding of the subject is far from being complete. Stability of the in-phase dynamics in laser arrays was recently theoretically studied for both solid state [3-6] and semiconductor [7-9] lasers, It is well documented [10] that the most common behavior in laser arrays is, indeed, the anti-phase behavior where the phases of adjacent lasers differ by z Therefore, an external forcing is required to induce stable in-phase dynamics. To overcome the antiphasing tendency and to maintain stable and coherent operation of the array, one possible technique is to inject a controlled electromagnetic field into the cavity of each laser. This field will synchronize the array and control chaos if it arises. Some of the challenges associated with the successfid implementation of this idea are:

. Achieve effective unr~orminjection into each laser with a moderate power single-mode laser. . Phase lock the array (though lasers are almost identical, the desired in-phase state is unstable for a broad range of parameters) and maintain the coherence.

Injection locking has been successfully used to obtain single mode emission in high power diode lasers or laser arrays [11]. The general method is to inject an external beam from a master single fi-equency laser into the cavity of the slave laser (see Fig. 1). The incident angle can be adjusted to stimulate a specific mode, which gives high coherent output power. An alternative approach is to feedback part of the output beam through grating, etalon, or phase conjugate mirror.

Broad-StripeLaserArray

Figure 1 Schematicdiagramof ordinaryinjectionlocking.

A free-running broad area diode-laser array usually generates output with a broad spectrum (- 3 rim). Its fro-field intensity distribution exhibits large divergence. When injection-locking is introduce~ the spectral distribution will follow the injection laser. As a result, both the spatial and spectral power density are improved [11,12]. The injection-locking efficiency relies on the injected power, which may range from 0.1 YO to 10% of the output power depending on the injection structure. For closely spaced and internally coupled laser arrays, uniform or even single stripe injection can achieve a satisfactory effect at low current. However, for broad stripe and widely separated high power laser arrays, the lateral mode structure is more complicated. High power operation also brought robust conditions for maintaining coherent operations. Maximum injection effect can be achieved via individually controlled mode matching. Individually controlled phase modulation gives us another freedom to fine-tune the injections. To our knowledge, these techniques have not been used on broad stripe laser arrays.

To achieve phase locking, couplings among diode laser emitters are required. To phase lock broad stripe laser arrays, external coupling might provide the only viable approach. Global couplings [13,14] can provide automatic phase locking via gain control. However the stability region in global

40 coupling is small compared with nearest neighbor (series) couplings. With larger drive curren~ the system can be driven into chaos easily. With nearest neighbor coupling more external controls can be applied, thus helping us to collect information on phase locking high brightness diode laser arrays.

Here wc presentpreliminaryresultson the theoretical analysisand experimentalimplementationof the idea discussedabove.

PHASE MODEL ANALYSIS FOR TWO-LASER ARRAY

Solid state [3-6] and semiconductor [7-9] lasers are considered class B lasers and are described by similar dynamical equations. For solid state lasers, under certain dynamical conditions [3,15],the main fatures of the full dynamics are adequately captured within a simplified description, called the phase model. Here we present the analysis of the entrainment of coupled solid state lasers over a Iarge range of injection fields [15] (work on semiconductor laser arrays is in progress). In particular, we elucidate a newly observed dynamical behavior of the total output intensity, namely, strongly nonmonotonic growth as the function of the injection strength [4]. Our starting point is the system of equations describing the dynamics of two evanescently coupled lasers, where the polarization is adiabatically eliminated [3-6]:

E,=(G, - aj -+iJ,)E, + K(l?,+, + l..,-,)+ E=(t)

(1,1) G,=%, -(1+1 E, tM,l> j=l,2 “’f

The variables Ej and Gj are the dimensionless complex electric field and gain for thejth laser. All times and frequencies are scaled relative to the cavity round trip time, z.. and ~is the fluorescence time of the laser medium, crjand Pj are the dimensionless cavity decay and pump mtes for thejth laser respectively, K is the evanescent coupling constant between the two lasers, and E.(ij is the slowly varying amplitude of the external field which drives each laser. Eqs. (1.1) are written in a *e rotating with frequency ~, at which the external field has a non-zero Fourier component. This frequency is tuned to minimize the detuning from the cavity resonances. In practice, the output power emitted from an array depends on the tuning of external field to the cavities [16]. The detuning 4- @ -a=j, where ~j is the cavity resonance frequency for liner ~. For solid s~te lasers, the latter dyn~ic contribution to the detuning is generally ignored. A variation in detuning amongst the lasers would result from a variation in cavity lengths for the laser elements. However, we have in mind a single . cavity containing the array.

In the following, we allow for a smalI spread in dctunings as a way to test the robustness of the entrainment mechanism to a physically reasonable parameter spread. We assume q = Q pj = p, p > a Substituting Ej (t) = ~, (t) exp(i+~(0), where ~{fl and ~(tj arc the intensity and the phase of lascrj and assuming Ec (t)= J1, to be a constant field, the model equations for two lasers reads: i, = 2(G, – a)~, + 2KJ_Illz Cos(+z- ~1) + 2J_I,ZJ cos#,

(1.2)

Tc G,=—(p- Gj-Gjl, ) ‘f

Eqs. (1.2) have been studied theoretically for N coupled lasers [4] and the condition for fill entrainment has been derived. This condition assumes small deviations in detunings and small coupling. Wc denote the dimensionless amplitude of the injected field by

~, = r It/1 whereI = p/a -1. Ideally, to entrain an array of N identical lasers requires injected field amplitude A,~r= 4K, or~e~ti= 4KJ 1. The ii.mction?dform of the total output intenSity may significantly depend on the parameters of the array (such as detunings and the coupling constant). In Fig. 2 wc show the normalized total intensity 1,., =(1 E, f + 11$ f) i 41 of two coupled lasers as a function of A. The injected field frequency approximately corresponds to the average of frequencies of each laser, thus it is tuned to minimize the detunings from the cavity resonances.

E 0.00- 8 c 0.0 0.5 1.0 1.5 2.0 2.5

injection amplitude A$KI

0:0 0:5 1.0 1.5 2.0 2.5 injection amplitude A,/\~l

Figure 2. The normalized total intensity, 1,., = (1E, r ~ IEz 12)141, as a fimction of the strength of the dimensionlessinjected field, A, = c 1,/1 . An inset shows the averagednormalizedtotal intensity, 1,.,, as a functionof }It.

42 We continuouslychange the strength of the injected field to mimic an experimentwhere the injected field is gradually increased. Initially, the total intensity grows with the injected $eld. When the injection strength reaches the critical amplitude, AOthe total intensity drops discontinuouslyto a significantlylower level. We notice that, just belowAO the total output intensity of the array is about 70?40of the maximum intensity (at full entrainment), but requires only about 20’%of the entrainment injected field, l?e,,~,We estimatethat if we apply a different set of initial conditions, the probability to obtain qualitatively very similar behavior, as demonstrated in the Fig. 2, is in the vicinity of 60°/0.Our estimation is based on simulating a sample of 500 realizations of distinct initial conditions. In the inset of Fig. 2 we present the averaged value of the normalized total intensity of two coupled Iascrs versus the dimensionless amplitude of the external field A, = ~. The curve is obtained by numerically solving Eqs. (1.2) for two coupled lasersand averagingover 500 realizationsof the initial conditions.

A characteristic feature of independent solid state lasers (i.e. without coupling and external field) is that, for any initial data their intensities and gains relax to a stationary state (I,G) = (p/a - l,a), i.e. the amplitudes 1I, -1 I and IG, - G I decay to zero. Numerical experiments [4], using physically realistic parameter values, show similar transient behavior of intensities and gains in the fill laser army systeu where both coupling and excitation terms are present. Once these transients have decayed it turns out that the dynamics of the phases no longer depend on intensities. This motivates, at least at a heuristic level, the use of the phase equations in Eqs. (1.2), with 1, = 1, as an approximation model to the fi.dl system. It turns out that the phase equations retain the essential features of the dynamics and can be used to explain the nonmonotonic behavior displayed by the solution of the complete system (1.2) [15].

To better understand the dynamics of laser array, phase models are widely used. Phase model is a very powerfbl tool to study dynamics of coupled lasers [3] and laser arrays [4]. It is used mostly in analysis of solid state lasers (rather than in semiconductor lasers) in situation where the fluctuations of the intensities and gains of each laser are small. The phase equations in (1.2) provide a significantly reduced description which captures nevertheless the essential dynamics, including the sudden drop in output intensity depicted in Fig. 2, as we now show. The frequency of the external field is tuned to minimize the detunings from the cavity resonance, thus wc may assume (61+ dz) = O. This assumption allows us to reduce the dimensionality of the parameter space and carry out the (simplified) analysis of the dynamics and of the fixed points in the plane (d, -32 ,~). On this plane, we usc experimentally suggested parameters for weakly coupled solid state Nd:YAG lasers [17], therefore we look in the rectangle K e (-0.5,-3) and d = d, -6, e (O,1).

With these assumptions, the stationary form of the phase equations in Eq. (1.2) reads:

sin~l i- sin $2 = O (1.3) i$l-62 ~ 2K(sin(@,- #,)) - Ae(sin@2– sin~l) = O.

The first equation in (1.3) implies that either a): ~z -$1 = (2m + l)z or b): $, + +2 = Zm, where m is an integer. Solutions of class (a) imply sin(42– 01) = O, yielding sin+, = d,/Ae , sin42 =32 /A, and sin($, -#z) = sin(sin-l(3, /A,) – sin-’(6Z/Ae )) *O, i.e. inconsistency. Hence, the

43 only possibility is the class (b) of solutions which, in turn, can be divided in two sub-classes: m even and m odd. Form even, the second equation in (1.4) becomes:

~(x) =-J-2 ~sinx-2AesinZ=0 (1.4) 2 where we substituted 3 = 61- Z$z,and x = $2- ~,.

For small values of A,, this equation has two solutions, one stable and one unstable. By increasing the strength of the injected field A., a saddle-node bifln-cation occurs at a critical value, AC. For A. > A. Eq. (1.4) has no real solution. To determine A=, we solve the system

f(x) = –~ – 2Ksinxc – J4csinxc/2 = o, and f’(x)= -2K COSXC– Ac cos XC /2 = O. Making the substitution tan x=j 2 = z and eliminating Ac we obtain a cubic equation for z that admits the explicit solution:

(1.5)

where D = (p/3)3+ (qf2)2, p = - C$21L18K2, and q = 6/4K + 631864K3. Then up to higher order terms, z== (3/-12K)”3 + 6/12K and the critical amplitude where the jump in intensity occurs is [15]:

1–22 A= = ‘2K . (1.6) r 1+Z2

For m odd, the second equation in (1.3) reads:

g(x) = –6 – 2rcsinx + 2Ae sin: = O. (1.7) 2 A similar analysis shows that this equation has two solutions, one unstable close to x = Oand one stable, close to x = n. Thus, at small values of the amplitude of the injected field A@,the system has two stable solutions, one close to ti2 that solves the Eq. (1.4) and one close to z that solves Eq. (1.7). Since the total output intensity is given by 1,., = 4 COS2(x/2), one solution has high intensity, while the other one has low intensity. Each of these stable solutions has a basin of attraction and the selection of the solution depends, of course, on the initial conditions. When A. = A=, the high-intensity solution disappears at the saddle-node point and for higher values of A. only the low intensity solution remains. We obtained an excellent fit between the numerical and analytical expressions. The numerical simulations and theoretical analysis for larger arrays is in progress.

EXPERIMENTAL SETUP

The objective of the experiment is to investigate the feasibility of extracting high coherent power from a semiconductor Iascr array using optical injection of self and/or external optical fields. The experimental setup whose conceptual scheme is shown in Figure 3 is of master-slave type. For the

44 master laser we have chosen a single mode tunable diode laser. For the slave laser we have chosen a high power (30W)broad area diode laser bar composedof 19differentnon-coupled emitters.The key point in this setup is the ability to access light rays associatedwith each emitter separately. This setup enablesus to measurethe intensityand relative phase of each emitter separately,This informationwill then be used to decide howto modifythe systemparametersso a high power coherent radiationcan be achieved. The information from the emitters’ radiation profile will be used as control measure for modifying the amplitudes and relative phases of the injected optical field to each emitter separately and alsoto changethe magnitudeof the couplingbetweenthe differentemitters. The detailed experimentalsetup is as follows: The master laser used for injection is a single modetunable diode laser (DL1OO).The laser line-widthis 1MHz and maximumoutput power of up to 120mW. To avoid optical feedbackinto the master laser cavity, a Double Faraday Isolator (DLIfrom LINOSPhotonics)with morethen 60 dB isolationis used. Part of the beam is then sampledby a beam splitter (BS1)to be used as referencebeam for the coherence measurementsand the rest of the beam passes through a computer-generated hologram (CGH) optics (Rochester Photonics Corp). Illuminatingthe CGHwith one beam produces an array of 21 equal spots. The size of those spots can be manipulatedby the size of the spot in the entranceto the CGH.The distancebetweenthe CGH and the collimating optics (collimator2) determinesthe distancebetweenthe spots. The collimatedbeams can be phase or amplitude modulated by a spatial light modulator (SLM1). The individually modulated injection beams are then passed through two beam splitters (BS2 and BS3) and a micro- Iensarray, and enter the cavity of the diode laser bar as a seedingbeams. The Diode laser bar (Bl-81- 20c-19-30-Afrom Coherent)is composedof 19emitterswith 500pm spacing betweencenters and 1 x 150 pm2 emitting surfhce. The output from the laser array is collimated by a micro-lens array with astigmatism compensation.The micro-lens array is coated with a low reflection coating, which will provide nearest neighbors coupling between the different emitters in the diode laser array. The couplingstrengthcan be adjustedby changingthe reflectivity of the coating and the distancebetween the laser array and the micro-lensarray. The output beam flom the diode laser bar are then past trough .another SLM (SLM2) which can be used to select certain beams from the total output of the diode laser bar for measurements.The measurementsystemconsists of irdlared CCD cameras for near-field and far-field pattern observation, Mach-Zender interferometerfor coherence measuremen~ scanning Fabry-Perotfor modestructuremeasurement;and a monochromatorfor wavelengthmeasurement.

“PEl

Cdhmw2 \\ ‘..’” 121 CGH w&4

‘%Camatcd & Muf,rfa.r cGH _Camputer GeneratedHologram. sLM_ SpatialLkhtModulator. SS _ Beanwfitter Figure 3 Schematic diagram of the experimental arrangement

45 The experimental setup suggested in Figure 3 was essentially realized (Figure 4). The measuring instruments were installed including the software and the hardware needed for the computer control over the instruments and the experiment. The main part of the measuring equipment include, CCD cameras for characterizing the far field and near field patterns of the emission from the diode laser bar, and a monochromator (From CVI) with resolution of 0.07nm for spectral characterization of the diode laser bar output. For higher spectral resolution a Fabry-Perot spectrum analyzer with 2GHz free spectral range and 100 MHz resolution is used.

External optical injection into all tic emitter cavities by the master laser was achieved. The optical characteristics of the free running diode laser bar were measured, Without injection of external optical field or injection of optical feedback, the emissions from the different emitters are mutually incoherent and the beam divergence is large (beam divergence of about 10x35 degrees) as expected. Prelimimuy results of the influence optical feedback using partial reflective mirrors suggest that an in- phase coherent radiation mode can be induced in the diode laser bar.

One of the most important parameters that may affect the injection locking is the thermal stability. When the environment temperature changes, the resonant wavelength of the laser changes. When this change is larger than the longitudinal mode spacing &l.w, mode hopping occurs and injection locking ftils. The cooling system and the materials used for thermal contact were chosen as to avoid such a failure. The diode laser bar produces about 80 watt of heat power, while our cooling system (from “Neslab) is able to remove 500 watt of heat power. The cooling system seems to be efficient enough even when the diode laser bar is operated at fill power.

Figure 4: Actual Experimental Setup

46 SUMMARY

Wc have describedpreliminarywork on the feasibilityof a compactsource of high power and high intensity coherent radiation emitted from the array of semiconductor lasers. Theoretically, we have studied how the total output intensityof Mo coupledlasers dependson the injection strengthand elucidatedmechanismof nonmonotonicbehavior. In particular,we notice tha~ just belowAo the total output intensityof the array is about 70°/0of the maximumintensi~ (at full entrainment),but requires only about 20°/0of the entrainmentinjcctcd flel~ -l?.nfpThis result is of great experimentalimportance, since obtaining high power injection in to laser arrays is not a simple task. In addition, by reducing injection strength the input power for device operation is reduce~ and we will explore thk phenomena for larger laser arrays. Experimentally,we have essentially implemented the proposed designand we are in the processof fine-tuningthe apparatus.

In this paper we discussed in detail the in-phase synchronizationof laser arrays. Besidesthe in-phase synchronization,other modes of synchronized behavior are of great interest for variety of application,as well as for betterunderstandingthe dynamicsof laser arrays.We are planningto pursue studies on periodic and chaotic [18] synchronizationbetween lasers in arrays, as well as betweentwo distinctarrays.

ACKNOWLEDGMENT

This research was partially sponsored by the Engineering Research Program of the Office of Basic Energy Sciences, U.S. DOE, by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the U. S. DOE under Contract No. DE-AC05-OOOR22725, and by the OffIce of Naval Research.

REFERENCES

1, D. BOTEZ and D. R. SCIFRES, Diode Laser Arrays, Cambridge Universi& Press, (1994). 2. N. W. CARLSON, Monolitic Diode-Laser Arrays, Springer-Verlag(1994). 3. A, I. KHIBNIK,Y. BRAIMAN,T. A. B. KENNEDY,K. WIESENFELD,Phase Model Analysis of Two Lasers with Injected Field, Physics D 111,295 (1998). 4. Y, BlLMMAN,T. A. B. KENNEDY, K. WIESENFELD, and A. 1. KHIBw Entrainment of Solid-State I.aserArrays, Phys. Rev. A 52, 1500, (1995). 5, M. SILBE~ L. FABINY, and K. WIESENFELD, Stabili& Results for In-Phase and Splay-States of Solid State LuserArrays, J. Opt. Sot. Am. B 10, 1121 (1993). 6. H. ADACHIHARA, O. HESS, R. INDIK and J. V. MOLONEY, Semiconductor-Laser Array Dynamics-Numerical Simulations on Multistripe Index-Guided Lasers, J. Opt. Sot. Am. B 10,496 (1993). 7. S. S, WANG and H. G. WINFUL,Dynamics of Phase-Locked Semiconductor-Laser Arrays, Appl. Phys.Lett. 52, 1774(1988). 8, R.-D, LI and T. ERNEUX,Preferential Instability in Arrays of Coupled Lasers Phys. Rev. A 46, 4252 (1992). 9. J. MERCIER and M. McCALL, Stability and Dynamics of an Injection-Locked Semiconductor Laser Array, Optics Communications 138,200 (1997).

47 10. T. FISHMAN and A. HARDY, Injection Locktng Analysis of Vertical-Cavity Lase~ Arrays, J. Opt. Sot. Am. B 16,38 (1999). 11. L. GOLDBERG, H. F. TAYLOR, J. F. WELLER, and D. R. SCIFRES, Injection Locking of Coupled-Strip Diode Laser Arrays, Applied Physics Letters 46,236 (1985). 12. B. BEIE~ J.-P. MEYN, R. KNAPPE, K.-J. BOLLE~ G, HUBER, and R. WALLENSTEIN, A 180 inW I?d:LaSc3(BOJd Single-Frequency TWOO Microchip Laser Pumped by an Injection- Locked Diode-Laser Array, Appl.Phys.B58,381 (1994). 13. J. R. LEGE~ G.J. SWANSON, and W.B. VELDKAMP, Coherent Beam Addition of GuAIAs Lasers by Binary Phase Gratings, Appl. Phys. Lett. 48, 1240 (1986). 14. J. R. LEGE~ M.L. SCOTT, and W.B. VELDKAMP, Coherent Addition of AIGaAs Lasers Using Microlenses and Di&active Coupling, Phys. Lctt 52,1771 (1988). 15. A. KHIBNIK, Y. BRAIMAN, V. PROTOPOPESCU, T. A. B. KENNEDY, and K, WIESENFELD, Amplitude Dropout in Coupled Lasers, submittedto Phys. Rev.A (May,2000). 16. M. K. CHUN,L. GOLDBERG,and J. F. WELLER, Injection-Beam Parameter Optimization of an Injection-Locked Diode-Laser Array, Opt. Lctt. 14,272 (1989). 17. L. FABINY, P. COLET, R. ROY, and D. LENSTRA, Coherence and Phase Dynamics of Spatially Coupled Solid State Lasers, Phys. Rev. A 47,4287 (1993), 18. R. ROY and K. S. THORNBURG, Experimental Synchronization of Chaotic Lasers, Phys. Rev. Lett. 72,2009 (1994).

48 Experimental Tests of Radiative Tr~sfer Incorporating Statistical Optics Using Blackbody Sources

Yu Sun, Roland Winston, and Joseph J. O’Gallagher Entico Fermi Institute, Universityof Ohicago,Ohicago, .lllinoise 60697 Keith A. Snail Naud Resewch Lahorato~,.#5550verlookAvenue, SW, Washington,DC20375-5320

Abstract In thii symposium we present twu experiments us”mgblackbody sources that show departures horn radiative transfer theory based on geometrical optics but are in accord with the predictions of statistical optics with the inclusion of measurement. In the first experiment, an infkared camera is used to scan an edge illuminated by a blsrkbody source. DHiaction effects resulting in negative values and osd]ations are predicted using Walther’s second definition of generalized radiance. With the inclusion of measurement a prediction that is independent of the choice of definition used, does not go negative, and has no oscillations is found to agree well with experiment. In the second exp=iment, an infkred camera is used to scan distant square blackbody sources. The experimental conditions are such that we have partial coherence at the entrance plane of the camera. Important parameters are identified showing when large departures fkom geometrical optics will take place. It will be seen that under these conditions, the radiance level is significantly 10VKX than predicted by geometrical optics.

1 Introduction

Radiative transfer is an important subject with applications in astronomy and astrophysics, particle beam physics, medical physics, and macldne vision. Yet it is still grounded in geometrical optics. Central to the subject is the quantity radiance and the equation of transfer. The equation of transfer ie an analogue of the Boltzmann equation in statistical mechanics with radiance serving as the distribution. The distribution however is a power distribution in phase space rather than a probability distribution. As a distribution radiance can be used to calculate the energy density, the energy flux density, and the radiation pressure as a function of position. Attempts have been made in constructing the foundation of radiative transfer by defining a generalized radiance based on the two-point correlation function of the wavefieId.Major contributions along this line of research have been made by A. Walther [1][2]and Wolf and Meschool (see [3]for further references). The equation of transfer, Boltzmann equation for light, would then result from IIelmholtz equation and the definition for generalized radiance. This program, however, is mired in questions about the choices of definitiona. In a soon to be published paper, we propose a fommlism of radiative transfer including statietkal optics that is independent of the phase space representation used. We use the W@mr representation in this paper for the reason that we want a representation for which transformations of distributions based upon geometrical optics in phase-space (classical Harniltonian mechanics) would serve as a good approximation. The most important ingredient of the theory is measurement. The output signal of an instrument is posited to be described by the expression [4]: d%l&kL W(rl, kL; @,z)M(rL,kJ . (1) Q = J (27r)2

49 .. .

Here, W(rL, kl; w, z) is the diatibution in ray plxw+space of the wavefieldat the entrance plane of the instrument, and M(rl, kl) is the distribution for the instrument. The conducted experiments presented in this paper test how well this expression agrees with the actual registered signal.

2 Theoretical expression

The scans, done by internal mechanisms of the camerss, are angle scans. The signal curve is then posited to be given by d%l~kl Q(4) = / (2T), W(r~,kl;w, z)M(r~, k4; d) , (2) where # ia the angle position of the instrument. In arriving at the theoretical expression for the signal curve, we fist need an expression for the distribution ofthe waveiieldat the entrance plane ofthe camera. The detailed calculation of the blackbody Wlgner function at the souce plane for both an edge and a square source can be done analytically using Kirchhoff’sapproximation and the sine correlation for a blackbody. The result for an edge is:

* F(2~041 - EWYw(l + b))]: m 20 W(rl, kl; w,O) = – b))+ (3) { O:x

W(rL, kl; w,.z) = W(rL – *z, kl; w,O) . (7)

For the instrument, we use a simple model: a detector placed at the focal point of a lens. The relevent dimensions are given in the figure (l). The Wigner distribution for th~ instrument in %d phase space is derived in [4] and is given by

1(27,k) = :Si (8) [~(1+:)(1-1:1)]+$si[y(l- :)(1-1:1)]. In this expression, Ooko fi. — (9) 2’ and N is, ~ = d60ko d(?o d = 2a. (lo) F=—; A

50 Figure 1: Model for camera. The focal length of the lens is i, and the pixel size is 2h 00 = 2b/~

Of great importance is the value of N, which is an estimate of the number of phsse-space cells occupied by the instrument (in >d phasespacea cellhas an area of 2n), or as a rough estimate of the number of spatial modes the instrument accepts. From equation (10), we see that if the detector of the camera lies with its edges at the first zeroa of the Airy dfiaction patiern then N = 2.44. For large IV, JV >>1, 1(z, k) goes over into the clsssical expression for the instrument. To see this, use the large z limit of Si(S),

(11)

We then have for N >>1 1(s, k) = 1=(3, k) , (12) where

(13)

is the classical window function. It selects the phase space cells over which one wants to take the average of a quantity. We will use the expression, ~(XL, kl) = ~($, kz)~(y, ky) , (14) as the 4d phase space Wigner dktribution of the instrument. Physically, we are modelling our instrument as having a square aperature instead of a circular aperature. To arrive at the signal curve we need M(rl, kl; +). We will model the angle scan as displacements of the instrument distribution in the direction transverse ta the optic axis.

M(rl, kl; q!J)= M(m - z rj,~,kL) (15)

In performing the integration, the rapid oscillations of the blackbody distribution can be integrated out under the right circumstances by the much slower oscillations of the instrument distribution. This occurs when 2koa y>>l, (16)

and (17) Under the conditions of our experiments, N R 1 and A << a, zfJ. Therefore, when performing the integration, we can basically approximate the blackbody Wlgner function as a classical distribution. For the edge, the distribution at the source plane is W(rl,kL; w,O)= B.(T) Q(z) (18)

For a square source of dimksions D X D, the distribution at the source plane is

W(rl,kl; u, O)= B.(T) [@(z+ D/2) – @(z– D/2)] [@(g+ ~/2) – @(g– ~/2)] (19)

In this sense, how non-classical a dktibution is depends on the other distribution which it is integrating against. By making this approximation, we reduce the 4d phaw+space integration, equation (2), to >d phase-space integrations. For the case of scanning an edge we have the expression:

(20)

For the case of scanning a distant square blackbody source with dimensions D X D, we have the exprwion:

Q(d) = EN’)QI/ AI(z - z4,~)WZ+~/2 –L)~. – @(z - ~/2 - :z) , (21) / [ 1 where Qv = / %~(Y,k) WY+ D/2- +2) –@(v -D/2– :2) . (22) [ 1 In the conducted experiments, we aim to see departures of the measured sigxd from the prsdktions of geometrical optics but are in agreement with our formalism. The differences in the two predictions can be traced to the fact that 1(z, k) occupies a larger region in phase space than L(z, k). This is a consequence of accepting k values larger than the restriction placed by geometrical optics. Thbi characteristic becomes more pronounce aa N becomes smaller. In the edge scan experiment, N <<1. For the scans of distant sources, N s 1 and N s 2. Most instruments have N ~ 1. Using N <<1 may not be the recommended thing to do in practice, but our intentions are to verify the theory.

3 Edge scan Dtierent aluminum aperture plates were placed in front of the camera lens to control the value of N. The camera performs an angle scan. The output signal of the camera ia sent to a computer which performs a ten frame averaging. In comparing experiment with theory, the following steps were taken to circumvent the problem of obtaining absolute power levels. The plateau for the theory curve as well as the curve for geometrical optics was raised to coincide with the plateau of the data. The background level was taken aa the zero Ievd. The theoretical curve plotted againat the experimental data points is shown in figure (2) for a particular case. It shouId be noted that the use of the classical blackbody distribution, i.e. no negative values or oscillations, in equations (18) and (20) is a result of using the W@m basis. If one had used the Kirkwood basis the real part of the blackbody dtiribution for small k values would be [6], neglecting the J%(2!’) i%ctor, W(x~,k~;w, z) = [C(u) + S(u) + 1]/2 (23) with u given by k~ U.J%(X– ~ z) . (24)

52 ApertureZa=4mmdia; 0.2mradifov;DlslancebefweencameraandeourcaD=30m L?cq I I 4 I I 1

250- . .- ......

0-xexperiment 2 .+:geomelrlcaf eptlqspredldfon $ g I(XI -,...... -:iwei ““””+’””’’”””””’”””- %

......

scamangle(mrad)

Figure 2: Edge scan. Open circles are data points. The dotted curve is the geometrical optics prediction, and the solid curve is the theoretical prediction.

C(u) and S(u) are I%xnel integrals. This expremion is also valid up to the Ihmel dMraction regime. The plot is shown in figure [3). Because of the ~--factor, this distribution does not correspond to a shearing in phase space upon propagation. nom the figure one sees that oscillations and negative values are prominent. The distribution becomes less classical as z increases [7]. If we had chosen to calculate Q using the Klrkwood basis for huge z values we would not have been able to use the classical distribution for the wavefield in the integration. However, since our formalism is representation independent, the result would have been the same as using the W@er representation, although we would have to use the Khkwood representation for 1. The role of 1 in the Kirkwood representation is thus to smooth out the oscillations and to give positive and real values for the predicted power.

4 Partial coherence for distant sources

In this experiment, an infrared camera is used to scan square blackbody sources whose dimineione and distances from the camera are chosen for the appearance of partizd coherence instead of having simple plane wave Mfrtilon at the entrance of the camera. The condition to be satisfied is for the transverse coherence length of the radiation field, 1., to be smaller than the diameter of the camera lens, d,

(25)

where OSis the angle subtended by the source at the entrance of the camera. From above, a useful parameter characterizing the source is N*=~~l. (26)

Assuming that at the entrance plane of the camera, the camera aperture is completely filled by the wavefield. N8 then provides an estimate of the number of cells in phase space, the number of spatial modes of the wavefield, reaching the camera. Using the definition for N, equation (10), we can express

53 u

F@re 3 Plot of (C(u) +S(u)-tl)/2. C(u) and S(u) are Fhsnel cos and sin integrals. u = J-(I1~ z– & z)

Iva as N.=+ (27)

The source size, D, is related to Oaby 0,=? (28) z A convenient scale to measure the source ske is the “footprint” , sometimes known as the beam size of the instrument. The footprint is deked as

FP=d-i-zOo . (29)

In using the footprint, we are in a sense propagating the instrument function in the negative z-direction instead of propagating the correlation in the positive z-direction. Let

(30)

We use F and Ns as the parameters replacing z and D. They are related by

(31)

FN.A D= . (32) 00 %–F () The three parameters, N, N., and F, allow us to scale the problem. The scaliig is a particular type of canonical transformation. N and NS are invariant under a canonical transformation where the z dimension is stretched (shriiked) and the k dimension is shrinked (stretched). F and No then set the D and z values.

54 Knowing that 1(z, k) accepts k values larger than the restriction placed by geometrical optics, the cross section of the beam at large distances will be larger than FP. The experiment consist of looking for the drop in radiance level as z is increased, or lV8is decreased, fir fbced F and N. This of course requires us to vary D when N8 is varied. The prediction of geometrical optics is that the radkmce level should be the same for J’ ~ 1. For large distances, the power level stops decreasing with increasing distance. From equation (31), this corresponds to Na = FN. The experiments were conducted us-kg the following camera characteriaticw the aperature diameter after being stopped down is 3/8 in. The field of view per pixel ia 1.5mrad. A= 9.3pm and AA = +0.75~m. As our model of the instrument assumes a square camera aperature, we have to decide whether to use an inscribed square or a circumscribed square of a circle for the cmnera aperature in our model. After some trial and error, the theoretical curves for the inscribed square aperature agree better with experiment. For our camera characteristics N = 1.54 for the circumscribed square and N = 1.09 for the inscribed square. The source size ia controlled by placiig aluminum masks of thickness 1/16” and with square aperature of dlmensione D X D over the aperature of the blackbody sources set at 2’ = 600°C for F = 1 and T = 100°6’ for F ~ 2. The maximum power level reaching the detector as predicted using geometricrd optics is unchanged as z is changed, while the two theories agree at short distances. The power level reaching the detector as a fraction of the meximum power level predicted using geometrical optics can be measured by tit measuring the maximum power for a close distance, z R lm, and using it as the maximum level for geometrical optics at all distances. We will call the close distance measurement our calibration measurement.

N=I.09; 1.5mradhv; )4s-231; F-l .25;vfavelengih.9.3microns

1-..,...... -.:-i:...... i...... :.: ::: .::: i O,a ...... ’ ...... ”...... : :... ~ 0,6 ...... z T=

$ 0.4 - -...... - .. . .

‘a ~ 0,2 - ...... j

o(J-() “ u ‘u ,0. < I

t t t -0,2 , t -15 -lo -5 5 10 15 SCSIIaflje (mrsd)

Figure 4 Radkmce Drop. Open circles are data points. The dashed curve is the geometrkzd optics prediction, and the solid curve is the theoretical prediction.

The contribution of the background to the power reaching the detector is not negligible. In comparing experiment with theory, the power reaching the detector is measured from that due to the background, i.e. treating it ss the zero level. This is also done for the dlbration mesmrement. The difference between the maximum measured value and the background in the calibration measurement is taken as the maximum level for geometrical optics. The ratio between the meesured value minus the background level and the maximum level for geometrical optics is compared with theory. This protocol in processing the data for comparison with theory allows us to sidestep the problem of obtaining absolute power and , . . .. —. —.. . ,.

temperature values. In taking these steps, we have essentially gotten rid of the B.(T) factor in front of equation (21). A plot of theory versus experiment is shown in figure (4), The global behavior for the height of the radiance level when iV = 1.43 is shown in figure (5).

N=l.~wavelenglh=10mluons I ......

0.8 - ......

g w z

~sourw$ze-lxfp ;

......

2 3 4 5 6 7 a 9 10 11 12 Ns (numberofphssespacx?ceffsat thecsnseraapetture)

Fi~e 5: Global behavior. Plot of the theoretical predicted height as a fraction of the geometrical optics predicted height as a function of N. for different F vahw.

5 Acknowledgements

We have greatly benei3ted from discussions with Robert Littlejohn. This work was supported in part by the U.S. Department of Energy, Engineering Research Program of the Officeof Basic Energy Science.

References

[1] A. WaJther, “Radiometry and coherence: J. Opt. Sot. Am. 58,1256-1259 (1968). [2]A. Walther, “Radiometry and coherence: J. Opt. Sot. Am. 63,1622-1623 (1973). [3]Mandel and Wolf, Optical Coherence and Quantum Optics, Cambridge University Press (1995),

[4]R.G. Littlejohn and R. Whton, “Generalked radance and measurement: J. Opt. Sot. Am. A. Vol. 12, No. 12(1995) 2736-2743.

[5] R.G. Littlejohn, “The Semiclassical Evolution of Wave Packets: Physics Reports, June (1986).

[6] R. Wmton and X. Nxng, “Generalized ra.dance of uniform Lambertian sources: J. Opt. Sot. Am. A. Vol. 5, April(1988) 516-619.

[7] R.G. Littlejohn and R Winston, “Corrections to classical radiometry: J. Opt. Sot. Am. A. 10, 20242037 (1993).

56 LUBRICATEDTRANSPORT

D.D. Joseph Aerospace Engineering and Mechanics University of MinnesoPa Minneapolis, MN 55454

Lubricated transport of viscous liquids and solids are discussed. Distinctions are made between lubrication of core annular flows in which water is continuously added and emulsions in which water is present. Further distinctions are between oil in water emulsions, in which lubrication occurs because oil particles migrate away from the wall, and water in oil emulsions that self-lubricate due to the breaking of the emulsion near the wall at high shear stress.

SOME FLOW TYPES

Stratifiedflow

Perfect core annular flow

Wavy core flow

Slugs (low speed)

Concentratedemulsionsof (say30%)oil in water. Dispersionof solidsin water

Stable (say 30VO)emulsions of small water droplets in oil

Figure 1. Some Flow Types -. .—— P~

Figure 2. Ideal Core-annular Flow Oil moves as a rigid body impelled forward by the pressure AP = PI - P2 and resisted by the shear stress in the water. Choose a/b to maximize the total volume flux of oil and water (o/w) for a given AP. This problem has a solution a # O. You can transport very viscous oil in water more cheaply than water alone. You get drag reductions of the order

1 ~oil i Vwatcr = 10001:0 = 105

A 0.1

0.01

●

0.001 102 103 104 105 106 91

Figure 3. Luminur and Turbulent Core-annular Flow

Smooth Wave +High Pressure

-K,owPressure Steep Wave

Figure 4. Steep Waves Arise from Smooth Waves

58 . .. . .—— —.. ------—— G ~ = 0.78

0 1 2 —-- —-—-— H ~ = 0.82 r—“. - -e~.,,... .. -—------...... 7 0 1 2 3 4 5

I ~ = 0.85 1.21’ I 0.76 0.78 0.8 0.82 0.84 0.86 0.88 o 1 2 3 45 2.510

Figure 5, Wave Shortening and Sharkskin Numerical calculation of BKJ (1996). Wavelength L = 13.5 -14.1 q for (IR, h) = (600, 1.4). The wavelength and amplitude tend together to zero as ?I+ 1 (see JBCR 1997).

Figure 6. Self-Lubrication At a critical value of the velocity, the emulsion breaks away from the wall and self-lubricates. The formation of lubrication layers in olw emulsions requires that the emulsion breaks and forms a lubricating layer at the wall. This is self-lubrication because water is not added. There are no papers other than the two here on this subject.

Self-Lubrication of Bitumen Froth The fouled wall is an excellent wall preparation

Figure 7. Mechanism of Self-Lubrication “Powdering the Dough” After the froth breaks it remains lubricated. 100 L 1 1 I I 1 I 1 1 1 f 1 1 t 1 1 1 1 i 1 I 1 I 1 1 1 I 1 1 1 1 1 L

3.5-38 c A 41-45 c m 45-47 c + 49-52 C x .54-.5s c — o l:,)?cc~?ltw![(%! % — Blasius m In Q 35-47fif 49-58fu

0.01 1 10 100 1000 104 U1”7SIR~1”2s

Figure 8. Blasius Correlation for Self-Lubricated Bitumen Froth

SELF-LUBRICAT/OkV of an EMULSION of WATER in MIDWA Y SUNSET CRUDE The only other experiment on self-lubrication of oil in water emulsions were done in a l/2-inch pipeline by Veet Kruka at SHELL HOUSTON. His results are for Midway Sunset Crude oil and are described in his patent. In this case there are no clay particles, nothing special. Self lubrication of w-o emulsions is of interest to other oil companies but there is no data other than Kruka’s patent and our bitumen froth. We would like to know effects of crude oil type, water fraction, pipe size, etc.

60 10 I i 1 I I 1 1 1 1 I i I 1 I 1 I E I I

I o Data from Kruka Fitted curve ● Predicted value (5 m/s) \ ~ Svncrude data -:

J a) o L%%

10 100 1000 Viscosity (poise)

Figure 9. Critical speed vs. viscosi~ Kruka’s three data points fall on a strdight line (see figure 9). The critical speeds for self lubrication are smaller when the viscosity is larger. Our Syncrude data does not lie on the line but it is for a l-inch rather than l/2-inch pipeline. We don’t know of any other published data.

LUBRICATION OF CONCENTRATED EMULSIONS

~If Shear thins ~ = KY

Figure 10. Concentrated Emulsion say 70% oil(lejl). Viscosity reduction (right). 70% oil is unstable against inversion; stabilized with surfactants The viscosity reduction is a form of lubrication. Three Commercial Lines Have Used o/w Emulsions to Transport Oil: 1. Indonesia (Shell) carries 40,000 barrels/day of 70% waxy crude in 20’’x238 km pipeline. 2, California (Shell) carries 50% heavy crude in 8“x13 mile pipeline.

——- - ~.?~\-,.:,,,.:,f.&~,,!,:~.,:,..q,:t,-,,-,.>.,,..,.,,,,;.,?,,.,:,;:. ->,.’.%‘.~;:;;&-..:,.‘-.;,,.,,,,-*,;z,.-,..,-,.>,.,’+,..,.,. ‘-. ...”..-, . .-.:.:!,. , 3. Venezuela (Bitor) carries 70-80% heavy crude in 36’’x3OOkm pipeline.

Other oil companies are working with us to evaluate this transportation option, The MAIN QUESTION is if, when and how o/w emulsions can be made to enter into core annular flow, giving an additional benefit. “Self-lubrication” of o/w emulsions involve migration of oil away and water toward the pipe wall. Self-lubrication of w/o emulsions involve breaking the emulsion at the wall; it is altogether different. Because the o/w emulsions shear thin, it is not easy to tell if they self-lubricate.

, Comparison of Rheometer and Pipeline Data We can use the rheometer studies giving K and n to predict pipeline data for a shear thinning fluid. Dodge-Metzner correlations:

~@@p DAPg R= f. gK8(@) 2L~V2

Reynolds number Friction factor

DAPg Laminar flow f= 2L~V2

14 0.4 Turbulent flow — = -In Rf (1‘: -— .2 I 0 n [1 n

Rheometer Studies

—— . 1000 E 1 Shearstressvs.shearrate - 1s[freshoilblend( 7030 watercxtmsril) - 100 ———..

—. - ——. - 10 /“

z = 4.4087y0’5bb2 1 -._..— — . 0,1 0.001k~y”0.1 10 1000 100000- Shear rate (s ‘1)

Figure 11. Shear stress vs shear rate.

62 Rheometer studies are used to get K and n for z= Ky “ The sample may lubricate in the rheometer. If the sample lubricates you will get a different K and n when you change the distance between the plates.

Shear stress vs. shear rate -1stoilblendajler1 week( 70:30waterexternal) -

’000 ~-”~

$ *1 w

0.1 0.0001 0.01 100 10000 Shear ;ate (s ‘1)

Figure 12. Shear stress vs shear rate.

100 —..———-...... ——. ———. r I ■ [__ ’% + Istoilblcncl- fmh F■ 1stoil blcntl -1 week later o 2nd oil Mu-xl- fresh - x 2ndoiIblend-4 days later — Dodge-MetznerCo~elation for kaminarflow ! $ , , 0.1 0.1 100 Generalized Reynolds n;”mber

Figure 13. Friction Factor vs. Reynolds Number The data points are below the theory line suggesting lubrication Lubrication of Solids in Liquids Lubrication occurs when particles migrate away from walls. We study this by direct numerical simulation, see www.uem. urnn,edldSoli~l_Liquid_Flows

Figure 14. Migration of Neutrally Buoycwt Particles in Pressure Driven Flow by DNS (Huang & Joseph JNNFA4 1999). You can isolate and study effects by switching physics on and off in the simulations that you could not do in experiments. (a) Newtonian, (b) Generalized Newtonian with shear thinning index n=0,5, (c) viscoelastic, (d) viscoelastic with shear thinning.

64 INTBRFACIAL WAVE TRANSITIONS IN LIQUID-LIQUID FLOWS AND INSIGHT INTO FLOW REGIME TRANSITION

M. J. McCready, B. D. Woods, M. R. King Department_ofChemical Engineering - University of Notre Dame Notre Dame, Indiana 46556 USA

ABSTRACT Measurements of developing interracial waves on oil-water channel flows show that long wave modes form and grow to large amplitude even though they have much smaller linear grow rates than shorter waves. There is evidence for a “triggering” of these long waves by interaction with much shorter waves, although most of the energy for wave growth comes from the mean flow. Thus linear instability of these long waves is a necessay condition for their formation and consequently, for flow regime transitions from a stratified state. However, experiments in a rotating Couette flow show regimes of no wave growth, even when long waves are unstable. The apparent reason for this is given by numerical integration of the equations that describe weakly- nonlinear wave modes at the interface. The simulations show a cascade of energy from long to shortwaves and no preferred wavenumber in the spectrum.

INTRODUCTION Multifluid flows exist in oil wells, oil production and transportation pipelines, heat exchangers, gas-liquid reactors with solid catalyst and various other process piping and vessels. An important emerging issue for multifluid flow research will be how to best solve the contacting/mass and heat transfer problems that will greatly increase, as anew generation of “molecularly-engineered” catalysts developed with much higher dispersion of active metal and more elaborate possibilities of interconnection of pores on different scales. However, given the current uncertainty that exists in the simplest case, gas-liquid flow in pipe, these new problems may be difficult to solve.

Even in light of the need to understand multifluid flow on small scales, their defining characteristic, in channels, pipes and even packed beds is the strength of the largest scale disturbances present. For gas-liquid pipe flows, where 6 different flow regimes are possible, slug flow [1] is the regime with large coherent disturbances cause large pressure fluctuations [2] and variations in the gas and liquid flow rates that can affect process equipment. For gas - liquid packed bed flows, the corresponding region is the pulsing flow regime[3], for which the large disturbances have been shown to have the beneficial effect of increased mass transfer rates that can favorably affect the reaction outcome[4].

The existing problem in the prediction of large disturbances leading to slug formation is there are multiple mechanisms that are at work [5] and slugs can form directly from growth of waves on flat layers or by coalescence of several large rollwaves. The standard techniques for the prediction of slugs are various linear stability theories, based on different assumptions and some work that addresses the stability of a slug once it forms. Figure 1 shows several such models, It is readily seen that significant disagreement exists between the different procedures for slug prediction -- even those that are based on the same premise of unstable long waves. If these models are plotted for a model oil-gas flow at 100 ATM in a larger pipe, even bigger disagreement exists. From these results it can be concluded that considerable uncertainty exists in the prediction of slug flow for engineering purposes...... “, .

Slug transition models - Kelvin-Helmholtz ■ m==aWa[lis & Dobson (1973) —Taitel&Dukler(1976) -.-”-’ Lin&Hanratty(1986) ...... Barnea (1991 ) -1 .-. differential Crowley’ et.fd’(1993) I I + Bendiksen & Espedal (1992)

i I 1 1 1 111] 1 1 1 I Ill I 1 1 1 I I ill i I < 1 1 1

0.1

0.01 jj # 0,001 a) 3Q ~1 “’0.0001 P~=l CP /L~O18 C/3 , j,,,,,, II I I I 1 t 0.01 U.1 1 10 superficial gas velocity, tis

Figure 1. Different slug transition models for air-water in a 2.54 cm, horizontal pipe.

------Barnea (1991) -. channel=20 cm - Kelvin-Helmholtz ...... Taitel-Dulker (1976) liquid 9= ■ =~======sss=Wallis & Dobson (1973) p~=.9glcm 3 /)~232 g/cm 3 ------Crowley et al. (1992) /4=50 Cp /.@=.0371Cp ,_,--- “--- Lin & Hanratty (1986) *.- ,wn,.#.,— Differential, Iaminar ~Bendiksen&Espedal(1992) E l“’” 1 I I I 1( II 1 1 1 I I 111 r 1 1 1 1 I Ill I I I I ~ .- 0 0 1 – ...... ‘3 > -., -...” _- ”--- .--0 -%%.i~--- 5 0.1 – .,.-..”:—*— ‘- :,:-: .-U’ 7 ? 0.01 - ~ 000, ~n. 1 1 I 111II 1 ! I I I IIll 1 1 1 I 0.01 0.1 1 10 superficial gas velocity, mls

Figure 2. Different slug transition models for oil-gas in a 20 cm horizontal pipe at 20 ATM.

66 The specific problems addressed in this paper are the mechanisms of wave development on a two-layer stratified flow. Experiments are presented which show that the presence of a long wave instability does not mean that large disturbances will form -- casting doubt on the use of linear stability as a predictive tool for the transition from stratified to slug flow, The development of waves in an oil water channel flow is examined, as a fi.mctionof distance, showing the development of a long wave peak after the more unstable shortwaves appear. Numerical simulation of the weakly-nonlinear mode equations is used to provide an explanation of the observed experimental behavior.

EXPERIMENTAL SYSTEMS

Figure 3 shows a schematic of the oil-water channel that is used for the experiments. Data are obtained from visual and video observations and from conductance probes. The fluids are water, with Sodium Silicate added to improve its ability to wet the Plexiglas@channel and a light hydrocarbon oil with a density of 0.88 g/cm3 and a viscosity of 17.8 cP. More details about the flow system and its construction are included in a thesis by McKee[6].

Figure 4 shows the optical system that is used to obtain data in the oil-water channel flow. The behavior of the interracial waves is obtained by measuring the time varying wave slope with an optical refraction technique. A laser beam is split into 2 vertical beams a distance db apart and focused onto the interface. The beams are refracted at the interface according to Snell’s law due to the instantaneous wave slope. The refracted beams are focused onto position sensing detectors, which provide the displacement of the refracted beam in x,y coordinates from its initial vertical position. From the geometry of the optics and the location of the refracted beam, a time series of the interracial wave slope is created for each of the two beams. The signals from the two beams can be used to measure the wave velocities.

Experiments were also done using two matched-density liquids in a rotating Couette device, Details have been published previously [7,8].

I 2.44 m I I .5-1cm 1

I t , I FIGURE 3. OIL-WATER CHANNEL FOR STUDYING INTERFACIAL WAVES H = lcm ~ W=16cm Length=240 cm / \ .. .i 10 mW HCNCImcr ~—’ElEl\ Pwaffinic Mineral (Xl p=lxcp p =855~cm3 PlmmconvexLens c 3 c 3

1= = “-”-.\., --- .=...... - — ~ .- ....-.-’ - —.. . . . - NcuIml DensityFilter L-.’‘--- - ‘- ~

f- Water 100 mm BiconvcxLens c 3 c 3

PositionSCnsirtgDetector m m & FIGURE 4. SCHEMATIC OF LASER-SLOPE DATA ACQUISITION SYSTEM FOR CHANNEL FLOW

THEORY

Theoretical analysis for this system is based on the complete two-layer Navier-Stokes equations and boundary conditions. The linear stability problem has been soIved by Yih[9]and Blennerhassett [10] among others, The weakly nonlinear problem has been formulated with a multiple scales technique by Blennerhassett [10] and an eigenfunction, center manifold approach by[11] and [12]. Instead of confining our analysis to the Stuart Landau equation [12]

[1] where A is the complex wave amplitude, L(X) is the linear eigenvalue, ~ is the Landau coefficient, we do not use a center manifold approach to simply the equations. The result is then a system of many mode equations of the form

Anl = Lnl&l + ~@nl,Pr,qsAPrAqs + p q m,r,~,;lZ&Zl pi-,qs,mzAprAqsAmz [2] P,97,S *Y where the nonlinear interaction coefficients, for the quadratic terms, v and the cubic terms, & are functions of liquid depth and wavelength and weaker functions of the degree of shear and the shape of the velocity profile. These equations are solved by numerical integration. Further details on the derivation of these equations and their solution are given in a paper from our group[13].

68 RESULTS

Figure 5 shows our previous data [7] that indicate regions of the rotation rate- depth ratio space where Iong waves are linearly unstable and no waves appear. Thus according to the premise of most sIug formation theories, large disturbances are expected in this region. Even though this experiment is not channel flow, it calls into question the idea of using instability of long waves m-a general criteria for flow regime transition.

stable x 50 longwaves x steady2-Dwaves occur in most of uthis range

B Nowaves A steady periodic 10 X unsteady waves X solitary n — long wave stability boundary o! I 1 i I 0.0 0.2 0.4 0.6 0.8 h

Figure 5. Wave regime map of a rotating Couette flow (left), Simulated spectrum for conditions of h= 0.4, U = 25 Cm/S.

A movie of the simulations at h = 0.4 and U = 25 ctis is available at http://www.nd,edu/-mjm/ specsim.mov. It shows that as the waves grow, there is a cascade of energy from long to shortwaves, that acts to stabilize the formation of long waves. Further the apparent absence of any waves can be possibly be attributed to the lack of preferred wavelength. Figure 6 shows these spectra at different times during the simulation. At the shortest time, the spectrum matches the linear growth curve. At all longer times there is a continual broadening of the spectrum. However, there is never a clearly-defined wavelength that could be visible in experiments. All of the apparent peaks oscillate in magnitude.

Figure 7 shows wave spectra for a developing oil-water channel flow. It is seen that at the first two positions, the spectra match the predictions of linear growth. However at 60 cm, the spectrum shows a number of distinct peaks that are involved in nonlinear interactions. This is confirmed by the bicoherence spectrum of figure 8. Bicoherence spectra [14] show the strength of quadratic -2 10

10-3

104 l--

10-5

10-6 1 I 1 1 I I [ 1 I ! 1 1 2 345 6789 2 34 1 10 wavenumber

Figure 6. Amplitude spectra for Couette flow. At longer times there is no preferred wavenumber.

Figure 7 shows the spectra of a developing oil-water channel flow for Rew=900 and Reoil=5.5. The linear growth curve is also shown.

70 ...... 1 I 8 b 15 -

10 -

uA f2

Figure 8. Bicoherence spectrum for oil-water flow of figure 7 at 60 cm. Significant coherence exists between short-short (5,10 Hz) and long short (18,1 Hz). interactions of the form f 1 + f2 = f3. Perfectly coherent modes will have a value of unity. Figure 8 shows that there are interactions between some distinct peaks around 10 Hz and their overtones (fl = f2) (that are not shown on the power spectra of figure 7) and also with their corresponding subharmonic around 5 Hz. For this subharmonic, fl= f2= 5 Hz. A very strong interaction is seen between a wave mode of about 18 Hz and 1.5 Hz. This is probably a difference interaction, f l-f2 = f3, so that the other mode involved is probably about 16.5 Hz, This long-short interaction may be responsible for triggering the formation of a low frequency mode, 1.5 Hz, that is seen to growth substantially between 60 and 80 cm and which completely changes the character of the spectrum.

DISCUSSION The experiments and simulation presented above provide insight into several different issues. First, figures 1 and 2 show that current predictive methods for the transition to slug flow differ greatly and probably none can be trusted to give reliable results. Second, the presence of no waves in regions where long waves are unstable, calls into question any methods for which long wave stability is the sole criterion for transition. It does appear, however, that long wave stability is a necessaty condition for instability. The spectral simulations for the Couette flow suggest that a reason for the absence of visible waves is the lack of a persistent dominant wavenumber. This statement has not been confined and it is still possible that imperfections on the experiment maybe the reason for the lack of observed waves.

The spectra of developing oil-water flows show that linear growth is followed by nonlinear interactions that can cause subharrnonics or trigger low wave modes. These low modes can be precursors of roll waves and slugs. Subharmonic have also been implicated in the transition to slug flow[15]. These results suggest a need for improved procedures for prediction of regime transition that account for the nonlinear processes. They also suggests methods for controlling the transition and perhaps picking the frequency of the large disturbances --by controlling the frequency of shorter waves that trigger these long wave modes.

Finally because the Iarge disturbances that occur in packed-bed flows[3], pulses, are very similar to slugs in pipe flows -- but not as easy to study --it could be profitable to look for analogies between the two different system to better understand the reaction processes that are performed in gas-liquid catalytic reactors.

ACKNOWLEDGMENT This work has been supported by the U. S. Department of Energy, Office of Basic Energy Sciences

REFERENCES

1. P. Y. Lin and T. J. Hanratty, “Prediction of the initiation of slugs with linear stability theory”, Int. J. Mult. Flow. 1279-98 (1986). 2. P. Y, Lin and T. J. Hanratty, “Detection of slug flow from pressure measurements”, M. J. Muh. Flow. 1313-21 (1987). 3. D. A. Krieg, J. A, Helwick, P. O. Dillon and M, J. McCready, “Origin of disturbances in cocurrent gas-liquid packed bed flows”, AIC?ZE J., 41, 1653-1666, (1995). 4. R. Wu, M. J. McCready and A. Varma, “ Effect of Pulsing on Reaction Outcome in a Gas-Liquid Catalytic Packed-Bed Reactor “, Catalysis Today, 48, PP 195-198, (1999). 5. Z. Ruder, P. J. Hanratty and T. J. Hanratty, “Necessary conditions for the existence of stable slugs”, Int. J, Mult. Flow. 15209-226 (1989). 6. William McKee, “An experimental study of interracial waves in cocurrent oil-water flows” -- M.S. Thesis, University of Notre Dame, (1995). 7. M. Sangalli, C. T. GaIlagher, D, T. Leighton, H, -C. Chang and M.J. McCready, “Finite amplitude wave evolution at the interface between two viscous fluids”, Phys. Rev. Let. 75, pp. 77-80, (1995), 8. C. T. Gallagher, M. J. McCready and D. T. Leighton, “Experimental investigation of a two-layer shearing instability in a cylindrical Couette cell”, Phys. Fluids, S, PP. 2385- 2392, (1996). 9. C. S. Yih, “Instability due to viscosity stratification”, J. Fluid A4ech. 27,337-352 (1967). 10. P. J. Blennerhassett, “On the Generation of waves by wind~ h-oc. 1?.Sot. Lend. A 298, 451-494 (1980). 11. M. Renardy and Y. Renardy, “Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows”, Phys. Fluids, A 5, 2738-2762 (1993). 12. M. Sangalli, M. J. McCready and H, -C. Chang, “Stabilization mechanisms of short waves in gas-liquid flow “, Phys. Fluids, 9, PP. 919-939, (1997). 13. M. R. King and M. J. McCready, “Weakly nonlinear simulation of planar stratified flows”, Physics of Fluids, 12, PP. 92-102, (2000). 14. L. A. Jurman, S. E. Deutsch, S. E, and M. J. McCready, “Interracial mode interactions in horizontal gas-liquid flows,” J. Fluid Mech. 238, 187-219 (1992). 15. Z, Fan, F. Lusseyran, F, and T. J. Hanratty, “Initiation of slugs in horizontal gas-liquid flOWS, “AIChE J. 391741-53 (1993).

72 ,.: ‘.7< - ...’. , ‘. ., ,

Simulating Complex Dynamics In In~ermediate And Large-Aspect-Ratio Convection Systems

Ming-Chih Lai Department of Mathematics, Chung Cheng University, Minghahmg, Chiayi 621, Taiwan

Keng-Hwee Chiam and M.C. Cross Department of Physics, California Institute of Technology,Pasadena, CA 91125

Henry Greenside Department of Physics, P. O. Box 90305, DulceUniversity, Durham, NC 27708-0305

Abstract

Buoyancy-induced (Rayleigh-B6nard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of experimental data and the quantitative comparison of theory with experiment, we have developed a three-dimensional finite-differencecode that can integrate the three-dimensional Boussinesq equations (which govern the evolution of the temperature, velocity, and pressure fields associated with a convecting flow) efficientlyin large box-shaped domains with experimentally appropriate lateral boundary conditions. We dkcuss some details of this code and present two applications, one to the occurrence of quasiperiodlc dynamics with as many as 5 incommensurate frequencies in a moderate-aspect-ratio 10 x 5 convection cell, and one to the onset of spiral defect chaos in square cells with aspect ratios varying from I’= 16 to 56.

Introduction

A frontier of great importance for DOErelatecl research is the study of sustained mmequilibrium dynamical systems, for which imposed external fluxes of energy and matter can lead to states that vary temporally and spatially in a complex way [1]. lhspite the collaboration of theorists, computational scientists, and experimentalists over the last thirty years and despite the great need to solve numerous practical engineering problems, many basic questions about sustained nonequilibrium states remain unanswered. Researchers would like to know what possible states can occur for specified external fluxes, how to predict when one state will change into another as some parameter is varied, how transport of energy and matter depends on the spatiotemporal structure of a state, and whether one can select particular states by appropriate external perturbations so as to optimize a system for a particular goal. While experiments and simulations have been useful in suggesting what possibilities cau occur (e.g., the surprising experimental dkcovery of the spiral defect chaos state [2], a numerical example of which is shown below in Fig. 3), there remains a great need to develop a stronger theoretical and conceptual foundation that can unify the many observations and that can improve both experimental and computational investigations. Perhaps the simplest and best idealized experimental system for exploring basic questions and principles of nonequilibrium systems is Rayleigh-B6nard convection, which has become an experimental and theoretical paradigm for many researchers [1]. A Rayleigh-B6nard experiment consists of a thin layer of fluid confined between two horizontal spatially-uniform constant-temperature metal plates such that the bottom plate is maintained at a constant higher temperature than the upper plate. As the temperature difference (or its dimensionless equivalent, the Rayleigh number R) is increased in successive constant steps, the fluid first makes a transition from a motionless structureless state to cellular overturning convection rolls and then to ever more complex dynamical states which eventually become nonperiodic in space and time. Convection has significant advantages over other experimental systems in having static homogeneous boundary conditions, in having no net flow of fluid through the system, in allowing precise and reproducible experiments with

73 good visualization, and in being amenable to a quantitative mathematical description through the so-called Boussinesq equations. In this paper, wc report applications of a new computer crrde to two intriguing convection experiments. The code is the first of several being developcxl and applied by a Caltech-Duke collaboration whose long- term goal is to understand convection phenomena more quantitatively, especially in the large-aspect-ratio limit (cells whose widths are large compared to their depths) which experiments have shown to be of great interest even close to the onset of convection, where analytical progress is most likely to be possible [1], Our code differs from some other recently developed codes [3] primarily through the inclusion of experimentally appropriate lateral boundary conditions (rather than periodic boundary conditions) on the velocity and temperature fields so that the forcing due to lateral boundaries can be taken into account. In the following sections, we give a brief summary of the code followed by a discussion and demonstration of how the code can provide new insights about two poorly understood experimental phenomena, the occurrence of dynamics with many incommensurate frequencies in a moderate-aspect ratio convection cell first observed by Walden et al [4] and the onset of spiral defect chaos in domains of varying size (which has not yet been studied experimentally). These results provide new and detailed examples of the substantial influence of lateral boundaries on nonequilibrium dynamics.

Numerical Integration Of The 3D Boussinesq Equations

Since technical details of our numerical algorithm will be available elsewhere [5], we provide only some motivation for and highlights of our numerical met,hcxl. ‘l’he goal is to integrate the five coupled thrce- dlmensional nonlinear partial differential equations known as the Boussinesq equations which state (under certain assumptions not given here) the local conservation of momentum, energy, and m~s for parcels of fluid subjected t-o buoyancy forces. By scaling time, space, and field magnitudes in appropriate ways, one can write the Boussinesq equations in the following dimensionless form:

&u= -u ● Vu – Vp+ d% + aRT2, (1) 8~T = –u*VT + V2T, (2) V“u=o, (3) where u(t, x) = (Uz(i, x), uU(t, x), Uz(t, x)) is the velocity field at time t and position x = (z, v, z), T(t, X) is the temperature field, p(t, x) is the pressure field, a is the fluid’s Prandtl number which is assumed to be independent of temperature and so a constant, and R is the llayleigh number which is the key parameter that is varied in most experiments and simulations, usually with all other parameters held fixed. In this paper, we study these equations in a simple box geometry of dimensions r:, x 17ux 1; the quantities 17Zand I’v are ratios of lateral widths to the unit fluid depth and arc called aspect ratios. Since the fluid is confined by stationary material walls, the vek~city vanishes at, these walls which provides the following boundary condition on u: U=o on all walls. (4) With our resealed variables, the constant temperature boundary conditions on the bottom and top plates (z= Oandz= 1 respectively) are simply

T(t,:qy, O) = 1 a,nd T(t,z,y,1) = 0, (5)

The temperature field T satisfies an additional boundary condition on the lateral walls which, for this paper, we take to be a no-flux condition corresponding to a perfect thermal insulator

&T=ri” VT=O on lateral walls, (6) where ii is the normal unit vector at a given point on the wall. However, the code is more general and can treat thermal boundary conditions that interpolate between conducting and insulating sidewalls. The numerical challenge is to integrate these equations and boundary conditions efficiently and accurately over long time intervals in large cells of simple geometry; boxes and cylinders cover nearly all the experimental cases while a box with periodic sidewalls is useful for comparing with theory. Rayleigh-B6nard convection

74 ,. . :, ‘..,?: ,’” -,; ,,,4

is so important that many numerical methods have been developed and tried over the years although, somewhat unfortunately, most of these methods have not been compared with each other to determine which best achieves a practical balance of efficiency, accuracy, ease of programming, and parallel scalability on some specific computer architecture. Because our interest is to study fundamental questions in simple cell geometries, we chose not to use finite element or spectral element methods whose main strengths are the ability to handle irregular boundaries. Because our short term needs are for modest accuracy, simplicity and flexibility of coding, and good parallel scaling on Beowulf-style computers, we chose second-order-accurate finite-difference approximations on Cartesian meshes instead of spectral methods. Our code uses a traditional time-splitting method in wh!ch higher-order linear operators are advanced implicitly in time and lower-order nonlinear terms are advanced explicitly [5], achieving at each time step an overall accuracy of second order in time. The incompressibility condition V ● u = O is treated by a standard projection method [6]in which the momentum conservation equations are used to update the current velocity u(t, x) to an intermediate field u* that is not divergence free, and then u* is ‘(projected” onto a divergence-free field u(t+At, x) by solving a Poisson equation for the new pressure field. To advance one time step At, four 3D Helmholtz equations and one 3D Poisson equation must be solved with appropriate boundary conditions, and the solution of these linear equations constitute the most time consuming part of the code. For this first generation code, we used FISHPACK fast direct solvers (available through www.netlib.org) which are well suited for modest-aspect-ratio problems on singleprocessor Alpha workstations. Future codes will use parallel iterative methods whkh are also better suited for the non-constant-coefficient linear operators that arise in a cylindrical geometry. Our code was innovative mainly through the use of colocatedmeshes, in which all field values and all operators of field values were evaluated on the same set of mesh points. For two- and three-dimensional fluid simulations of incompressible flow, empirical studies and some analysis have suggested that staggered meshes (in which scalar quantities are stored at the centms of grid boxes while vector components are stored on the faces or vertices of the boxes) were n(+(x~~si~y to i~void uumerical instabilities associated with the pressure [7]. Our colocated-mesh 130ussinesq code proved to bc?numerically stable which led to a substantial reduction in the effort of writing and validating the code compared to a staggered-mesh code. For lack of space, we refer to our forthcoming paper for further details, e.g., how our code was validated and its efficiency and accuracy as a function of various parameters [5].

Applications

We now report on two preliminary applications of the above convection code. First we try to simulate an intriguing experiment [4] that goes to the heart of how chaotic behavior arises in a continuous medium, here through the occurrence of quasiperiodic states with as many as five incommensurate frequencies. The mystery to understand is the spatial structure of the different oscillations and their dependence on aspect ratio and Rayleigh number. Second, we investigate how the onset of spiral defect chaos state [2] depends on the aspect ratio 17of a square box, which we increase in small successive increments. Varying the aspect ratio is difficult in laboratory experiments and these calculations demonstrate the usefulness of having quantitatively accurate codes to complement experiments.

Multi-l%equency Dynamics at Intermediate Aspect Ratios Our first calculation was motivated by the experimental paper of Walden et al [4], which reported in 1984 the unexpected occurrence of spatiotmnporal quasipcriodic states in a convecting flow with as many as five incommensurate frequencies. This result seemed to contradict one of the major mathematical insights of the time, a theorem of Newhouse, Ruelle, and Take~ls[8]which argued that chaotic behavior should be typically observed after at most three successive Hopf bifurcations since quasiperiodlc dynamics with three or more incommensurate frequencies can be perturbed infinitesimally to become chaotic. Although the abstract mathematical arguments were difficult to interpret for laboratory experiments and despite clarifications of this theorem by later numerical simulations on simple map systems [9], it is still not understood how a physical continuous medium can develop so many independent oscillations or whether a physical mechanism can be identified for each independent frequency. To make contact with this experiment, we have carried out the first (to our knowledge) simulations in a box-liie domain with parameters nearly identical to those of the experiment. Thus we performed numerical integrations of the 3D Boussinesq equations in a cell of aspect ratio 9.5 x 4.5 x 1, for a fluid with Prandtl number a = 3.5 (corresponding to water with a mean temperature of 50°C) and over a comparable range of Rayleigh numbers up to R = 20&, where RC % 1708 is the critical value for the onset of convection in an infinite-aspect-ratio cell. The most poorly justified approximation was our choice of laterally insulating sidewalls Eq. (6) since the real experiment had finitely conducting glass sidewalls between a copper bottom plate and sapphire upper plate. (The thermal diffusivities ~ of copper, glass, sapphire, and water are respectively 1.20, 0.004, 0.113, and 0.00147 cmz/see,) A typical run used a resolution of 76 x 36 x 8 points and a constant time step of At = 0.001. A nm to collect 65,000 points took approximately 1.5 hours on a Compaq XP1OOOvmrlcstation using a 667 MHz 264 Alpha chip with a 4 MB cache. Some representative results are shown in Fig. 1. As the Rayleigh number R is increased in small steps, new incommensurate frequencies appear until, at R/& = 17.5, 5 incommensurate frequencies are observed just as in the experiment. The fact that these frequencies were incommensurate was supported by plotting (not shown) the ratios of frequencies corresponding to different peaks and observing that these ratios varied smoothly with R, i.e., no mode loclcing to a rational value took place. The numerical simulations did not

f3 f40 f2 f,-f2-f fl-f2 f, < I * FVRC=I7

I I \ FURC=17.1 t

I R/R =- 7.5 C

R/Rc=- 8.3 I I

WRC=18.7 1 , , ! 1 I I 1 I 0 5 10 15 20 25 30 35 40 Frequency (units of I/zv)

Figure 1: Power spectra P(f) versus frequency ~ for five values of the Rayleigh number R over the range 17< R,/F& S 18.7 in a cell of aspect ratio 9.5 x 4.5 x 1 and for a fluid of Prandtl number CT= 3.5. The top three panels show quasiperiodic motion with 2, 3, and 5 incommensurate frequencies respectively. The last two panels show spectra of chaotic dynamics with continuous broad-band features. reproduce quantitatively the magnitude of the lower frequencies observed in experiment. For example, for the 4ilequency convection state, the simulation has a low frequency peak at j4 s 0.17 which is about a factor of three smaller than that observed in the experiment. A first guess is that this discrepancy is a consequence of the convenient but experimentally inaccurate no-heat-flux boundary condition Eq. (6). In related simulations, we have also cxplorml how the dynanlics depended on aspect ratio, a question which is difficult to explore expcrixll(?xlt,:~lly.Fig. 2 shows several instantaneous convection patterns and the power spectra of the corresponding tilrl(?-(lepetl{lc[lt states over the range 9.5 s r= ~ 10.5 with I’v and R held fixed. A surprising and new result is that small changes in r lead to dramatically different patterns and dynamics. Indeed, for the states of Fig, 2 and others not shown over this same range, one can identify time independent, periodic, quasiperiodlc (with 3 and 4 frequencies), and chaotic dynamics. The spatiotemporal dynamics is evidently highly sensitive to small changes in the system geometry at these intermediate aspect ratios.

76 ., ?. ,,.

Figure 2: Changes in convection dynamics as the aspect ratio rz is increased in small steps for fixed 17v= 4 and R = 181& The left column of plots are instantaneous density plots of the temperature field at the midplane z = 1/2 with light regions corresponding to warm fluid, dark regions to cool fluid. The right column of plots are corresponding power spectra ~(~) calculated from time series of 65,536 values of the temperature at the midpoint of the cell. Rows 1, 3, and 5 are chaotic, row 2 is periodic, and row 4 is quasiperiodic with three independent frequencies.

Onset of Spiral Chaos As the technology improved for exploring large-aspect-ratio convection dynamics, experimentalkts made a remarkable dkcovery in 1993 [2] of an intricate spatiotemporal chaotic convecting flow in a cylindrical geometry near onset, a regime that previous experiments in smaller aspect, ratios had suggested would show only simple convective patterns, and for which theory predicts that parallel time-independent convection rolls should be stable [10]. This spiral defect chaos state (so named because of the unexpected occurrence of rotating spiral structures) remains poorly understood seven years later and is now regarded by many convection researchers to be an especially important example of spatiotemporal chaos to understand. Intriguing and also poorly understood is the experimental observation that spiraJ defect chaos is observed only when the aspect ratio r of the cylindrical cell is sufficiently large, with the radius being at least 40 times the fluid depth. Using the code described above, we have explored for the onset and properties of spiral defect chaos in finite cells with experimentally realistic lateral boundary conditions and with varying aspect ratio, although for a square rather than cylindrical geometry. Representative results for two different values of the reduced Rayleigh number e = (R- R)/~ are shown in Fig. 3. For 17<24, the asymptotic dynamics are stationary wh:le time-dependent states are observed for larger r, with spirals being observed only for the larger Rayleigh numbers, Spirals appear in square geometries for smaller aspect ratios than those of a cylindrical cell at the same reduced Rayleigh number. As a first step towards quantifying and analyzing these complex patterns, we have calculated the time- averaged distribution P(q) of local wave numbers q as a function of aspect ratio and Rayleigh number. Following a recent suggestion of Egolf ct al [11], wc estimated local wave numbers g(t, z, y) from the ratio –V20/0 where O = O(t,z, y, 1/2) is the deviation of the temperature field T from its linear conducting profile, evaluated at the CC1lmidphuw z = 1/2. The distributiorr P(q) was then obtained by averaging many instantaneous histograms of q over time. A compilation of the mean wave numbers tj associated with each wave number distribution is shown in Fig. 4, which shows rather remarkably that the trend for the variation of ~ with R is nearly independent of the aspect ratio, and that ij decreases roughly linearly with increasing Rayleigh number up to R/& a 2. Near the value q – qO= –0.8 (with qOthe critical wave number at onset),

77 r=16, &=o.1 r=24, &=O.I r=32, &=o.l r=40, &=o.i r=56, E=O.1

B m

r=l 6, &=l.0 r=24, E=l.0 r=32, E=l.0 r=40, E=l.0 l_’=56,E=l .0

s p *N . L a zti-@ B .

Figure3: Instataeous patterns observed invarious aspect ratios fortwovdues of thereduced Wyleigh number e = (R – RC)/17c and for a fixed Prandtl number of o = 0.96, corresponding to the compressed C02 gas used in the experiments. The first two columns of states are time independent. there is a dramatic change with @becoming essentially independent of R. At this point, spiral defect chaos develops in the larger aspect ratio cells while the smaller cells are chaotic and lack spiral defects. The average spatial disorder of each pattern can also be quantified by a correlation length ~, which is defined here to be the inverse of the width of the distribution P(q). The inset in Fig. 4 shows that < is also insensitive to the aspect ratio and obeys approximately a power law dependence e–lj2 which is the same as that predicted by the amplitude equation theory [1] (although the range of Rayleigh numbers in the plot is much larger than the range over which this theory might be expected to hold). A similar trend has again been noticed in cylindrical geometry experiments, although an experiment in a rectangular cell found a divergence at a nonzero vahIc of E. The trend of ~(~) in Fig. 4, which has also been observed in cylindrical experiments, is far from that predicted theoretically by Cross and I%well [13], who argued that portions of circular rolls around a “focus singularity” such as those spanning the corners in the cells of F]g. 3 should lead to the selection of the same wave number qj as that selected in concentric axisymmetric rolls [14]. The discrepancy is particularly striking in the simple structures seen at low values of e such as Fig. 5, where theory [13] suggests that the focus singularities in the corners should determine the wave number over much of the system. One possible way in which arcs of rolls can act differently than complete circles is that arcs can drive a “mean flow”, which may then modify the wave number distribution. The mean flow is, roughly, the horizontal fluid flow integrated across the depth of the cell and cannot occur in axisymrnetric (or straight) roll configurations because of the incompressibility of the fluid. The mean flow is known to be important in producing the skew-varicose instability and in suppressing the zigzag instability for Prandtl numbers of order unity. Using the detailed knowledge provided by the code of the convection pattern, the wave number distribution, and the mean flow, we are able to assess for the first time the importance of the mean flow in producing the deviations of the measured wave number tj from qf. Fig. 5 shows the distribution of the wave number field and corresponding mean flow. In regions towards the center of the cell where the mean flow is small, the wave number is indeed close to the predicted value qj = 3.1. However circulating mean flow patterns develop in the cell corners and the wave numbers there are substantially reduced below qf. A plot of the distribution P(q) (not shown) indicates in fact that the largest q with significant probability is close to q~ but the spread of P(q) to smaller values of q means that the mean Q is considerably below qf. Given the characteristic form of the mean flowsthat form in the corners consisting of two regions of counter-rotating vorticity-- an analytic attack on this long staxlding question is an appropriate next step.

78 ,., ,, ,;., ;. .,4,’, “,?..

. o r=16 o r=20 4.5 0 1“=24 V 1“-32 4 A 1--40 ma r.56

\ & \ \ \ \ A \ $1.5 qf A \ K, \ k \ . O*O

-1.5 -1 -0.5 0 0.5 Local Wavenumber q-%

Figure 4: Plot of the deviation q– qoof the mean wavenumber ~ from the critical wavenumber go = 3.117 as a function of the reduced Rayleigh number ~. Also shown are the instability boundaries [12]which limit the range for the ideal roll state in a laterally infinite geometry (SV=slcewvaricose; O=oscillatory; E= Eckhaus; Z=zigzag), and the wave number qt (e) that is selected in axisymmetric rolls. Solid symbols denote states where dynamic spiral defects are observed. The inset shows the correlation length f defined as the inverse of the width of the wave number probability distribution P(g). The straight line has a slope 1/2 as would be predicted by the amplitude equation theory near threshold.

(a) (b) 3.1 I3

Fimme 5: (a) Roll ~attern and (b) wave number distribution (gray scale) at li!/RC = 1.15 in a cell of aspect ratio r = 40, The- corresponding mean flow (arrows) was es~-mated by integrating the horizontal velocity components of u vertically over the fluid depth. The maximum Euclidean norm of u has the value 6.1 in units of d/tvwhile the mean flow is much smaller, with a corresponding maximum magnitude of 0.12.

.— .— — , ,,’.,:.j’:1. ..,.-1!-,?.,Y..T.“...4.....,...~-l .... .C>;Z:,*.).,..,..,,,..,*..V-Y?..~~:-,.~~$~;~.y;;p.;:-~,.::.:.\,.,,0,,...,.~<;=~:~~tiw..,,..-....,,,4..,,.>-.;.,>...,....,....-:-..,.,.,?.:..-.>.,.:,..:;.l-: $ ,: -, — ,.,..<.,,..(--- Conclusions

As initial applications of our intermediate- to large-aspect-ratio fluid convection code we have studied two aspects of the onset of chaotic dynamics. In both of thmx? examples the role of the physical boundaries were found to play a vital role -in the intermediate aspect ratio by determining the basic structures about which dynamics develops, and in the large aspect ratio cell where the mean flows that form in the corners of the cell play an important roll in determining the wave number distribution-–and so the physical issues are not accessible to previous codes where periodic boundary conditions arc used. The preliminary results we present here suggest further directions to explore, both numerically and analytically.

Acknowledgements

This work was supported by the Engineering Research Program of the Office of Basic Energy Sciences at the Department of Energy, Grant DEF’T02-98ER14892. We also thank Paul Kolodner for useful discussions concerning the convection apparatus of Walden et al.

References

[1] M. C. Cross and P. C. Hohenberg. Pattern formation outside of equilibrium, Rev. Mod. Phys., 65(3):851- 1112, 1993. [2] Stephen W. Morris, Eberhard Bodenschat:~, David S. Cannell, and Gucnter Ahlers. Spiral defect chaos in large-aspect-ratio Rayleigh-B6nard concoction. Phys. Rev. Lett., 71(13) :2026--2029, September 1993. [3] W. Decker, W. Pesch, and A. Weber. Spiral defect chaos in Rayleigh-B6nard convection. Phys. Rev. Mt., 73(5):648-651, 1994. [4] R. W. Walden, P. Kolodner, A. Passner, and C. M. Surko. Nonchaotic Raylcigh-B6nard convection with four and five incommensurate frequencies. Phgs. Rev. Lett., 53:242-245, 1984, [5] M. Lai and H. S. Greenside, An Efficient Colocated Mesh Projection Method for Simulating Large- Aspect-Ratio Ra.yleigh-B6mard Convection. To be submitted to the Journal of Computational Physics, 2000. [6] John B. Bell, Phillip Colella, and Harlancl M. Glaz. A second-order projection method for the incompressible Navier-Stokes equations. J. Cmnp. Phys., 85:257-283,1989. [7] Francis IL Harlow and J. Eddie Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids, 8(12):2182--2189,1965. [8] Edward Ott. Chuos in Dy7mmical Sf]stems. Cambridge U. Press, New Yorlc, 1993. [9] C. Grebogi, E. Ott, and J. A. Yorke. Attractors on an N-Torus: Quasiperiodicity Versus Chaos. Ph@ca D, 15:354,1985. [10] Reha. V. Calcmur, David A. Egolf, 13rendan B. Plapp, and Eberhard Bodenschatz. Bistability and competition of spatiotemporal chaotic and fixed point attmtors in Rayleigh-B6nard convection. Phys. Rev. Ler%.,79(10):1853-1856, 1997. [11] David A. EgoIf, Llariorl V. Melnikov, and Eberhard Bodenschatz. Importance of local pattern properties in spiral defect chaos. Phys. Rev. Lett., 80(15):3228-3231, 1998. [12] F. H. Busse. Nonlinear properties of convection. Rep. Prog. P}ws., 41:1929-1967,1978. [13] M. C. Cross and A. Newell. Convection patterns in large aspect ratio systems. Physics, 1OD:299-328, 1984. [14] J. C. Buell and I. Catton. Wavenumber selection in large-amplitude axisymmetric convection. Physics of Fluids, 29:23-30, 1986.

80 .,

ENTRAINMENT IN HIGH-VELOCITY, HIGH-TEMPERATURE PLASMA JETS

J. R. Fincke, D. M. Crawford, S. C. Snyder, W. D. Swank, and D. C. Haggard, R. L. Williamson Idaho National Engineering and Environment Laboratory PO Box 1625, Idaho Falls, ID, USA 83415-2211

ABSTRACT

The development of a high-velocity, high-temperature argon plasma jet issuing into air has been investigated using a variety of diagnostic techniques. In particular the entrainment of the surrounding air, its effect on the temperature and velocity profiles and the subsequent mixing and dissociation of oxygen has been examined in detail. The total concentration of oxygen and the velocity and temperature profiles in the jet were obtained from an enthalpy probe. Coherent Anti-Stokes Raman Spectroscopy (CARS) was used to measure the concentration and temperature of molecular oxygen. Two-photon Laser Induced Fluorescence (LIF) was used to measure the concentration of atomic oxygen. It was found that both the incompleteness of mixing at the molecular scale and the rate of dissociation and recombination of oxygen have an effect on the observed jet behavior.

INTRODUCTION

The entrainment of cold gas into turbulent, high temperature, and high velocity atmospheric pressure plasma jets dominates their behavior [1]. Entrainment alters the chemical composition and quickly slows and cools the jet. Evidence suggest that entrainment is more of an engulfinent or induction phenomena [1-4], rather than gradient driven diffusion. In this description entrainment refers to the process by which the surrounding irrotational fluid is transported into the shear flow. The term mixing refers to mixing at the molecular level. A qualitative conceptual model, which describes the main features of the process, and estimates the important time scales, has been proposed by Broadwell and Briedenthal [5]. The model describes the entrainment and mixing process as a sequence of events initiated by the engulfment or induction of irrotational fluid into the jet shear layer. This initial process is kinematic and not diffhsive with the irrotational fluid immediately adjacent to the shear layer participating in the large-scale structure motion of the shear layer long before it has acquired vorticity of its own. These entrained or inducted “lumps” of fluid are subsequently strained and broken down into

81 smaller and smaller spatial scales or eddys. During this process the interracial area rapidly increases until the viscous Kolmogorov microscale, ~, is reached. Once LOis reached and the interracial zones intermingle, molecular diffision and heat conduction quickly annihilate the local concentration and temperature gradients homogenizing the mixed fluid.

For large Reynolds numbers the time to reach the Kolmogorov scale, ~,= kzdl I?c%,is -cb= k15/AU, where 8 is the thickness of the shear layer, AU = lA.UCCntCrlillC,and kl and k2 are constants. The Reynolds number, R.= AUiVv,is based on the shear layer thickness and AU. The time scale to diffuse across the small scale [5] A. is ~k = ~ SCRC-%where the Schmidt number SC is defined as the ratio of kinematic viscosity to mass diffusion coefficient. The other time scale of importance for the formation of a chemical product is the chemical reaction time, or Damkohler number; ~&~ for the large scales and ~L/~Cfor the small scales [6], where ~Cis the chemical reaction time constant. Large Damkohler numbers tend towards mixing limited chemistry while small values tend toward rate limited chemistry.

An intermediate stage can also be associated with diffusive processes, such as molecular mixing or heat conduction that may or may not precede to a significant extent the final stage. The relative importance depends on the relative magnitude of the corresponding molecular diffusivity to that of the kinematic viscosity or the Schmidt number [7]. The corresponding diffision scale ADdiffers from the Kolmogorov scale by the inverse of the square root of the Schmidt number, & = AOSc~. In particular for chemical reactions between entrained gases in a turbulent shear layer where the Schmidt number is of order unity the time scale for this process is comparable to ~A. This intermediate stage, sometimes referred to as infusion, is indistinguishable in gases from the final diffusive dominated process occurring at the Kolmogorov scale. Because of the very large temperature gradients present in high temperature jets, significant heat transfer at the boundaries of cold inducted eddies may occur before the fluid is mixed at the Kolmogorov scale making this intermediate stage process particularly significant. For the case of chemical reaction between the entrained fluid and the shear layer fluid, such as the dissociation of oxygen studied here, this stage of the entrainment process maybe very important.

Measurements of plasma velocity, temperature, and composition were obtained using an enthalpy probe integrated with a mass spectrometer [8-10]. Measurements of the concentration of atomic oxygen were obtained using two-photon laser induced fluorescence (LIF). Coherent anti-Stokes Raman Spectroscopy (CARS) was used to determine the temperature of the entrained molecular oxygen and to estimate the local molecular concentration. In the following sections the experiment is described, the measurement techniques detailed, and the general features of the flow field examined. These results will ultimately be used to benchmark a comprehensive computational model of the entire process that is under development. All testing was conducted using a commercial direct current plasma torch. The Miller SG- 100 plasma torch was operated at 900 A and 40 V, with a standard anode and cathode arraignment (Miller #165 and #129 respectively). The torch nozzle exit diameter was 8.0 mm. The argon flow rate was 35.4 slm.

The measured thermal efficiency of the torch under these operating conditions was 27 ?40, and the atmospheric pressure was 85,5 kpa.

82 ,,,,.. ,. ,,/: .,

ENTHALPY PROBE

Originally developed in the 1960s, enthalpy probes [11,12] have enjoyed renewed application to thermal plasma processing problems [13-15]. Their range of application has been extended by integration with a mass spectrometer for measurement of gas composition [8], and their performance has been validated by comparison to laser scattering measurements [9,10]. The enthalpy probe is a water-jacketed gas sampling and stagnation pressure probe from which the enthalpy, temperature, and velocity of a hot flowing gas can be derived once the composition is known, The probe used is copper with an outside diameter of 4.76 mm and a hemispherical tip. Probe survivability in high temperature and high velocity flows dictates a large probe size. The calorimetric method used to determine gas enthalpy and hence temperature depends heavily on a “tare” measurement. Observation of the coolant temperature rise and flow rate are made in the absence of gas flow through the inner diameter of the probe. Gas is then caused to flow and the same coolant measurements are repeated, together with measurements of the gas flow rate through the probe and gas temperature at the probe exit. The rate of heat removal from the gas sample is thus given by the difference between the measured delta of cooling water inlet and outlet temperatures,

where m~ = gas sample mass flow rate, m~w= cooling water mass flow rate, h. = unknown gas enthalpy at the probe entrance, hc = gas enthalpy at the probe exit thermocouple, Cp = cooling water specific heat, and ATCW= cooling water temperature rise. The unknown gas enthalpy h at the probe tip is now uniquely determined, provided that the gas sample flow rate and the gas enthalpy at the probe exit are known. The exit gas sample enthalpy is determined from the measured temperature and the gas sample flow rate is measured via a sonic orifice. While the probe is in the “no gas flow” mode the stagnation pressure is measured. The gas mixture composition is required to determine the gas sample flow rate and to relate measured enthalpy and stagnation pressure to thermodynamic properties and gas velocity. Composition is obtained by a quadrapole mass spectrometer interfaced to the enthalpy probe via a differentially pumped vacuum system. For low Mach number flows the flee stream velocity, U, is obtained from U=[2(Pt-P.)/p. ]’~ where Pt is the stagnation pressure and P. is the ambient or static pressure. The density p. is a fi.mction of the freestream enthalpy, pressure and gas composition. Centerline velocity and temperature data derived from enthaply probe measurements are shown in Figures 1 and 2. The axial coordinate is measured from the face of the torch. Particularly noticeable is the rapid increase in air content and the associated slowing and cooling of the jet.

COHERENT ANTI-STOKES RAMAN SPECTROSCOPY

Non-intrusive optical diagnostic techniques such as CARS, developed for combustion research, are also applicable in thermal plasma flow fields [14]. CARS has the advantage of high conversion efficiency, a laser-like coherent signal beam for high collection efficiency, excellent

83 14003- lCKI 120a

ImYl - 80 1coo

lcGf30 - + .* acoo - -i

6mo -

4cm -

2m3- o 2C41

-- fN.-..w-* --r——-. o I 0 I o 102030405060 7080 051015202530354045 543556065707560

&dal Position (mm) Axial Posilion (mm)

Figure 1. Temperature comparisons, Figure 2. Velocity comparisons, showing showing effect of gas and liquid injection. effect of gas and liquid injection.

fluorescence and luminosity discrimination, and high spatial and temporal resolution. The technique is applicable to the measurement of the concentration of any Raman active species.

The theory of CARS and its application as a combustion diagnostic are detailed in [7]. A CARS signal is generated when two laser beams at frequency 01, (termed the pump beams) and one laser beam at frequency 02 (termed the Stokes beam) interact through the third-order nonlinear susceptibility of the medium ~‘3). This interaction generates an oscillating polarization and thus coherent (laser like) radiation at frequency 03=201-02. The third order susceptibility is a complex quantity and is composed of a resonant (~,) and a non-resonant (~,,) component. The non-resonant component is proportional to the number density of the species present and is generally a slowly varying function of wavelength.

In general, the pump (ml) and Stokes radiation fields (032)have a finite line-width. The CARS signal is then proportional to

~s(03)~ p, (U’)dd p] ((N)]* (U’+U’’–U3)/#3@i)3_ d’) 2da)” .

Because our pump beam is transform limited in spectral bandwidth (= 100 MHz) the cross- coherence effects present when multi-mode YAG lasers are used have been neglected. Furthermore it is assumed that the CARS lines are superimposed without interaction (isolated line approximation) and are homogeneously broadened. Normalizing ~,= Z~3)/n and z,, = x,,‘3)/n. and noting that Z, = Rex, + i Im~, and that ~,, is a real quantity, 13(us) then, disregarding the convolution, is 13(cv3)cc ((no~,,)’ + 2no~,,nRe~, + ( nl~,l )2)1~12. For the case in which the non-resonant background is insignificant or is suppressed by choosing certain polarizations of the pump and probe beams (polarized CARS) then 13 wn2\~,121~12. The particle density is obtained by absolute intensity measurement of the CARS signal. The temperature is

84 ..

determined from the relative vibrational and rotational populations n(vj). A typical single shot Q-branch CARS oxygen spectra taken at 1000 K is shown in Figure 3. Overlaid with the experimental data is a theoretical spectra calculated using a modified version of the CARSFT [16] computer code. The feature between 579.0 and 579.2 nm is the so called hot band, originating from the v=2 to v=l rotational-vibrational transitions. The rotational temperature is determined by fitting the theoretical distribution to the data with temperature as a parameter. The particle density measurement, which is dependent upon measurement of the absolute intensity of the CARS signal, is complicated by intensity fluctuations of the lasers and changes in beam overlap, while the temperature measurement is dependent only on relative measurements and is less affected.

Figure 4 compares the rotational temperature of molecular oxygen obtained from the CARS measurement taken on the centerline of the jet. For locations closer to the torch face than 30 mm the concentration of molecular oxygen is insufficient to yield a CARS signal. As is evident in the plot the measured temperatures are significantly less than the mixture temperatures obtained from the enthalpy probe. This indicates that significant amounts of relatively cold air are rapidly inducted deep into the jet flow. These cold eddys have not yet been fully mixed and equilibrated with the hot plasma gas. At 60 mm the mixing process is relatively complete and the two temperature measurements converge.

104 I’tooa- Fitting Parameters *-,-*—w- Tayofawa 10s0!4 =B- -a- GMalpyPmh rnixwrc mpmtum 12000- --- OARSTnmparatum 80 Hc&lal Shift.7C0 VarticalShit 10.95 \ ProbeLineVJdti 3.05777 Pressuw.l.zabn $VavmutierExpansbw1.002 Inlenskv Expanslorx 1.005 A 20 ~l=a ~---.- Bac#t,kalv07.c-mTacM06!.P 0 0-! 57W3 579.0 579.2 579.4 579.6 579.8 580.0 560.2 5a0.4 0 102030405060 7080 Dye Laser Wavelength Axial Position(mm)

Figure 3. CARS Oz spectrum at approximately Figure 4. Comparison of CARS Oz 1000 K. temperature and enthalpy probe mixture temperature.

TWO PHOTON LASER INDUCED FLUORESCENCE

Multiphoton excitation techniques are required for laser induced fluorescence monitoring of the concentration of light atoms such as atomic oxygen [17-19]. Multiphoton excitation allows the creation, from the ground state, of observable populations of excited state O atoms. A simplified energy level diagram for O is shown in Figure 5. Two 225 nrn photons excite the ground 2p 3P state to the 3p 3P state. The fluorescence signal at 844 nm results from the 2p 3P to 3s 3S transition. The laser used is a Nd:YAG pumped dye. The fundamental of the dye is doubled and mixed with the 1.06 pm fundamental from the YAG in a KDP crystal yielding 1 mJ of 225 nm light. The two-photon LIF measurement is complicated by the extremely high quenching rates of the laser produced excited state. The observed lifetime of the two-photon produced excited state (3p 3P) is less than 2 ns as compared to its natural undisturbed lifetime of 35 ns, Figure 6.

3p3P 3p SP 844 nm 3s %“

3s %“ 225 nm

2p4‘s

225 nm 2p’ ‘D .-ox.” % 0.0+2 10 15 20 25 30 35 40 lime (ns)

Figure 5. Simplified atomic oxygen Figure 6. Time resolved fluorescence energy level diagram. signal.

The measured centerline axial distribution of atomic oxygen is shown in Figure 7. The decay time (quench rate) of the LIF signal is approximately constant over the extent of the flow field, hence the intensity of the LIF signal is approximately proportional to the atomic oxygen concentration. Also plotted in Figure 7 is the amount of molecular oxygen calculated as the difference between the total amount of oxygen measured by the enthalpy probe and the LIF measurement of atomic oxygen. The CARS measurement of molecular 02 is also plotted. Much of the variation in the CARS signal is due to laser intensity drifl, thus this plot illustrates the limitation of CARS in the measurement of concentration. The same data is also shown in Figure 8 along with the calculated amounts of atomic and molecular oxygen that would be present if the mixture were in equilibrium at the temperature measured by the enthalpy probe. In general the dissociation of molecular oxygen lags the equilibrium in the hot regions of the jet and the recombination Iags the apparent cooling of the jet. The fundamental question is which phenomena account for the observations, is the process mixing limited, or does the rate of chemical reaction, dissociation, and recombination account for the observations.

86 s

-0- LIFIO] + 02 -7- Eq@b$iim[0] -~ Ewiibdwm102] L1 ,,- .,/” ,,+’ /

0 10202040506070 ~ o.&lo202JJ4050Eo 70s0 AxialPosition(mm) A4al Position

Figure7. Atomic oxygen concentrations Figure 8. Measured and equilibrium measured by LIF and molecular oxygen concentrations of atomic and molecular concentration obtained from CARS and oxygen. enthalpy probe measurements.

DISCUSSION

The dissociation reaction for oxygen is Oz + M +-+ O + O + M where M=Ar,He,Oz,Nz,e-,... Initially the time constant for this reactions is approximately ~~(Ar) = l/(2[Ar]kD) where the reaction rate is kD(Ar) = 1.6x1014 exp(-54245/T) [19]. The time constant for dissociation -cdis on the order of 100 ps at 6000 K. The mixing time scales estimated from the model of Broadwell and Breidenthal [5] are ~k =20 ps and ~L= 10 ps in the jet near field, With respect to the data in Figures 2 and 4 the absolute upper limit on the time scale for mixing is on the order of ~ = .005 m / 500 m/s or 100 ps consistent with the estimates. The corresponding Damkohler numbers are @~= 0.2 and TA/Tc= 0.1. Thus the entrainment and mixing processes and the chemical reaction time have similar time scales. This is consistent with the apparent incompleteness of mixing illustrated by the temperature data in Figure 4 where large scale inhomogeneities still persist well downstream in the flow field and contribute to the apparent deviations from equilibrium. At the same time the recombination process (the reverse dissociation reaction) takes place at a relatively low temperature, on the order of 2000 K. At this temperature the time constant for recombination is on the order of 1 ms suggesting a greater influence of the rate of reaction. Additional experimental work and modeling are underway which will help to clarifj the observed phenomena.

ACKNOWLEDGEMENT

This work was supported by the U. S. Department of Energy Office of Energy Research, Office of Basic Energy Sciences, Engineering Research Program, under Contract No. DE-AC07-991D13727.

87 REFERENCES

1. E. Pfender, J. Fincke, and R. Spores, “Entrainment of Cold Gas into Thermal Plasma Jets;’ Plasma Chemistry and Plasma Processing, 11, pp. 529-543 (1991). 2. J. R. Fincke, R. Rodriguez, and C. G. Pentecost, “Coherent Anti-Stokes Raman Spectroscopic Measurement of Air Entrainment in Argon Plasma Jets, Plasma Processing and Synthesis of Materials III, Materials Research Society Symposia Proceedings Vol. 190, San Francisco, CA (1990). 3. J. R. Fincke, R. Rodriguez, and C. G. Pentecost, “Measurement of Air Entrainment in Plasma Jets,” Proc. of the 1990 National Thermal Spray Conference, Long Beach, CA, ASM International, pp. 45-48 (1990). 4. R. Spores and E, Pfender, Flow Structure of a Turbulent Plasma Jet,” Proc. of the 1988 National Thermal Spray Conference, Cincinnati, ASM International, pp. 85-92(1988). 5. J. E. Broadwell and R. E. Breidenthal, “A Simple Model of Mixing and Chemical Reaction in a Turbulent Shear Layer, “J. Fluid Mech. 125, pp. 397-410 (1982). 6. M. G. Mungal and P. E. Dimotakis, “Mixing and Combustion with Low Heat Release in a Turbulent Shear Layer,” J. Fluid Mech. 148, pp. 349-382 (1984). 7. P. E. Dimotakis, “Two-Dimensional Shear-Layer Entrainment,” AIAA Journal, 24, pp. 1791-1796 (1986). 8. W. D. Swank, J. R. Fincke, and D. C. Haggard, Rev. Sci. Instr., 64,56 (1993). 9. J. R. Fincke, S. C. Snyder, and W. D. Swank, and D. C. Haggard, “Comparison of Enthalpy Probe and Laser Light Scattering Measurement of Thermal Plasma Temperatures and Velocities,” , Review of $cientlj?c Instruments, 64, pp. 711-71 8(1993), 10. J. R. Fincke, W. Swank, and D. Haggard, “Enthalpy Probe Performance in Compressible Thermal Plasma Jets,” Review of Scientl~c Instruments, 64, pp. 3585-3593 (1993). 11. Grey, J., 1X4 Transactions, 4, pp. 102-115 (1965). 12. Grey, J., P.F. Jacobs, and M.P. Sherman, Review o~Scient~fic Instruments, 33, pp. 738- 741 (1962). 13. Brossa, M. and Pfender, E., Plasma Chemistry and Plasma Processing, 8, pp. 75-90 (1988). 14. Fincke. J. R. and Pentecost, C. G, “Laminar to Turbulent Transition in Thermal Plasma Jets” Heat Transfer in Thermal Plasma Processing, HTD-VO1. 161, K, Etemadi and J. Mostaghimi, Eds, ASME, New York, pp. 101-106 (199 1). 15. Levenson, M. D., Introduction to Nonlinear Laser” S~ectrosco~v, Academic Press, New York, 1982. 16. Palmer, R. E, SAND89-8206, Sandia National Laboratories, Livermore, CA (1989). 17. Bischel, W. K., Perry, B. E., and Crosley, D. R., chemical Physics Letters, 82, pp. 85-88 (1981) 18. DiMauro, L. F,, Gottscho, R. A., and Miller, T. A., J Appl. Phys, 56, pp. 2007-2011 (1984). 19. Alden, M., and Westblom, U., Optics Letters, 14, pp. 305-307( 1989). 18. W. C. Gardiner, cd., Combustion Chemistl~, Springer-Verlag, New York, (1984).

88 FILM COOLING IN A PULSATING STREAM: RECENT RESULTS FOR LAMINAR M/B TURBULENT WALL JET

H. Fasel, A. Ortega,1.J. Wygnanski Departmentof Aerospaceand MechanicalEngineering, The Universityof Arizona, TucsonAZ 85721 USA

ABSTRACT

The heat transfer in a forced larninar, transitional, and turbulent wall jet was investigated with a combined theoreti@ experimenta~ and computational approach. When forcing is introduced into the laminar wall je~ two staggered rows of vertical disturbancesdevelop.At high amplitudes,these structures increasethe mixingwithin the wall jeg which in turn increases the spreadiug rate and reduces the skin fiction. In addition,the large structuresentraincoldfluidfromthe ambiem and hot fluid is convected away flom the waI~ which leads to an increase in tie effectivethermal diffision. It is found that forcing both the principal and subharmonic modes is most efficient. Experimentalinvestigationsof the turbulent wall jet showthat forcing at all frequencies generally decreases the wall friction because the growth rate of the jet increases. The decrease in wafl fiction does not seem to have a comparable efMct on the wall heat transfer. This is possibly because the outer shear layer vortices that dominatethe flow when forcing is introduceddo not necessarilyproducothe small scale turbulence in the inner region that is so important in scalar transport. Preliiary computational investigationsof the turbulent wall jet show that the turbulence model is capable of predictingthe turbuient meanflowaccurately.Qualitatively,the tiect of the structures on the turbulentflowis very similarto the larninarflow.

NOMENCLATURE

ReJ Reynoldsnumber measuredat exit plane Ym maximumnormal distancefrom the wall = p~d/p (forthe integrationdomain),m T localmeantemperature,K Cp specificheat of air at free-stre~ J/kg-K To &e-stream temperature,K d walljet slotwidth,m T. walltemperature,K k thermal conductivity,W/m-K u local streamwisemeanvelocity,mh m mass flow rate, kgls q jet exit velocity,m/s t’ fluctuatingtemperature,K u., localmaximumstreamwisevelocity,rds u’ fluctuating streamwise velocity,nds u. free-streamvelocity,IU/S X,y coordinates,m Greek symbols Subscripts 6 denotesboundarylayerthickness,m .i jet exitplane & local hydrodynamic boundary layer m maximum thickness,m o free-stream 4 local thermal boundary layer thickness, t thermal m v hydrodynamic P free-stream dynamic viscosity, N-s/m2 w wall P flee-stream density, kg/m3

INTRODUCTION

Along with the bounda~ layer and the flee j% the wall jet is one of the most important of all flows. The wall jet is a fluid jet introduced tangentially along a surfbce. The flee-stream can either be w-flowing or quiescent and the characteristics of the flow are strongly related to the ratio of the jet velocity to the free- stream velocity. Wall jets have important technological applications such as in film cooling of gas turbine components. In film cooling, a turbulent wall jet is used to shield blades and other surflices exposed to high temperature free-stream flow. In this multiyear investigation, we are investigating the fimdamentd mechanisms by which the transport of heat to or from a surfbce may be enhanced or suppressed by exploiting the naturally occurring instabilities of the flow. We have chosen to focus on a strong laminar, transitional, and turbulent wall jet flow since it exhibits characteristics of both free shear layers and boundary layers that make it particularly susceptible to external excitation. It is thus an ideal flow for fi,mdamentalstudy of heat transfer control by external forcing.

RESULTS FOR THE LAMINAR WALL JET

By a combined experimental and theoretical approach, we previously showed that selective forcing of the laminar and transitional wall jet at its dominant instability modes produced profound changes in the momentum and heat transfer from an isothermal wall. The strong wall jet can be viewed as a combination of a boundary layer (near the wall) and a free shear layer fbrther away from the wall. These two basic flow types exhibit very different stability characteristics, a l%%that can be exploited to alter the mean flow by introducing controlled perturbations at specific frequencies and at large amplitudes. The linear stability characteristics of the laminar jet have now been well establish~ Likhachev et al. (1998) and experimentally confirmed, Likhachev et al. (1999), Quintana et al. (1997). We now have substantial experimental evidence that suggests that forcing with a frequency for which, according to linear stability theory, the boundaxy layer mode is unstable, is much more effective than forcing the shear layer mode. For the laminar walI jet, the experiments definitively established that forcing the inner boundary layer mode at levels of only 2Y0,the skin friction can be reduced by as much as 65% and, for the same flow, the wall heat flux can be increased by 45%, Quintana et al. (1997). Substantial progress has been made in applying Direct Numerical Simulation (DNS) to the Iaminar wall je~ Seidel and Fasel (2000). Our understanding of the physical mechanisms leading to the profound changes in the momentum and heat transfer has been greatly enhanoed. DNS computationswere conducted based on the incompressibleNavier-Stokes equations solved in the vorticity-velocityformulation in conjunctionwith the energy equation. A 4th-order accurate Runge-Kuttamethodwas used for the time integration. For the spatial discretization,4th-orderaccurate compactdifferenceswere used in both the x- and y-directions.The solution procedure of the vismus terms in the vorticity transport equations was extensivelymodifiedto facilitate the introductionof a wide variety of turbulence models.For the results shownhere, an equidistantgrid in the x-direotionwas used. In the wall normal direotion,grid points were clusterednearthe wallto resolvethe steepgradients.

90 ,, . .,.G, ., .

Beforeapplyingthe codesto extensivesimulationsof our laboratoryexperiments,the codewas tested and validated to demonstrate its ability to efficiently obtain accurate results. Mler computing the undisturbedwall jet mean flow, disturbanceswere introducedinto the flow field by periodic blowingand suctionthrougha slot inthe wall near the inflowboundary.At low disturbanceamplitudelevels,the results of the computationsshowedexcellentagreementwith results from linear stability theory. Increasingthe disturbanceamplitudecaused a mean flow distortiondue to nonIinearinteractions.As in the experimental investigations,two frequencieswere investigate j3j=(the shear layermode), and ~j = (the boundarylayer mode).

Case CaseOl Case02 Case03 Case04 Case05 Case06 Case07 A&i 5X104 Ixlo-z 1.5X102 IX402 1X10-2 1.5X102 1.5X102 AJUi - - - 1X10-3 IXIO-2 Ixloa ~xloa

Table 1Disturbanceamplitudesforthe fundamental(bj=0.094)andthe subharmonic(b,=O.047)frequency

X/b.lz .XM=l6 XM=20 2.5 2.5 2.5 — ezsellow — CeseOl ‘\ 2 2 “\ 2 -\, ---- cfN302 “\ x. --- ceseo2 1.5 “L% 1.5 ‘.-~. 1.5 \ ‘-, \\,\. .’.<\ ‘ \ -.<--- ‘e07 . . \\ -. d’ --..<, *1 --~ 1 ‘-.’.<\* 1 j \ -& ‘> ,/. 0.5 0.5 ,.-./..‘/ 0.5 ./ /, / - -.>~. =-” / <.*. “ ❑ ❑J<’ 0 0 D 0 0 0.2 0.4 0,6 0.8 1 0 02 0.4 0.8 0.8 1 o 02 0.4 0.6 0.8 1 u u u 2.5 2.5 2.5 i 2 2 2 i ; 1.5 15 1.5 ~~ ,1 g ./” 1 ,) 1 1 ,) /’ ,<.i,<-- 0.5 As 0.5 0.5 /-“ ./’ ❑--- 0 0 o 0 0.2 0.4 0.6 0.8 I 0 02 0.4 0.6 0.8 1 0 02 0.4 0.6 0.8 1 DT T T

Figure 1. Comparison of mean flow distortion of u-velocity and temperature for dii%erentforcing amplitudes.

Forcingthe shear layer mode does not show a significant distortion of the mean flow profiles. In contrast,forcingthe boundarylayermodehas a pronouncedeffectonthe meanflowprofiles.Thetop three graphs in Fig. 1 showthe mean velocityprofiles. Clearly,the disturbancescause a reductionof the local maximumvelocityand the displacementof the location of maximumvelocity away from the wall. Both changes of the mean flow profile contribute to the significant reduction in skin friction. The mean temperatureprofile is shownin the bottomthree graphs in Fig. 1. When large amplitudedisturbancesare

91 introduced into the flow, the mean temperature profile develops an inflection point near the wall, which results in an increase in the wall heat transfer. Even though forcing with bj= 0.094 has a significant effect on the mean flow, the reduction in skin fiction and the increase in heat transfer is not nearly as large as our experiments suggest. Scrutinizing the experimental power spectm, the emergence of the subharmonic was observed. This prompted us to introduce forcing at the subharmonic frequency in addition to the fundamental fkquency (see Table 1 Cases 04- 07). Figure 1 shows that with this subharmonic, the mean flow distortion is significantly increased. The spreading rate of the wall jet increases dramatically and the inflection point in the temperature profile becomes more pronounced. The effect of forcing on the near wall mean profiles can be seen more clearly in the change of the analogy factor in the Reynolds analogy, 2St/Cf. This quantity is plotted in Fig. 2 as a fiction of downstream distance. The graph shows that only if tbe amplitude of the subharmonic disturbance is sufficiently high can a mean flow distortion mmparable to the experiments be achieved. This clearly shows that it is not the amplitude of the fimdamental itself but rather the subharmonic resonance that results in the significant mean flow distortion observed in the experiments.

41 ., — PS9110W : : —— C&sool 1’ 35 1: 0 Expofimenl.unlorced 1’ -.—. Casew? I :. 3 ---- casm5 uExpmlment.10,4 1’,: -— cas003 lo’ 25 ---- ca5eoB 7‘,.X” ––- Caseur /, * mpefiman!,2?4 ~..~e-- ,’ ..- / .’ , ,J?:a::-.-”- ‘--” 15 ...... “ ./”. . . ~:~.:.:..-’. —— .-._ ------_ ------—= 1 . > 05

I Ill I 0 5 10 15 20 26 m

Figure 2. Analogy factor for bj=0.094. See Table 1 for explanation of different cases.

To qualitatively analyze the effect of forcing, the size and location of the large structures is shown in Fig. 3 for different forcing amplitudes. Color contours show the temperature distribution and the contours lines identifi vertical structures using the k criterion by Jeong & Hussain (1995). For comparison, Fig 3(a) shows the undisturbed mean flow. Note that the x- and y-directions are scaled with the nozzle height b to show the spreading of the wall jet in the streamwise direction. If only single frequency disturbances are introduced, Figure 3(b), a very regular, staggered double row of vortices develops. In addition, the figure shows that the temperature distribution is governed by the local, unsteady convection. The structures near the wall turn clockwise, convecting high temperature fluid away fkomthe wall on the upstream side while convecting low temperature fluid towards the wall on the downstream side. The outer row of vortices, tinning cmnterclochvise, enhancesthis flow pattern. It in addition, subharmonicforcing is introduced, vortexpairingoccurs,Fig. 3(c).This leadsto a doublingof tie size of the structures,significantthickening of the wallj% and consequentlyan increasein heat transfer. Increasingthe amplitudeof the subharmonic movesthe vortexpairingupstream,Figure3(d).

92 X/b I

X/b

Figure3. Instantaneoustemperaturedistributionand structuresinthe flowfield.a) Undisturbedbase flow,b) Case03,c) Case06,d) Case07.

The effbct of the Iarge— structures in the flow can be described quantitativelyby a local increase in viscosityand thermal conductivity.Typically,these quantities are written as a Reynoldsstress, =, and an eddy thermal diffisivity, ~. A comparison of both quantities is shown in Fig. 4. The agreement betweenthe three results is very good. The figure showsnegativeReynoldsstress near the wall, which is another manifestationof the skin fkictionreduction due to the structures in the flow field. In the right graphs, the eddythermal diffbsivityis shown.The strong peak near the wall coincideswith the reduced temperature gradient around the inflection point in the tempemture profile. These results clearly demonstratethat the large structures in the flow are responsiblefir the changesin skin fiction as well as wallheattransfer. am-la muo 2s -.-7---- -..-.,-. . .

2 ...

< ‘. ‘ . . “’x, 1 ; .) .,.~ \ a. . . Y. ,,” . 03 u . . ..’ . .. ‘+ *P. 8“ “ :1 0 [h----- .— ---- -1-.050051 , -08 0 06 -1-05005? -1 -0.5 u 0.5 1 1 b— Figure 4. Normalized iv’ (left) and v’t’ (right), CaseO1.Comparisonof simuktions (- - -), linear theory (...), and experiments(0).

The fbct that the time mean wall shear stress was reduced while the time mean heat transfer was increased is a powerfid reildation of the Reynolds analogy for steady flows and points out that intelligent control of convective flows may have a profound impact on rates of transport. In some cases, it may be possible that those transport rates may be significantly influenced while minimizing the penalty usually associated with the pressure drop in a heat transfer device. We next turn our attention to the turbulent wall jet which has greater application but also significantly greater challenges than the Iaminarjet.

THE STRONG TURBULENT WALL JET

The strong turbulent wall jet is characterized by having a mean jet velocity to free stream velocity ratio greater than about two. The heat transfer in the steady turbulent wall jet has been extensively studied. Seban (1960) and Seban and Back (1961) measured the heat transfer coefficient and the effectiveness for tie wall jet with variable slot heights and mass-velocity ratios. lt was found tha~ for mass-velocity ratios of less than unity (weak wall jet), the effectiveness followed a power law decay with downstream distance. The power depended on blowing ratio. For mass-velocity ratios of greater than unity, the heat transfer coefficient could be expressed simply in terms of the slot Reynolds number and the relative downstream distance of the slot. This simple behavior of heat transfer coefficient arose from its primaxy dependence on the flow immediately adjacent to the wall. In contrast, the effectiveness was related to the velocity distribution in the external part of the boundary layer, between the velocity maximum and the free-stream value, and this distribution depended more critically on the blowing ratio and system parameters. Myers et al (1963a,b) predicted the maximum velocity decay, jet thickness, and the shear stress, and compared with those results analyzed by momentum-integral methods. Myers et al (1963b) studied heat transfer under the condition of a step change in wall temperature with jet Reynolds numbers ranging from 16,600 to 38,100. Mitachi et al (1974) reviewed some of these investigations and proposed an analytical solution to the temperature field using a mixing length turbulence model. Under the condition of constant heat flux, Nizou (1981) attempted to supplement the relation between heat transfer and skin friction for turbulent wall jets. He found that St /Cj increased slightly along with X/b, hence confirming the applicability of the Reynolds-Colburn analogy.

,. !,. . ~ ,k. ,,!. ,,.. .’{, - ..

The use of externallyintroducedforcing in the turbulent wall jet was demonstratedby Katz et al (1992). Theyexcitedthe turbulentwalljet by a loud speakerat differentfkquencies and amplitudes.They found that forcing had no appreciable effkct on the rate of spread of the jet nor on the decay of its maximumvelocity, but this external excitation caused a significantlocal reduction of skin ffiction, and enhancedthe twodimensionality and periodicityof the coherentmotion. For a turbulent walljet with an externalfieestream,Zhou et al (1993a) summarizedtheir experimentaldata, togetherwith other available data from the literature, and wliapsed them onto a set of universal curves independentof Reand the thickness of the upstream boundary layer. In the natural turbulent wall jet without fbrcing, Zhou et al (1993b) observeda I%equencyfkctor of approximately1.7 betweenthe inner layer and outer layer which dependedonthe velocityratio R unless the two modelswere coupled,In the case of weak excitation,Zhou et al (1996) foundthat, the skin friction was reducedby about 7V0between X/b= 100 and 200 and the — — intensity of U*2was signiilcantiyincreased by forcing. The excitation also increased the intensity of V’2 in the outer region, but didnot affectthe spanwisefluctuations ~.

StabilityConsiderations

A theoreticalstabilityanalysiswas performedto gain insightintothe stabilityof the strongheated turbulentwaUjet and understandthe mechanismsthat mightbe exploitedfor its control,Likhachev(2000). Unlikethe Iaminarwall jog the theoretical analysis pointed out that the turbulent wall jet has no strong dominantmodesbut rather respondsover a wider frequencyspectrum.The propagation and amplification of the small-ampl@dedisturbancewaves were modeledas linear instabilities of the mean velocity and temperatureprofiles.Becausethe flow is incompressibleand experimentaltemperature d.i&erenceis small, temperature can be treated as a passive scalar. The influenceof incoherentturbulent fluctuations on the large-scaleexternalperturbationswas taken into accountwith an eddyviscositymodelthat was consistent withthe meanflow. Sincethe Reynoldsnumberbased onthe local maximumvalue of the eddyviscosityis not sufficiently large, non-parallel effects should be considered in the stability calculations. The multiple- scales expansion method was used in conjunction with similarity laws of the mean flow to predict the influence of the jet growth on the linear stability characteristics. Calculations of the perturbation behavior were made for a variety of imposed frequencies. It was shown that some significant experimental conclusions based on local measurements could be attributed to the divergence of the flow. In particular, the existence of different predominant frequencies in the outer and inner regions of the turbulent wall-jet flow can be attributed to non-parallel effects rather than to nonlinear effects or to the possible existence of anothermodeof instability.A comparisonof the stability calculationswith the experimentaldata and the Large-EddySimulationsis ongoing.

Experimental Measurements

The experiments were performed in a thermally controlled, closed return, low speed, air wind tunnel shown in Fig. 5, The wind tunnel provided a thermally controll~ low speed main flow at a velocity U. of 5.0 rds and temperature T. of 23.7 ‘C. The test section was 711 mm wide, 165 mm high and 2,362 nun long. A slot type wall jet apparatus was used which essentially duplicates the design of Zhou et al. (1993a) used in the study of a turbulent wall jet with forcing. The wall jet is introduced tangentially just upstream of the isothermal stiace. Flow is delivered by a 0.5 hp centrifugal blower. The flow enters an air-water heat exchanger followed by a difWier that decelerates the flow into a plenum chamber. The plenum chamber is fitted with an awustic speaker that is used to introduce controlled disturbances (forcing) into the jet. Three screens of 30,40 and 50 mesh size and a contraction having a variable area ratio complete the apparatus. In the present experiments, the jet contraction ratio is 18:1 resultrng in a jet slot width b of 5.0 mm and a jet exit velocity Uj of 21.0 rids. The jet temperature Tj of 23.7 “C was held constantby an air-water heat exchanger and a recirculating chiller.

a0no?cLc5m R6Ttml W“DllMHSL

—/

y&ll&l?.uw

— 5JW.CS

Figure. 5 Experimental apparatus

An isothermal heat transfer surfhce is located downstream of jet exit plane, and has an unheated starting length of X/b= 7. This surf%e consists of a 19-mm thick, 508 mm wide and 1219-mm long highly polished ahuninum tooling plate, which is held at constant temperature by means of, heated water from a recirculating chiller that flows through milled slots inside the plate. A 50.8-mm thick sheet of honeycomb is placed beneath the plate and serves as an insulator and as a rigid suppoti for the top plate. Another plate with heated flow is placed beneath the honeycomb to stabilize any backside thermal losses. The excited jet flow passes along with a 50.8-mm diameter aluminum Coanda cylinder and flows tangentially over this heat transfer surfbce. The side and top walls of the test section are fabricated of Plexiglas to allow visualization studies to be accomplished. The measurements of streamwise velocity and temperature were conducted using two side-by-side (12 mm apart in spanwise direction) standard DISA 55-PI 1 single hot and cold wire probes, which were held by a welldesigned probe holder. Both the hot and cold bridges were manufactured by AA Lab System (model AN-1OO3).The cold wire was calibrated against a NIST traceable lab standard thermistor probe, and the hot wire probe was calibmted in the exit of a thermally controlkxl vertical axisymmetric jet against a standard Pitot tube and an MKS Baratron pressure transducer. Due to temperature gradients in the flow field, the hot wire output voltage required temperature compensation. The hot wire output voltage was thus calibrated at different velocities for the range of tempemtures, which were used in the experiment. A polynomial relationship between voltage and temperature fir each velocity was produced and used to find the temperature compensated voltage by iteration. Using this method, the actual velocity can be found due to the small temperature difference between TWand ambient. In order to observe the effkcts of external forcing on the velocity and temperature fields, pressure fluctuations were artificially introduced into the wall jet with a 304.8-mm loud speaker placed in the diffhser section. Four fhquencies, 37.5Hz, 75.O& IOOHZ,and 1051-Iqand two amplitudes, 5% and 10Yo,were chosen in present experiments. Detailed experiments were performed to first determine the time averaged mean flow and heat transfer characteristics of an unforced, plane turbulent wall jet flowing over an isothermal surface that was

96 ,,. ,, ...... , -.! *1,

heated above the jet and ambienttemperature. All experimentswere performed in air. A jet velocity of 21,0 m/s and free-streamvelocityof 5.0 m/s formedthe base case for the measuremmts. Figure 6 shows the mean velocityprofiles, comparingthe unforcedcaseto forcingat 100 Hz, 10% amplhude. The near wall profiles shownin Fig. 7 accentu~ the decrease m the near wall gradient and hence the wall shear stress when forcing is introduced. The near wall temperature profiles, Fig. 8, do not show appreciable changes,except at fir do~stream ~l~nces” Subsequently,the wall fiction caefficien~Cfidecreasesat all downstreamdistances,with forcingat all frequencies,Fig. 9, but the wall Stantonnumberexhibitsonly modestchanges,Fig. 10. Althoughthese resultshave not yet been studiedin great detail, a signifi@ clue as to the insensitivityof the wall heat transfer to forcing is provided by examinationof the fluctuating temperaturedistributio~ Fig. 11. It is seenthat evenat a 10%forcingamplitude,the near wall fluctuating temperaturesare not stronglyinfluenced. Becauset’isa primary componeti of the turbulentheat flu%W, oneplausibleexplanationis that the two-dimensionalstructuresin the outer shear Iayerdo not necessarily cascade downwardsat sufficientlysmall scales to augmentthe near wall heat transfer. This is an area currentlyunderintensestudy.

0.10

0.05 j

0.00 I 1 1 1 i 1 I ! i 7U o 1 2 3 4 5 e U (mIs) u (mrs)

Mean velocity profilesnear Figure 6. Mean velocity profiles with Figure7. and without forcing the wall 1 1 Wllhhm! tmsfw n w!mcd fudmz 0 wlrn fcdno 0! 75H2. 5$4 A wth fadrg d 1W-h. 1G%) K r 1

Xi12 T(C)

Figure 9. Wall friction coefficient with fbrcing Figure 8, Meantemperature profiles with and without forcing 110 , , 1 1- ‘ 1 1 , 1 2 1 I .xAW$xl I.Wlg F- ~ 100- ;20 -a- .’. 126- ~m-v- !i’I”! \tm -A- 90- -!4- 1 ,40 -0 , I.OQ. i“” N ; : 80- \\ 0’:, 0.76- \)” 1 ~’ .)!, F 70- ‘ ‘: g u i =- O,EO \\ “ { V - 60 ,*3 ~, J ‘t :, ‘, , ., 50-‘ ;\\ ( :: 0.26 GE Myers J J 3C2XIUC,.,,,111.1l. fx-;ti<( 1W3) : ,#,&,b,; 40- i ‘f <\, S2.a 12(x/h)” -“.’(,W, / ,,) < /[ I-(X1 lx)” ‘ ]“ ‘ 0.0 0.1 02 0.2 OA 0,6 0.6 0.7 0.2 OS 1.0 1.1 .0- .WIIIOIJ brcn,g ~. - ?Y \q\g, “m . . RMS,t (C) .A— FOKIIIjIa Irxw. III% “ A .4?, ~ Wb$?%$$

:& 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0:7 0:8 0:6 1:0 1:1 1:2 RMS, t’ ( C)

Figure 10. Normalized Stanton Number Figure 11. Fluctuating temperature

Computational Results

The DNS code described previously was used to investigate the effect of large coherent structures on the turbulent wall jet. A state-of-the-art two-equation turbulence model was implemented in the code. This necessitated the development of an accurate and robust solver for the k-s equations. The code has been tested for the flat plate boundary layer and the turbulent wall jet mean flow. Figure 12 shows the turbulent mean velocity profile in outer coordinates. Excellent agreememtwith the theoretical and experimental data is achieved. III inner coordinates (Fig. 14), a slight discrepancy in the maximum velocity exists, but the overall agreement with the theoretical curves and the experiments is ve~ good. In Figs. 13 and 15, the mean temperature profile is shown in outer as well as wall coordinates. Very good agreement is achieved between the measurements and the computations. For compariso~ various logarithmic laws found in the literature are included in the figure.

08 08 -~— 0.8

g OB s 00s 01 015 02 025 03 M 1-

0 02 . 02

0 0 0..5 1 7s 2 25 3

0 ..-..-—-—— _-_... ------0 1 2 Y [1Y%,

Figure 12. Mean velocity profile in outer Figure 13. Mean temperature profile in outer coordinates coordinates

98 20

~ 10

v’

Figure 14.MeanveIocityprofileinwall Figure 15.Meantemperatureprofile in wall coordinates coordinates

h orderto understandthe heat andmomentumtransfer associatedwith complexunsteadyfihn-cooliig problems,the plane, huninar, wall jet was investigatedexperimentally,theoretically,and numericallyfor the constantwalltemperatureboundaryconditionandwith no fke-stream. When fbrcingis introduced,two staggeredrows of vertical disturbancesdevelop.At high amplitudes,these structures increasethe mixing withinthe walljet, which in turn increasesthe spreadingrate and reducesthe skin friction.In addition,the large structuresentrain add fluid fromthe ambient,and hot fluid is convectedaway fromthe wall, whidi leadsto an increasein the effectivethermal diffision. Locally,the highly unsteadyflow field leads to the developmentof very high wall temperature gradient and in the mean to an inflection point in the temperatureprofileand an increasein the wal[ heat transfer. It is fbundthat forcingboththe principal and subharmonicmodesis most efficient. Experimentalinvestigationsof the turbulent wall jet show that forcing at all frequenciesgenerally decreasesthe wall friction because the growth rate of the jet increases. LoLMy,thedem=seMwall fiction doesnot seemto have a comparableeffecton the wall heat transfer. The wall heat transfer is not stronglyinfluencedby the forcing,possibly becausethe outer shear layer vorticeslhat dominatethe flow whenforcingis introduceddo not necessarilyproducethe small scaleturbulencein the inner regionthat is so importantin scalar transport. Preliminarycomputationalinvestigationsof the turbulent wall jet show that the turbulence model is capable of predictingthe turbulent mean flow accurately. In the next step, disturbanceswill be introducedto investigatethe effect of large, coherent structures on the mean flow characteristics of the turbulent wall jet. Towards this end, preliminaw investigationshave been initiated. Qualitatively,the effectofthe structuresonthe turbulentflowis very similarto the laminarflow.

ACKNOWLEDGMENTS This work was supportedby the UnitedStates Departmentof Energyunder grant number DE-FG03- 93EIU4396.

99 REFERENCES

1. Jeong,J. andHussain,F., 1995.“Onthe Identificationof a Vortex:’ .70urnal of Fluid Mechanics, 285: 69-94. 2. Ka@Y., Horev, E. and Wygnanski, l., 1992, ‘The Forced Turbulent Wall Jet’’,Journal of F7uid Mechanics, 242:577-609. 3. LIMachev,O., 1998, ``Resonti-tiad hteratiion baWall J~''Physics o~~uids, Vol. 10,3:627- 636. 4. Likhachev,O. A., Quintana, D. L. and Wygnanski,I., 1999, “On the Stability of a IaminarWall Jet withHeat Transfer,”Jownal ofFlow Turbulence and Combustion, 62:137-162. 5. Likhachev, O., 2000, “On Harmonic Perturbations in a Turbulent Wall Jet,” manuscript in preparation. 6. Mitachi, K. and Ishiguro, R., 1974, “Heat Transfer of Wall Jets (Lst report: Theoretical Discussions of the Temperature field),” Heat Transfir, Japanese Research, 27-40. 7. Myers, G.E., Schauer, J.J. and Eustis, R.H., 1963, “Plane Turbulent Wall Jet Flow Development and Friction Factor,” Journal ofBasic Engineering, Trans. of the ASME, 47-54. 8. Myers, G.E., Schauer, J.J., and Eustis, R.H., 1963, “Heat Transftx to Plane Turbulent Wall Jets,” Journal of Heat Transfer, Trans. ofthe ASME,209-214. 9. Nizou, P.Y., 1981, “Heat and MomentumTransfer in a Plane Turbulent Wall J~” Journal of Heat Transfer, Transactionsofthe ASME, 103:138-140. 10. Seban,R.A., 1960“Heat Transferand Effectivenessfor a TurbulentBoundaryLayerWith Tangential FluidInjection,”Journal of Heat Transjer, 303-312. 11. Seb~ R.A. and Back, L.H., 1961, “Velocity and Temperature Profiles in a Wall J~” ht. J Heat Mass Transfer, 1961,3:255-265. 12. Seidel, J. and Fasel, H. F., 2000, “Numerical Investigations of Heat Transfer Mechanisms in the Forced Laninar Wall J~” in press, 1 Fluid Mechanics. 13. Quintana, D.L,, Amitay, M., Ortega, A. and Wygnanski, I., 1997, “Heat Transfer in the Forced Laminar Wall Jet” Journal of Heat Transjiw, Trans. of the ASME, 119:451-459. 14. Zhou, M. D., Heine,C. and Wygnanski,I., 1993, ‘The ForcedWall Jet in an External Strea~” AM-4 93-3250, 15. Zhou, M.D. and Wygnanski,I., 1993, “Parameters Governingthe Turbulent Wall Jet and External StreaW’’AIAAJournal, 51(5): 843-853. 16. Zhou, M.D., Heine, C. and Wygnanski,1., 1996, “The Effects of Excitation on the Coherent and RandomMotionin a PlaneWall Je4° Journal of FluidMechanics, 310:1-37.

100 OPTIMIZATION OF HEAT TRANSFER EFFECTIVENESS IN HETEROGENEOUS MEDIA VS.Travkin,LCattonand K. Hu Universityof California,Los Angeles Mechanicaland AerospaceEngineeringDepartment Los Angeles,CA 90095-1597

ABSTRACT Developments of Volume Averaging Theory (VAT)to describe transport phenomena in heterogeneous media are applied to optimization of heat dissipation from a heterogeneous media. The media is an unspecified porous (heterogeneous) layer and the optimization process is accomplished with rigor using the idea of scaled energy transport. The enhancement of heat transport is stated mathematically in a way that the lower scale conventional pin heat transport enhancement and the perfommnce of the total device are incorporated for optimization. The problem is addressed in three steps: 1) solution of a two-temperature problem with inclusion of experimental data correlations, 2) statistical design of experiments (simulating the problem) for problems with many optimization parameters, and 3) optimization of 2D heterogeneous volumetric heat removal by conduction and convective exchange. The analysis distinguishes certain classes of distributed parameter optimization statements whose solutions determine global “in-class” upper limits of heat enhancement (for a given set of physical assumptions). 1. INTRODUCTION Developmentofa VATmathematicalbasisandmodelsforoptimizationofa heterogeneous,hierarchicalscaled media beganwith work by Travkin, Gratton and Catton [1] and is followed by a series of papers [2-4] documenting the development of a method that is applicable to a wide variety of transport phenomena ranging from fluid mechanics to cqwtal photonic band-gap problems [5], clearly demonstrating the interdisciplinary nature the multi-scale VAT description of transport phenomena. The theoretical development of transport phenomena in heterogeneous media with multiple scales has now been brought to the level where a specific application can be chosen for demonstration. The application chosen is enhancement of heat transfer dissipation from a heterogeneous media while minimizing the frictional resistance (a problem of importance to all designers of heat exchangers). This problem has been under investigation for more than 3 decades and in spite of its longevity and importance as a problem, it has not been satisfactorily treated. A majority of past investigations focused on solutions to a specific optimization task with a very limited number of spatial parameters to be varied, usually a fixed geometric configuration, that they tuned in their search for a maximum level of heat exchange (see, for example, Bejan and co-authors [6,7] and references therein). This approach is a “single-scale” approach yielding an optimum for a certain morphology and flow intensity without giving an explanation for why it was achieved. Whhout an explanation, there is no guidance on how to change the design to improve its performance, For each new morphology, the experiment, whether real or numerical, needs to be performed again. In the heat exchanger industry there are countless research studies devoted to tits problem, In this work we outline how earlier studies [1-5] can be applied to a practical application. The present treatment of the heat exchange optimization process can be applied to any specific hierarchical heterostructure with the aim to optimize its performance. What has been done is a demonstration of the only heterogeneous media modeling tool that combines both mathematical and morphological descriptions in one problem statement. 2. VAT EQUATIONS IN THE FORM OF CONTROL EQUATIONS The averaged Iaminar momentum equation

1 6’((7.72(Z))p) ~+((m(z))~)+ UMC..V + uMF.icti.n – UMIW.~ = ~ ~z * (1) is “controlled” by the three morphological terms that are defined as the “morpho-convective” fluctuation field distribution based term UMCOIW(ii, ti, ~%, AQj, A$U = : ((-=),), (2) the interface sutiace skin friction term (3) a% - and the solid phase drag resistance term

(4)

where the second Ieft hand side term d (_(–00) ~) /& presents cross-fluctuations effect. The presence of the vertical velocities - W and W, or fi = W – W, seen in the first term, do not exist at the macrolevel because z direction momentum transport is only present locally close to obstacles. In traditional (homogeneous) one-scale shape optimization approaches these three terms are not presented (see, for example, Ledezma et al. [7]) and, as a result, optimization methods are very restricted in their value and clearly the macroscopic behavior cannot be related to the bottom scale enhancement. The laminar fluid energy equation is

+ T’Mconvx + TjA{convz + TjMs,Lrfx + TfMSUTjZ + l“jM,%chan9e. (5) with the five additional control terms being

(6)

(7)

TfMsw.fx (k, Tj, E%) =‘~ & Tf ds , (8) [/-] as”,

TjMs,,rfz (’, Tj, a%) = ‘: & Tf ds , (9) [v]asw

!?3 ~., TfMac},m,oc (’, Tj, EM,) = + (lo) J ax~ as. Finally the solid phase energy equation has the similar additional terms. In the turbulent regime, the momentum, fluid energy and solid energy equations are similar to what are shown but with an increased number of control terms and more complexity. They are not reproduced here and can be found in [2,4,5]. Some discussion about how they will be dealt with is found in the final section of this papec The control equations are made general by non-dimensionalization with the following scaling, see Fig. 1,

s. = S~Su.,, z = z,,,.z*, z., = ~, ~ = u,.u*, T~ = %, v = .z,r,u,nv”, (m (z)) = m. (m*) , W171 2U:, L* = _& cd = C; @n,, W,n = — kjm = %’%n%f Qf, ‘f = ~~zmumcpfef, ‘. = ‘~zmum+~.- U; ‘ Qf dx Znt‘ The parameters resulting for laminar flow through a morphology that is constant normal to the flow direction are given in the following table with there possible ranges, These parameters are at the discretion of the designer of a heat transfer device and can be used for optimization.

102 Name variable min max Physical meaning of the parameter L3N = Rentf cell.C~S~ 10–~ 5 x 107 influence of media resistance to flow LM4N = Re,nf (l/me) 10-3 105 media Reynolds number =~=w LPG PC,” [bf 2.1 2 x 107 Peclet number, Pe = (#Q (-~ ~)]\2)/af af,s,,, LPO = ‘tS:J = UL,,,SL,,, 1.0 lo~ heat exchange between p;;ses, cY~,S~= ,,,,&~L5;W,,, LP7N = A&;-l)a~s~ o 1020 parameterfrom solid phase energyequation LB8 = * = A~Lp5 10–3 1012 parameterfromII kind BC, see [8] Thereare six nondimensionalcontrolParametersand fimctions,denotedMediumSpecificControlFunctions (MSCF),thatcontrol the heat and momentum~ransportin the selectedporous medium and that can be modifiedto optimize the performance. The two terms with the broadest range also have the greatest influence on the outcome. If the morphology timctions denoting porosity (m(z)), and specific surface area, SW(z) ,are coordinate specific, then the equations and parameters sets are different yielding eight control parameters instead of six. A similar exercise for turbulent flow with (m) = const, SW= const will yield eightoptimization parameters. 3. P1.l13LIMIN~Y OPTIMIZATION METHODS Some simulation results using VATbased transport and closure models for flow in a channel with rib roughened walls, spherical beads, round tube banks and square tube banks yielded optimal configurations. The morphology models used in the numerical simulations are shown in Fig.1(see [9]). The parameterschosenfor simulationof flow acrosssphericalbeads in a channelwere pitch, P = 20mm, channel height, 2h = 200mm,. and bead diameter, 0.001mm < & < 20mm. When the diameter of the beads is large, the disturbance of the porosity across the channel is large and the flow resistance plays an important role. As a result the disturbance of the velocity profile is large. When the porosity approaches unity the disturbance of velocity profile disappears and the velocity distribution approaches the theoretical distribution. From a physical viewpoint this is obvious. When there are no obstacles in the channe[, the channel the results are consistent with the theoretical results in contrast with some other models. The pitch chosen of the rods are the same as those for the beads. The height of the rods is the same as channel height. , The porosity is easily varied from Oto 1.0. by ranging the tube dimension, ~. The friction factor for flow across square tube banks and circular tube banks were developed from the micromodeling results of Souto & Moyne [10] and llhtanabe [11] respectively. By application of SVATclosure models to some general morphology models (orifices and plane slits), in limiting cases, it was demonstrated earlier [1-3,8,9] that both the transport model and the closure scheme are reasonable. At the same time, studying the limiting cases of porosity in the channel highlighted mistakes in other studies. The numerical results demonstrate how the simplest morphological properties of a porous layer such as porosity fiction and specific surface along with closure models naturally affects the transport features and that it can be helpfhl in the development of optimized morphologies. Fig, 2 shows the dependence of the effectiveness number, -Eff, on the porosity for different morphologies at different Reynolds numbers. -Ejf is a combination of the Nusselt number, the filction factor and the pore Reynolds number. Nu Zz&r 4 (m) G d], AP ‘.ff = Rel,mj 1/3‘ with Nu = —, RePm = — andf=— — (11) kf vsl” 2Q,52 () = Fig 2 showshowEf f increasesas theporosityof the channeldecreases.Whentheporo&y decreases,the beadsinside thechannelplaya moreimportantrole in increasingtheheattransferwhileincreasingthe flow resistance.(forchannel filled with regularly arranged spherical beads, the porosity of the channel has a lower limit of 0.4). Fig, 3 and 4 clearly demonstrates an optimum valueof Ef f .When the porosityis higherthan somecriticalvalue, theporousmediaplaya more important role in increasing the heat transfer than in increasing the drag resistance. But when the porosity is too low, the drag resistance will be high and Eff will approach Owhen the porosity approaches O. When the problem becomes multi-dimensional, 6D or 8D, according to [12- 15], it is convenient to use the statistical design of experiment (DOE) methodology. An optimal response surface was found in two steps. First numerical simulation was carried out based on statistical selection of the parameter values. Second a statistical analysis of the results was used to develop a response surface. Thk procedure was implemented using a commercial computer code based on DOE. When the optimization variable is chosen, in our case Ejf,the variables are systematically defined, see the table of parameters developed above. Next, the numerical experiment design type is selected,e.g. a classical two level,

103 mixed level,or nested level. The design type used in this work is the classical two level design. The classical two Ievel designs are based on standard orthogonal arrays that contain two levels for each experimental variabIe. It enables estimation of the effects of some or all terms in a second order model of the general form Efj = aIJ+alXl + azXz + .,. + a,, X,, + MIX? + a12XIX2 + ... + a,,,,, -IX,, L-I -f-a.bnxi The independent variables X1,X2, ...X,, are the design variables L3N...LU8, Based on the design type and design variables, experiment design options will be created. Each option is a set of input parameters for numerical simulation. Description of what was done to obtain the “experimental results” fi-omthe VATbased laminar or turbu[ent transport equations for flow in a specific porous media is described elsewhere (see [8,9]). Afler numerical simulation, the numerical results are rigorously analyzed using statistical analysis tools and graphics tools. These tools include nonlinear response/error analysis, experimental error analysis, regression analysis, residuals analysis, two dimensional graphing, three dimensional response surface graphing, and multi response optimization. One of the response surfaces of our study is shown in Fig. 5. The three dimensional figure shows Ef~ as a tlmction of two variab[es Lp2 and LM4 (these were chosen for simplicity from the eight independent variables analyzed) when the other variables are fixed. Although limited by the range of the variables, the optimum point is shown on the figure, and the trend of the response surface clearly shown in Fig. 5. 4. TWO- AND THREE-SCALE OPTIMIZATION STUDY

Closure of the turbulent regime VATequations for a porous flat channel also requires closure of additional terms in the governing equations. This is done (as for Iaminar regime) using Direct Numerical Modeling (DNM). The four terms arising in the momentum equation are

the seven terms in the fluid temperature equation

and five terms in the solid phase temperature equation

The mathematical implementation needed to obtain closure of the momentum resistance terms, for example, for optimization of the morphology of straight rib fins, see Fig. 6a,b; is dictated by the geomet~ of the fins. For + example, if ds = ~ ds, ; = (-i, O,O)IOS,U,,and ~ = (i, Q O)kt.,, ! then the surface integral over the 8S,. in each of the intermediate REVS not including portions of the flee volume above the fins and those at the bottom of the solid phase of the channel will be, for the x-coordinate frictional resistance component,

The calculation of the form drag portion of resistance loss in momentum VATequation is done in the same

104 This is the cIassical form drag potion of the total kinetic energy loss (shown here only for the x-component). Closure of othertermsin the VATequationsarebasedon the specifictwo- or three scalemorphologieschosen. Ouranalysisof manyexistingmorphologicalsolutionshas led us to concludethat the scaledhierarchicalVAT descriptiongives us the abilityto find an optimummorphologythat cannotbe improvedwhen the selectionof fluids and solid phase materialshas been made, and the pressuredrop through the media is specified. Given these initial conditions(restrictions),it is possibleto find a morphologythat cannotbe improvedbased on two scaleheat transport meaningthat there is no othersolid phasecofilguration that can be more efficientthan the onethat has beenfound, 5. SUMMAW Inthisbrief paper we have illustrated a method hierarchical optimization of two- and three scale heat transport in a heterogeneous media.. It is shown how traditional governing equations developed using rigorous V4T methods can be used to optimize surface transport processes in support of heat transport technology. The difficulty in treating a multiparameter (more than 3 ) problem, even linear, are well known to be very diflicult to overcome using a parameter sorting process. The combination of VATbased equations and the theory of statistical design to was used to effectively begin treating 6D or 8D optimization volumes. Wehave shown how a tsvo scale heterogeneous heat transfer optimization problem can be solved using exact procedures for closure of additional differential and integral JAT terms. This method is shown to be as simple as calculating the appropriate integrals over the morphologies with coordinate surfaces of interfaces pertinent to a morphology of interest, For more complex or even unknown morphologies, as initial spatial morphologies the mathematical methods were out[ined in detail. These three tasks were carried 0U4albeit for some elementary morphologies, for the first time. 6. ACKNOWLEDGMENT This work was sponsored by the U.S. Department of Energy, Ofllce of Basic Energy Sciences under the Grant DE-FG03-89ER14033 AO02. 7. REFERENCES 1. Travkin, VS., Gratton, L., and Catton, I. (1994), “A Morphological-Approachfor Two-PhasePorous Medium-Transportand Optimum Design Applicationsin EnergyEngineering,”Proceedings of the Twe~thSympo- sium on Ene~ Engineering Sciences, Argonne National Laboratory, Conf. -9404137, pp. 48-55. 2, Gratton, L., Travkin, VS., and Catton, I. (1996), “The Influence of Morphology upon Two- Temperature Statements for Convective Transport in Porous Media,” JournalofEnhancedHeat Transfer,Vol. 3, No. 2, pp.129-145. 3. Catton, I. and Travkin, W. (1997), “Homogeneous and Non-Local Heterogeneous Transport Phenom- ena with VATApplication Analysis”, Proceedingsof the 15thSymposiumon Enetgy Engineering Sciences, Argonne National Laboratory, Conf. -9705121, pp. 48-55. 4. Travkin, VS. and Catton, I., (1998a), “Porous Media Transport Descriptions - Non-Local, Linear and Nonlinear Against Effective Thermal/Fluid Properties”, in Advancesin ColloidandInter face Science, Vol. 76-77, pp. 389-443, 5. VS.Travkin and I. Catton, (2000), “Transport Phenomena in Heterogeneous Media Based on Volume Av- eraging Theory”, in print Advances in Heat Transfer,Vol. 34. 6. Bejan, A. and Morega, A.M. (1993), “Optimal Arrays of Pin Fins and Plate Fins in Laminar Forced Convection,” Journal of Heat Transfer, Vol. 115, pp. 75-81. 7. Ledezma,G., Morega,A.M., andBejan,A.(1996), “OptimalSpacingBetweenPin Fins with Impinging Flow,”Journal of Heat i?ansfer, Vol. 118,pp. 570-577. 8. Travkin, VS. and Catton, 1.“A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer,” J. Fluids Eng., 117,181 (1995). 9. VS. Travkin, I. Catton,and K, Hu (1998), “Channel Flow In Porous Media In The Limit As Porosity Approaches Unity”, in Proc. ASME HTD-W. 361-1, Vol. 1, pp. 277-284. 10. Souto, H.I?A. and Moyne, C., (1997), “Dispersion in Two-Dimensional Periodic Media. Part II. Disper- sion Tensor”, Phys. Fhuiis, Vol. 9, No. 8, pp. 2253-2263.

105 .

11 W&anabe, H., 1989, Drag coefficient and voidage fiction on fluid flow through gmnular packed beds, International Journal of Engineering Fluid Mechanics, Vol. 2, No. 1, pp. 93-108. 12. Atwoo~ C. L. (1969), “Optimal and Efficient Designs of Experiments”, Annals of A4athematicalStatis- tics, Vol. 40, No. 5, pp. 1570. 13. Box, G. E. F?and Draper, N. R. (1987), Empirical Model Building andl?esponse Surfaces, John Wiley& Sons,NewYork. 14.Diamon&W.J. (1981),Practical ExperinrentDesignsfor En@”neersand Scientist,Wdsworth, Inc. 15. Montgomery, D. C., (1991), Design and Analysis of Experiments, 3rd Editio~ John Wiley& Sons, New York.

Flow ~h Flow 2h *

1~ ‘r 4 I “ t+

a. Two dimensionalsemi-cylindricalrib type b, Two dimensionalrectangularrib typeroughnessmodel roughnessmodel ,1O.OOOOOO1 ‘Q QoPloo2~ I-L-d IJLI

c. Channel flow across the lattice of spherical beads

/ ■ ■ ,,.’/ -f ,IOW Side view

& T“’’”” ,,,

P d, 4—* / ->

d. Channel flow across rectangular and circular tube banks

Fig. 1 Some channel flow morphologies

106 1 1.2

0.8 1

0.8 0.6 w! $ 0.6 0.4 0.4

02 0.2

0 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Pomsity Porosity

Fig. 2. Channeleffective numberversus l’i~o3. Channel effective number versus porosity for flow across spherical beads. p&osity for flow across square tube banks.

&3 ii

1 moo

0 llm o 0.2 0.4 0.6 0.8 I Porosiy

‘“woq)olw UUIRI?

Fig. 4. Channel effective number versus Fig. 5 Channel flow across circular tube banks porosity for flow across circular tube banks. optimization response surface

107

--- —.. . “i?;#$~;?.;&.>??:“M3&?.:?— .,$’ : . Last REV \ within < intermediate dissipating REV with layer changeable thickness f \ ) 1 I Flow J.:H \l I

Fig. 6 a Flat Channel with Regular Heat Dissipation Layer - in each phase averaging done separately mm

\ Close to bottom REV with changeable thickness

bottom REV with I changeablethickness I A

Fig. 6 b Solid phase temperature 1 and 2 and fluid phase 3 and 4 integrates in volumes separately for each REV and then represents point temperatures in the next scale of the problem

108 USE OF HOT-FILM ANEMOMETRY TECHNIQUE IN HORIZONTAL BUBBLY TWO-PHASE FLOW

Ma Iskandrani and Gunol Kojasoy

Universityof Wisconsin-Milwaukee Departmentof MechanicalEngineering Milwaukee,Wisconsin53201,U.S. A

ABSTRACT

Utilityofhe hot-filmanemometrytectilque in a horizontalbubblyflow-patternis examined. It is shownthata singleprobecanbe usedfor identi@g thegasandliquidphases,Analyzing the natureof the voltagesignal,a signalprocessingschemeis developedfor measurementsof time-averagedlocalvoidfractiondistributionas well as for the measurementsof local mean axial velocityand turbulentintensityin the liquidphase.The signalprocessingschemeis optimizedsoit canbeusedin a ve~ highvoid-fractionregiontowardthetop ofthe pipe,which is the uniquecharacteristicof bubblytwo-phaseflow in horizontalchannels.To veri& the accuracyofthe proposedmethod combined effects of the local void fmction and liquid velocity measurements are checked against the global measurements of liquid flow rate. The results are found to be satisfactory within the experimental uncertainties. Furthermore, the area-averaged void fraction obtained from the hot-film probe measurements compared weI1 with the quick- closing valve technique measurements. The results show that the hot-fihn probe method is accurate and reliable for the local measurements of void fkactiou liquid veIocity and turbulent intensity in horizontal bubbly flow provided that the data is processed properly. Some results of the local measurements of time-averaged void fraction, axial mean velocity and turbulent intensity at relatively low and high gas flows are also presented for a horizontal air-water bubbly flow in a 50.3 mm ID pipe.

INTRODUCTION

Void fraction is considered one of the most important parameters in gas-liquid two-phase flows from an engineering point of view. Several methods are available at present to measure void fraction. These are photogmphic,light attenuation ultrasonic attenuation, double-sensorprobe, impedancetomography, and Laser- DopplerAcmometer (LDA).Thesemethodsfor measuringthe void fmctionare effectiveonly in certainidealized cases. The photogmphic and light attenuation methods cannot be used with opaque walls and are limited to transparentdispersed two-phaseflows with volumetricvoid fraction Icss than a few percent [1]. The ultrasonic method is not restricted to such conditions, and thus expands the measurement of the void fiction beyond the presently available range of fluids and non-opaque systems [2]. However, the ultrasonic attenuation method has a major limitation due to the reduction of the measurement certainty because of the scattering echoes, and thus it is

109 restricted to low void fkaction bubbly systems. The X-ray computed tomography, impedance tomography and ring- type conductance transducer were used to determine the cross-sectional or volume averaged void fmction [3]. However, the local void fkaction cannot be measured by such technique, Several attempts have been made to extend the use of LDA to bubbly flows [1,4]. In a ve~ recent work of Suzanne et al. [5], it was concluded that at void fraction greater than about 2% the LDA signal is no longer suitable because of the inc~ase of the beam interruption mte by the bubble crossing. In this case the hot-fihn anemometry was recommended. It is to be noticed that with the exception of the work of Kocamustafaogullari and Wang [6], tdl of the bubbly flow experiments were carried out in vertical flow channels. Even in the case of well-studied vertical flow configuration experimental resuIts from fairly diverse sources are controversial regarding the void fraction distributions and the effects of the bubble size and flow conditions causing void profile transformation from a saddle shape into a convex shape. The difticukies in obtaining completely similar general results undoubtedly stem from our lack of understanding of the mechanisms involved in determining the internal structure of bubbly flow. Furthermore, due to basic internal structural differences between the vertical and horizontal bubbly flows, it is impossible to extend the vertical bubbly flow results to horizontal bubbly flows. In light of the above discussion, it is evident that much experimental work is still necessary to attain a thorough physical understanding of the internal structure of horizontal bubbly two-phase flows. In view of the intention to measure local variables in a horizontal bubbly two-phase flow with local void fraction possibly ranging from O- 65?Z0,it is unavoidable that a probe method must be used. In this contex~ an experimental investigation has been underway at the University of Wisconsin-Milwaukee to study the air-water bubbly two-phase flow characteristics along horizontal flow channels using the hot-film probe technique. The primary purpose of this research is to show that the hot-film anemometty technique can be successfully used in horizontal bubbly two-phase flows ● to identi& liquid and gas phases (phase separation), from which the local volume fraction can be evaluate~ ● to evaluate the local time-averaged axial liquid phase mean and turbulent fluctuating velocities, . to measure the local void fraction and local bubble passing frequency of the two-phase flow, and finally, . to investigate the dependence of the local parameters on other flow variables,

2. HOT-FILM ANEMOMETRY TECHNIQUE

2.1 Princiule of Measurement Hsu et al. [7] and Delhaye [8] were the first to study the response of hot-film probes in a liquid-gas two-phase flow. Since the% this technique has been used extensively [9-14] in vertical bubbly flow pattern. However, only limited effofls were made to examine two-phase flow characteristics in large scale experimental programs in horizontal bubbly flow channels. In principle, the hot-film probe provides information about the flow field by relating the changes in this field to changes in the heat transfer at the probe tip surface. As the fluid flows past the constant temperature hot-film probe, changes in the fluid velocity, including turbulence fluctuations, cool the sensor at different mtes. These changes in cooling rates result in voltage changes in the anemometer. In the case of an air-water two-phase flow, very shaqJ variations occur in the anemometer voltage output as the probe tip goes through a gas-liquid interface because the heat-transfer characteristics of air is completely different than water. Atypical sensor output for two- phase bubbly flow is illustrated in Fig. 1. As seen in this figure the sensor encounters both liquid and small gas bubbles several times in a very short period. After the sharp initial drop, caused by the probe piercing the front of a bubble, the voltage gradually continues to decrease while the sensor stays inside the bubble. This is due to the evaporation of a thin film of liquid that remains on the sensor. On the other&m& the output signal from the probe shows a very sharp increase to the previous voltage level upon exiting the gas bubble due to wetting of the sensor. It is interesting to notice thag when the liquid wets the sensor, the signal rebuilds after a very short period during which it exhibits an overshoot. This is usually the case because the hot-film anemometer circuitry tends to overcompensate the voltage increase when liquid suddenly envelopes the tip of the probe. In the upper portion of the pipe, the probe encounters plenty of bubbles, or partial bubbles hits, where the residence time in gas bubbles and liquid is too short to show the basic output characteristics of the probe and

110 >..,

consequently becomes harder to aurdyze such signals. When the probe is in the ~ the signal is no longer representativeof the velocity, it is thus necessay to removethis part of the signalas discussedin the next section,

2,2 Signal Processing 2.2.1 Phase Separation The first requirement in evaluating a two-phase flow with a hot-fihn probe is the ability to identi@ and differentiate the gas and liquid phases on a record of the anemometer signal. A number of investigators have reported utility of the hot-film anemometry in two-phase flows. In these investigations a variety of bubble detection techniques, consisted of detecting the voltage changes associated with a change in phase, have been used. In the present investigation%Farmr et al. [15] and Lewis [16] methods were combined to develop a reliable detection technique based on an interactive amplitude and threshold procedure. This new technique tackled the inherent problems in high-speed, high void fraction bubbly flows. Serious problems associated with previous methods when applied to a horizontal bubbly flow can be summarized as follows: FMIy, very small bubbles or partial bubble hits produce signals that do not fall below the voltage level corresponding to the lowest continuous liquid phase velocity fluctuations. Therefore, they can not be detected. Secondly, the overshoot in the hot-film signal results in a significant negative slope during the decay process following the overshoot. This may be interpreted as being due to the passage of a bubble front interfaces. The overshooting may cause serious errors in time-averaged void fraction calculation or it might cause major incorrect evaluation of turbulence. The voltage output was recorded on disk. The derivative of this output signal with respect to time was then calculated This derivative represents the slope of the output signal. By plotting the anemometer output and the slope on the same time scale, the effects of a bubble striking the probe can be seen as in Fig. 2a &b, For each bubble passage, the slope signal shows a sharp negative spike for the nose of the bubble foIfowed by a sharp positive spike for the tail of the bubble. The power required to heat the sensor in the gas phase is considerable less than in the liquid phase. Similarly, the positive spike in the slope signal is a result of the increase in power required to maintain the sensor tempemtnre as the probe reenters the liquid phase. From here, it is a matter of determining the proper threshold values to detect the spikes in the slope signal. The first threshold is used to determine the rear of the gas bubble. Its value must be positive. This slope threshold value is the most important because it has the largest magnitudes and is unaffected by any of the flow characteristics. Therefore, it is the easiest to detect. Its value should distinguish between the peaks caused by liquid interface and those from the turbulent fluctuations. The turbulence slope values were of a magnitude of less than 250. By plotting the anemometer output voltage data and the corresponding slope, as seen in Fig. 2a &b, the positive value of the slope can be recorded for each liquid slug occurrence by visual inspection. This was done for experimental data covering the entire range of gas and liquid flow rates.Therearofbubblewasfoundto causea positivepeakwitha magnitudegreaterthan500.Thisvaluewasusedasthethresholdforthebubblereardetection or liquidslugbeginning.Whenthis thresholdvalue is reachedor exceeded,in the positiveplane, the phase separationstepsignal,&is setequaltounityindicatingtheliquidphase(Fig.2c). Similarly,a secondthresholdvaluewasfoundforthenegativespikecausedbytheprobehittinga gasbubble. Thesenegativepeakswerefoundto havea magnitudegreaterthan300in the negativeplane.It is obviousfrom Fig.2bthatthe magnitudeofthis slopeis usuallysmallerthanthepreviousone,becausethe dropin thevoltage occursgradually.Soit is harderto detectand easierto be feignedby the turbulencefluctuations.Thisk whya conservativevalueof-500 hasbeenusedas a bubblefrontdetectionthreshold.Thisvalueis usedto identi&the bubblesonlywithrelativelycleartail voltagesignal.The principalslope is going to be incorporated to double check the validity of the negative slope as discussed later. To ensure that all bubbles have been dctcctcd and to take care of the overshooting, the program works backward whenever thefirstthreshold occurs to indicate a start of liquid phase. Since this threshold is very distinct and impossible to miss, it sets up the base for the further signal analysis. The signal processing program works backwardly forcing all data to be gas until another first threshold value or a third threshold event (whatever comes first) takes place, The third assigned slope theshold value is of importance when the second threshold bubble start detection ihils. Because some bubbles, small ones in particular, in!roduce intermediate negative slope, which may be hard to differentiate from velocity fluctuations negative slopes, the third slope threshold makes the detection of gas phase more lenient Therefore its value is set to -250. This, in its absolute plane, i; much less than the slope associated with intcrfaca passage but slightly greater than the slope of most velocity fluctuations. h this way we get a narrower band of liquid voltage signal, which results in detecting smaller bubbles. The third threshold works in conjunction with an amplilude threshold, which will be discussed in the next section.

111 When the entire data signal has been analyzed in this way, the progmrn returns the phase separation step signal. This signal is used for the void fraction analysis and helps to assign the liquid phase data used for velocity analysis. One problem with the above method, and any other method involving an immersed probe in the two- phase flow, is as described by Wang et al. [17], the probe deforms and deflects the bubbles prior to piercing. This would lead to an underestimation of the void fraction.

4.5

4.0 2.0 ; ‘“5 1.000 1.002 1.004 1.006 1.008 1.010 3.0 15000 12500 2.5 &M: 2.0~ -5000 0.000 0.002 0.004 0.006 0.000 0.010 2500 Time (s) 4 -2508 .5000 1.000 1.002 1.004 1 .Ooa 1.008 1.010 Figure 1. A TypicaI Hot-Film Output in a Horizontal

Bubbly Flow G- *~-.-..~K.m ....~K.-m glJ- . ..~ ...... k. . .. i ! & -1 , , 1 4.0 1.000 1.002 1.004 i .006 1.008 t.oio la la 3A

20 1.000 1.002 1.004 i .006 1.008 1.010 TIME (s) 24 ———.—— 21 ——— (.1 13 ] “v 0 a 2000 4000 ~000 lb!, (,) V.U. B*Ft, q (If,) Figure 2. Anemometer Output and Signal Processing: (a) Anemometer Output Signal; (b) Slope of Figure 3. Determination of Threshold Voltage: Voltage Output; (c) Phase Separation Step (a) Sample Voltage Output(b) Probability Signal; (d) Velocity evaluation function. Density Function for Voltage Output.

2.2.2 Determination of Proucr Data Set for Velocitv Analvsis In the preceding section it was demonstrated that the proposed bubble detection technique can identify the starting and ending times of virtually every bubble event within hot-film signal. Nevertheless; using all iden-tiled liquid phase data for velocity analysis causes significant error. Similar to the phase separation method another method has been developed to identify the proper data set that should be used in liquid velocity data processing. The back-bone threshold value for this task is the voltage amplitude threshold Unlike the previous technique, this one is only of practical use if a method of automatically determining suitable values for the amplitude can be identified. This was achieved by using the probability density fimction (@f). Fig. 3 shows the digitized pdf corresponding to a large sample of hot-film probe data obtained at a certain probe position in a typical bubbly flow. A sample of the hot-film signal from which it was obtained is also shown in the figure. The pdf is observed to have a bimodal shape consisting of two peaks separated by a low level plateau region. The upper peak represents the high voltage associated with liquid phase, while the lower peak represents the low voltage associated with gas phase. In the current program the lower peak, which is located near the bottom of the hot-film signal% is not determined and thus our pdf is truncated to accommodate only the large peak. This peak corresponds to the voltage/velocity associated with the continuous phase turbulence. A point on the voltage scale of the pdf slightly below that corresponding to position “c” on Fig. 3 is an ideal choice for voltage amplitude threshold since it will be low enough to avoid mistaking any turbulence velocity fluctuations and high enough to detect the majority points in gas phase. After identifying the amplitude threshold vahe internally by the computer progr~ the points with voltage higher than this threshold value and their slopes within the first and second threshold slopes are only considered for velocity analysis. The data points associated with over-shooting, at the rear of bubbles, are excluded again by proceeding backwards. By working backwards, the current point is compared with the previous few points. If the current point voltage is higher than the voltage threshold value and its slope is lower than the second slope, then it

112 is identified as overshooting provided that the @nediate preceding points have the massive positive slope. In Fig. 24 the velocity evaluation step signal is shown for the corresponding anemometer output voltage, slope, and phase separation. In this figure, unity indicates acceptable data point for velocity analysis, zeros are not admissible points and should be excluded from any I%rthervelocity analysis,

2,3 Statistical Processing of The Data Although the actual voltage change in a hot-film probe signal due to the probe encountering the bubble is not important or accurate, the time that the probe is exposed to the bubble can be used to determine the local time- averaged void fractiou g at any poin~ r. It is defined as a time-average of the concentration%@,t), by

C@- lili~~(l - ~(r,t))dt (1)

where, 4 as a fiction of the space coordmte, r, and time, $ is equrd to Oif the probe sensor is in the gas phase and equal to 1 if the sensor is in the liquid phase. Equation (1) can be written in discrete form as follows

a(r) = —j .~1(t2i - t2i-1) (2)

where i indicates the iti gas bubble and t2i.1and tzideilne the time when the probe enters into the gas bubble and liquid, respectively, the number of gas bubbles passing the probe sensor in the totrd sampling time, L is n. The local meanaxialliquid velocity and the values of turbulent fluctuations were calculated by using

u~mn(r) = ~}lUk(r,t) (3)

and

u’(r) = (4) + XV =,[u,(r,t) -u mean(r)]’ /[[ 11 respectively. In Eqs. (3) and (4), uk(r,t) is the instantaneous axial velocity for the kti data point in the liquid phase, and N is the total munber of data points in the liquid phase of the digital sample, k = 1....N. To remove the error caused by the intermittent wave motion, the time-based filtering process was developed in calculating turbulence fluctuations, Iskandmni [18].

3. EXPERIMENTAL RESULTS AND DISCUSSIONS

A sample of the time-averaged local void fraction, U, liquid-phase mean axial velocity, U.~, and the turbulence structure as presented by the turbulent velocity, u’, and turbulent intensity defined as (u’AJ~,mld), are described in Figures 4 and 5 for relatively low and high values of

3.1 Void Fraction Profiles As described above, the time-averaged local void fraction measurement is calculated by Eq. (2). The void fraction distributions are illustrated in Figures 4C and 5c. It is evident from these figures that the void fraction distribution shows a shmp decrease toward the bottom of the pipe and practically becomes zero at a certain probe position r~ indicating the existence of a liquid layer free of voids except near the wall of pipe, where the profile of void fraction starts to build up again. This liquid layer thickness decreases by increasing gas flow mtes at a given liquid flow. It covers a liquid region between r/R= 0.2 and r/R= -0.8 at

113

-.. Bubbles tend to migmte toward the upper wall under the dominating influence of buoyancy force. Thu$ the void ffaction under all test conditions generally showed distinct peak near the top wall at about r/R aY0.8 to 0.9. This range corresponds to 2.5-5.0 mm distance from the wall. This observation is more pronounced at high gas flow rates, since at low gas flow rates the void fraction profile peaks at the wall itself, or too close to not reachable by the finite probe size. This peak which appears in most cases, can be attributed to the increased hydraulic resistance of the liquid path between the bubble and wall which may cause a sharp decline in void fraction. This phenomena is identical to the one that has been observed in vertical bubbly two-phase flows [9, 10, 17] and in horizontal bubbly flow [6] using double-sensor resistivity probe.

a 1.0 iii

0, .0 & _-...~-.-..:,.-. ..j....- ;0.4 ~ ~~ 0.2 ~: ~ (a) 2 0.0 -1.0 -0.5 0.0 0.6 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0H.0.6 0.0 0.5 1.0 -1.0 .0.5 0.0 0.5 1.0 PostIbrI, rlll Position, r/R Posllion, riR Po81Uon, rlR 1.0 0.25 . ::! ;; 0.20 ..+...... ;...... {...... ii: ::I:31EI 1°”20.0.16 .““-...... “~’’”’””””:--”’-””’”””””’”...y...... W-...j...... g o.~ .._j_...... _..&.. ~“/li x 0.4 ----.+--+’ --+-- ~i 0.10 ...... ;...... /..”.-f....” ,.-.... 2 (J,2 ._..+.._+. ...+.. -. % 0.06 ..- ‘,.. .--j--- , (c) :. : (d) 0.0 nb 0.00 ‘ ‘ -1.0 -0.6 0;0 0.6 1.0 -1.0 -0.5 0.0 0.6 1.0 :D!B-1:0 -0:5 0:0 0:5 1;0 -1~0 -0;6 0:0 0:6 1.0 Posltbn, riR Posltlon, rlR PoWlon, rlR Poslllon, r/R

Figure 4. Two-Phase Flow Data for = 4,4 nds and Figure 5. Two-Phase Flow Data For

3.2 Mean Velocitv Profiles The mean velocity profiles as documented on Figures 4a & 5a show asymmetric character with the largest velocities located at the bottom part of the pipe. The degree of asymmehy is shown to decrease with increasing liquid flows or decreasing gas flow. An interesting feature of the velocity profile is that the velocity distribution witlh the bottom liquid layer exhibits a fully-developed turbulent flow character as demonstrated by the l/7th power law profile. The l/7th power law was fitted by the experimentally measured maximum velocity located in the liquid layer. Obviously, the maximum velocity in this ‘liquid layer’ occurs slightly off the pipe centerline (i.e. - 0.2s r/R.5 O). It is interesting to note that although the value of this maximum velocity increases as either the gas or liquid flow rate increases, the location of the maximum remains almost unchanged. It is evident that within the high population bubble region at the upper portion of the pipe the mean liquid velocity decreases sharply towards the upper pipe wall. Its values go even below the single-phase profile. This sharp drop in the liquid velocity maybe attributed to two reasons. Firstly, when the bubbles present they induce additional turbulence which is called the bubble induced turbulence. As a result a shaqI increase in turbulence due to presence of bubbles naturally reduces the mean local velocity. Secondly, increased bubble population toward the top of the pipe creates an additional resistance to liquid flow resulting in retardation of the liquid meanvelocity in this region. These combined retardation of increased bubble population turbulence and the resistance to the liquid flow results in considerable reduction of the mean liquid velocity toward the top of the tube. On the other Inn& the reduction of the liquid mean velocity in this region causes considerable increase of velocity in the rest of the pipe to maintain the overall continuity requirement. This observation is most pronounced at low liquid flow rates, since in this case bubbles are concentrated at the uppermost part of the pipe and plenty of room for the liquid (i.e. easier path) to flow.

114 .,. ,. .<,.,,, ,, , .,.

3.3 Turbulence Structure The turbulence structure is presented in terms of the axial turbulent fluctuation and the turbulent intensity as defined by (u’/Um,al~). The turbulence fluctuations, u’, always increases when the gas introduced as seen in Fi~es 4b & 5b. In the lower pmt of the pipe, the slight increase is compared to the single-phase profile. However, at the upper part of the pipe where the population of bubbles is him it substantially increases until it peaks and then drops down abruptly in the region next to the wall. It is interesting to notice that the location where u’ starts to buildup is exactly the location where cxdistribution initiated to take off. Moreover, the level of void fraction profile determines the level of turbulence velocity. This indicates that the liquid turbulent velocity, u’, is a strong fimction of bubble population i.e., bubble induced turbulence. This observation is similar to what is observed in vertical bubbly flow [11] and others that turbulent kinetic energy increases strongly with void fraction. Figures4d & 5d of turbulence intensity (u’/tJ~~jA further ver@ our results of u’ values. The smprising identical trend of turbulence intensity in the lower part of the pipe between single-phase and two-phase confhm the liquid layer existence. That means introducing air has no effect on turbulence intensity in the liquid layer. On the other ha@ the intensity increases rapidly as void fraction increases. It is very interesting to notice that u’/u~W1~ is iimction of u for a certain setting of

4. SUMMARY AND CONCLUSIONS

The internal phasedistribution of concurrent air-water bubbly flow in a 50.3 mm ID transparent horizontal pipeline have been experimentally investigated by using the hot-film anemometry technique. The gas volumetric superficial velocity changed from 0.25 to 0.8 m/s while the liquid volumetric superficial velocity keptfixedat 3.8 rids,The time-averagedlocalvaluesof the void fractio~ the meanliquidvelocity,and the liquidturbulence fluctuationsweremeasured. An improveddigitalprocessingmethod based on a combination of amplitude and slope thresholds has been developed to ident@ the phases in the hot-film anemometer output signal due to the passage of bubbles in a high- specd bubbly two-phase flow. This technique has proved successful in iden@ing virhudly all bubble passages, including partial hits and very small bubbles and in determining the appropriate signal data for velocity analysis. The method has the advantage of incorporating the probability density iimction of the anemometer output signal to obtain automatically suitable value for the voltage amplitude tlucshold. The experimental results indicate that the void fmction has a local maximum near the upper pipe wall. For the horizontal bubbly flow, the observed time-averaged local void fraction can reach as high as 65%. It was found that increasing the gas flow rate at fixed liquid flow ratewould increase the local void fraction, The axial liquid mean velocity showed a relatively uniform distribution except neartheupper pipe wal~ where a sharp reduction in velocity was noticed. The local mean liquid velocity and turbulence fluctuations increased with gas flow rate. It was also concluded that the local turbulent intensity is mainly a function of local void fmction,

ACKNOWLEDGMENTS

The work reported in this paper was performed under the auspices of the U.S. Department of Energy, Office of Basic Energy Sciences. The authors gratefully acknowledge the support of the U.S. DOE/BES under the dmction of Dr. R. Price and Dr. R Goulard. REFERENCES

1, K. OHBA and T. ITOH, “Light Attenuation Technique for Void Fraction Measurement in Two-phase Bubbly FIow-11,”Experiment. Technol. Repofi Osaka Univ. 28 (1449) (1978) 2. H. P. BENSLE~ J. M. DELHAYE and C. FAVREAU, “Measurement of Interracial Area in Bubbly Flows by Means of Ultrasonic Technique: Proc, the Nat. Heat Tranfer Conf, Pittsburgh, PA.(1987) 3. H. LEMONNIER and J. F. PEYTRAUD, “Is 2-D Impedance Tomogmphy a Reliable Technique for Two- Phase FIowY OECDMeeting on Instrumentation, SantaBarbn CA. (1997) 4. T. G. THEOFANEOUS and J. SULLIVAN, “Turbulence in Two-phase Dispersed Flows; Z Fluid Mech. ~, 343 (1982) 5. C. SUZANNE, K ELLINGSEN, F. RISSO and V. ROIG, “Local Measurement in Turbulent Bubbly Flows; Nucl. Eng. andDes. .lS4, 319 (1998) 6. G. KOCAMUSTAFAGULLARI and Z. WANG, “An Experimental Study on Local Interracial Parameters in a Horizontal Bubbly Two-Phase Flow; M J Multiphase Flow ~, 553 (1991) 7. Y. Y. HSU, F. F. SIMONand R W. GRAHAM,“Applicationof Hot-WireAnemomeWfor Two-phaseFlow Measurements such as Void Fraction and Slip Velocity,” Proc. ASME Winter Meeting, Philadelphi~ PA.(1963) 8. J. M, DELHAYE, Hot-Fihn Anemometry in Two-Phase Flow: Two-Phase Flow Instrumentation, B. W. LB TOURNEAU and A. E. BERGLES, Eds., ASME, (1969) 9. A. SERIZAWA. I. KATAOKA and I. MICHIYSHI. “Turbulence Structure of Air-Water Bubblv. Flow-I. Measuring Tecl&iques,”Int. J Mul!iphase Flow 2!,221 (1975a) 10. A SERIZAWL I. KATAOKA and I. MICHIYSHI, “Turbulence Structure of Air-Water Bubbly Flow-II. Local Properties? lnt. J. Multiphase Flow z, 235 (1975b) 11. M. LANCE and J. M. BATAILLE, “Turbulence in the Liquid Phase in a Uniform bubbly Air-Water Flow: Z FluidMech. ~, 95 (1995) 12, T. J. LIU and S. G. BANKOFF, “Structureof Air-WaterBubbly Flow in a Vertical Pipe-I. Liquid Mean Velocityand TurbulenceMeasurements: Int. J Heat Transfer~, 1049(1993a) 13. T. J. LIU and S. G. BANKOFF, “Structureof Air-WaterBubbly Flow in a Vertical Pipe-II. Liquid Mean Velocityand TurbulenceMeasurement” ht. J Heat Tran#er ~, 1061(1993b) 14. T. HIBIKI, S. HOGSETI’ and M. ISHII, “Local Measurement of Intcrfacial Ar% Interracial Velocity and Liquid Tudxdence in Two-Phase Flowfl OECDMieeting on Instrumentation, Santa Barbw CA. (1997) 15. B. F~ A. L. SAMWAYS, J. ALI and H. H. BRUUN,, “A Computer-Based Hot-Film Technique for Two-Phase Flow Measurements,” Mess. Sci. Technol. ~, 1528 (1995) 16. S. LEWIS, Use OJ Hot-Film Anemometry in Horizontal Slug Flow, M.S. thesis at the University of Wisconsin-Milwaukee (1996) 17. S. K. WANG, S. J. LEE, O. C. JONES, JR. and R T. LAHEY, JR “Three-Dimensional Turbulence Structure ad Phase Distribution Measurements in Bubbly Two-Phase Flow,” ht. J MuItiphase Flow 13, 327 (1987) 18. A. ISKANDRANI, Use oJ Hot-Fihn Anemometry in Horizontal Two-Phase Bubbly Flow, M.S. thesis at the Universityof Wisconsin-Milwaukee(1997)

116 MICRO FOUR-SENSORPROBE METHODFOR INTERFACIALAREA MEASUREMENT ANDAREATRANSPORTEQUATION

M. Ishii and S. Kim

School of Nuclear Engineering,1290NE Purdue University, W. Lafayette, IN 47907-1290

ABSTRACT

A newly developed micro four-sensor conductivity probe is presented. The new probe is applicable to a wide range of two-phase flow and capable of acquiring the time-averaged local two-phase flow parameters of various types of bubbles. The data acquired by the probe are categorized into two groups in view of the two-group fluid particle transport; namely spherical/distorted bubbles as group 1 and cap/Taylor bubbles as group 2. Benchmark experiment employing the image analysis method is ~erformed. to validate the Probe method, and a good agreement is observed. The data obtained by the probe in the bubbly and bubbly ~o slug transition condition is compared with the one-group interracial area transport equation.

1. INTRODUCTION

[n the two-phase flow system, the interracial area concentration (a,) and the void fraction (a) are two of the key geometric parameters in fluid particle transport and heat transfer capability. 1n view of detailed assessment of the given two-phase system, many two-phase system analysis codes employ the formulation using the two-fluid model[l ], which is based on the detailed treatment of the phase interactions at the interface. However, since the two-fluid model solves the conservation equations for each phase separately, the phase-interaction terms arise. They are expressed in terms of a, and the driving force such that (Interracial Transfer Term) - a, X (Driving Force). (1) Therefore, the closure relation for the ai is indispensable for accurate assessment of the two-phase flow system using the two-fluid model. [n efforts of solving this closure problem in the two-fluid model, Kocamustafaogul lari and lshii[2] established the foundation in developing the interracial area transport equation. [t was followed by recent efforts by Wu et al.[3] and Kim[4]. Nevertheless, in order to evaluate the existing model, the detailed local measurement of the two-phase flow parameters should be established. The conductivity probe was first proposed by Neal and Bankoff15] accounting for the fundamental differences in conductivity between water and air. With the acquired signals from the multi-sensor probe, the local time-averaged two-phase flow parameters, such as a, and a, can be acquired. The double sensor conductivity probe has been employed in dispersed bubbly flow conditions, whereas the four-sensor probe has been applied in cap or slug flow conditions.

The measurement principle of the multi-sensor conductivity probe in obtaining the local time- averaged aj, is based on the definition given by lshii[ 1], such that

(2) where J denotes the j’” interface which passes a local point during the time interval, AT, Here, vi and ni are the bubble interracial velocity and unit surface normal vector of the j’h interface, respectively. In view of this, Kataoka et al.[6] formulated a mathematical method to determine the local time- averaged a, for both double-sensor and four-sensor probes. In the application of the double-sensor probe, it was suggested that 1 Z;(xo,yo,zo)= 2N, (3) ]VJ;OS$ where N, is the number of bubbles which pass the point (x(J,y(,,zJ per unit time, and @ is the angle between the unit normal of the bubble interface and its interracial velocity. In formulating equation (3), however, it was assumed that the bubbles are spherical in shape, and every part of the bubble has equal probabi Iity of being intersected by the probe. The application of the four-sensor probe, on the other hand, is important when the size of the bubbles become larger and they are no longer spherical in shape. In the four-sensor conductivity probe, the local a, is acquired by acquiring three components of interracial velocity. For example, when the directions of the three independent probes are chosen as the x, y, and z axes, the time-averaged a, can be acquired[6] by

(4)

Therefore, unlike the doubie-sensor probe technique, no hypothesis for the bubble shape is necessary in the mathematical formulation to calculate the local afi

In previous studies[7,8], however, some major shortcomings have been reported in applying the four-sensor conductivity probe, which had prevented the probe from being used in practice. These shortcomings included missing bubble signals and deformation of the bubble interface.

2. DEVELOPMENTOF THII MICRO FOUR-SENSORCONDUCTIVITY PROBE METHOD

To minimize the limitations of the conventional probe, new designs are sought for the new probe configuration. Both the conventional and the newly designed four-sensor probes are illustrated in Figure 1. The significant reduction in the cross-sectional measurement area of the newly designed probe and its sharply tapered tips of the sensors can effectively minimize both the number of missing bubbles and the deformation of passing bubble interfaces. The new probe also accommodates the double-sensor probe capability in the four-sensor configuration, such that it can be applied in two- phase flow regimes spanning over bubbly, cap, slug, and churn-turbulent flow.

118 . ,’

tl)ermocouplewim . .. .

S.S. tubing . . ,.

/ sensors -..

.- ‘n+’” : — ,’, ,w - I mawmmenf a-w S 0.2 umi~ I 7 Ji4k 3~1 * [ :; “, Figure 1. Schematic diagrams of the conventional and newly designed conductivity probes.

Furthermore, in the new signal processing scheme, the signals are categorized into signals of spherical, distorted, cap, and Taylor bubbles based on the bubble chord length information acquired by the common sensor (sensor O in Figure 1). In the present experiments, spherical and distorted bubbles are categorized as group 1, and the cap and Taylor bubbles are categorized as group 2. In identi~ing the bubble types, the maximum distorted bubble limit and the spherical bubble limit given by Ishii[9], and Ishii and Zuber[lO] are used as criteria, such that ~ _ ~ 2ts ~,,j ; spherical bubble limit where ~ Pf ([f- (5) 4–gAp ‘f Pj = !2 p,o ;:p [ r) and .-—- D =4 ~ ; maximum distorted bubble limit (6) (/llUl\ JgAp Recently, in view of the double-sensor probe application, Wu and Ishii[8] suggested a correction method accounting for the missed interfaces. In this study, they considered the effects of the lateral movement of the bubbles and the probe tip spacing (1u in Figure 1). By determining the calibration factor f the formula given by Kataoka et al.[6] was improved as “-

2fv - ~(A”) with Jo,”, =2+ ~ 2“2’ -1 for As= 0.36 al = .loI(t D~ -0.86 D~ (7) [)[”AsA; N; – Nn,in] [)VI,

where IVl,is the number of total bubbles obtained, vfi’ is the fluctuation of bubble velocity, ~ is the average bubble velocity obtained by effective signals, and At,, AT, As are the time delay obtained by effective signals for the j’” bubble interface, total sampling time at a local point, and distance between two tips of the sensors, respectively. For bubble sizes varying from 0.6 to 1.4 times the mean bubble size, it was found that the al calculated by equation (7) would result in a statistical error of ~7.v0 for a sample size of approximately 1,000 bubbles[8].

For bubbles whose shapes are not spherical, the local time-averaged a, is obtained by the signals acquired from the four sensors. Unlike the double-sensor method, the corrections for the defective signals from the distorted and cap bubbles are made in two steps in estimating the local ai, such that ‘f”f=zfff[%l+zir~(%) (8) where i?ii,etiis the average al calculated with effective bubble signals, ~g~ is the number of effective bubble signals, N,,,,.is the total number of bubbles counted by the common sensor, and subscripts f and r denote front and rare bubble interfaces, respectively. Furthermore, in order to account for the _-—

missing signals due to the steep interface of Taylor bubbles near the wall, the correction method by Ishii and Revankar[7] is employed such that (9) where A(,,i,.,is the number of missing Taylor bubble interface, [h is the residence time of the missing bubble signals, AT is the total sampling time, ~, is the average distance between three independent sensor pairs (i.e., 112,113,and /23 in Figure 1), and A.$is the measurement area of the probe.

3. BENCHMARK OF THE PROBE

Two separate benchmark experiments employing the image analysis method are performed in order to validate both the double-sensor and the four-sensor method. The benchmark experiments for the double-sensor probe is performed in a transparent air-water vertical rectangular flow duct[ 11]. A computer code developed by Zhang and Ishii[ 12] is used to process the captured images to obtain the location and the diameter of each bubble. The typical result from the double-sensor probe benchmark experiment is shown in Figure 2. The relative percent difference between the two- methods is within * 10-VO. Considering the limitation of the image method near the edge of the viewing window, the results from both measurement methods agree well.

In benchmarking the four-sensor probe, on the other hand, an adiabatic air-water two-phase flow loop of 5.08-cm ID with 375-cm in height is employed. Bubbles are generated through stainless steel hypodermic tubes of O.12-mm in ID, which are arranged in a 20x20 square matrix. The probe is traversed by a micrometer at a fraction of 1.27-mm from the center to the wall of the test tube. In the present experiment, the gas flow rates are varied by jg=0.052, 0.179, and 0.432-m/s while the liquid flow rate is fixed atj~O.321-m/s. The data acquired by the probe is then benchmarked by the images of Taylor bubbles captured in the test loop as shown in Figure 3. From the captured images, the contour of the Taylor bubble is calculated with respect to the slug length assuming symmetric front and flat rear interfaces. The agreement between the calculated values and the experimental data is quite acceptable in both czand a,. Some deviations may be due to the errors in estimating the Taylor bubble chord-length and to the fact that the image analysis assumes the smooth and symmetric front and flat rear interfaces.

4. EVALUATIONOF THE ONE-GROUPlNTERFACIALAREATRANSPORTEQUATION

The objective of developing the interracial area transport equation is to replace the flow regime dependent correlations for the ~i in the thermal-hydraulic system analysis. The approach employing such correlation does not dynamically represent the changes in interracial structure, such that it can not only induce non-physical oscillations in system behavior but limit the code accuracy. Therefore, improvements in the treatment of interracial structure and flow regime transition will greatly enhance the capability of the system analysis codes. In what follows, the one-group interracial area transport equation applicable to the two-phase flow in a round tube geometry is presented along with the evaluation results against the data acquired by the newly developed probe. For the detailed formulation procedures and the mechanistic modeling, however, authors recommend the readers to refer to references[3,4] given earlier.

120 o Illl(lgr Ind,l,l

— lJuulie.xtwwpmbr

I:/ii

Figure 2. Typical results obtained from the comparison between the al measured by the double-sensor probe and that from image analysis. Here, W=half-width of the total flow duct width in the x- direction.

M VR 10 0.0 m 1.0 n.o m ).0

mm In no 03 M Uo U3 1s JR’ rli (a) ;) “ (c) Figure 3. Comparison of the a and q. between the experimental data and the values calculated based on the image analysis for flow conditions;jJflxed at 0.321-m/s and jg varied at (a) jg =0.052-m/s, (b) jg=O. 179-m/s, and (c) jX=0.432-m/s

1n developing the one-group interracial area transport equation, the source and sink terms are established through mechanistic modeling of major bubble interaction phenomena in the bubbly flow regime. These include the number source/sink rates stemming from; disintegration due to turbulent impact (H), coalescence through random collision driven by turbulent eddies (RC), and coalescence due to the acceleration of the following bubble in the wake of the preceding bubble (WE). The one- group interracial area transport equation is then given by

where, the source and sink terms in the right hand side of the equation are given by

~,,= Cn(~)exp(-~)~~, whenWe.WeC,; (11)

(12)

(13) Here, the Crl, Cl{c, and CW,;are coefficients to be determined through experiments, and WeC,and cz~u are the critical Weber number over which the bubble disintegrates and the maximum packing limit, respectively, In benchmarking the model against the data, equation (10) is averaged over the channel cross-sectional area to simplify the evaluation procedure. This assumes all parameters exhibit radially uniform profiles, so that the covariance terms are negligible. Furthermore, noting from the experimental data that the bubble size across the flow duct at a given axial level is nearly uniform, the ai weighted bubble interracial velocity is approximated by the void weighted bubble veloci~. The local data are acquired in air-water vertical co-current adiabatic two-phase through the 2.54-cm ID and 5.08-cm ID tubes. In both test sections, the local measurements are made by traversing the conductivity probe in radial direction at three axial locations. The flow conditions of the present experiments are summarized in Table 1.

Table 1. 13xperiinentalconditions for the data employed in the model evaluation

Tube ID [cm] Run No. jx [mIs] jf [mIs] 1-1 0.055 0.262 1-2 0.078 0.262 1-3 0.041 0.872 1-4 0.143 0.872 2.54 1-5 0.046 1.750 1-6 0,257 1.750 1-7 0.051 3.490 1-8 0.201 3,490 1-9 0.702 3.490 2-1 I 0.242 0.986 0.986 2.010 2.010 5.000 k_lG1-K 5.000 In the present study, the coefficients in the model are determined based on the acquired data. 1n highly turbulent flow conditions, the Tl and RC mechanisms are assumed to be dominant, whereas in low Reynolds number flow condition, WE is assumed to be dominant compared to RC. Furthermore, the constant C in RC, which accounts for the effective range of influence of eddies in driving bubbles to collisions, is assumed to be 3. In estimating the critical Weber number, it is varied from 2,3 to 8, based on the previous studies [13,14]. Then, the coefficients were determined by finding the values, which yield the best agreement with the experimental data. They were given by: CJY,:=O.002; Cl{<=0.004; C=3.O; c4.,X=0.75; Cri O.085; and WeC,=6.0.

The results of the model evaluation are shown in Figure 4. The overall agreement between the model and the data is good within the measurement error of approximately *100/o. Some deviations in transition flow conditions are observed due to the error associated with the presence of the group 2 bubbles. Nevertheless, it is of noteworthy that the one-group interracial area transport equation generally predicts well in the wide range of bubbly flow conditions in different sizes of pipe flow.

The characteristic contributions from the individual source or sink terms to the total change in a, are also plotted in Figure 5. Under the given flow conditions, the bubble expansion due to the pressure change (EXI’) plays an important role in the increase in u,. The contribution from the Tl mechanism depends mainly on the given flow condition, such as liquid Reynolds number and the fluid particle Weber number, such that it is significant in Run 1-9, whereas it is minimal in Run 2-3, It can be also seen that the dominant mechanism among bubble coalescence mechanisms is attributed to RC.

122 ); ,

rim —. ..— —lull 1.1 ● Ilaut.1 —M13.l b dud.1

— mnl-2 + dahll-z o —-N&2 + 12ual.2 — IW”l-3 . dat,l.1 I

( b —mnl.4 x Ilaw.1 A A —- nn2.3 4 .b2J Atl, ccl,>:. t —Xln!-.f ■ Ilalal-$ [ 1/111] Ilhnl —Vm34 ❑ Ibtal-1 —IUO14 ❑ danl.h —A——— Q -—rent-7 A dlub7 —0————— –— ““— — nmz.s & w.> — -——- —WII.8 G Ibull.x —1 — rmz4 0 d5i2.6 —Nnl-’i 0 dalal.9 a 03 ml 13 1s 23 2.8 0.3 1.3 z [ml 23 3.3 z [ml (a) 1 (b) Figure 4. Evaluation of the Model with Experimental Data. (a) Data obtained in 2.54-cm ID pipe. (by Data obtained in 5.08-cm ID pipe. “

31M I—==-=&F/-1 0 /)’,1” —lie I —n 1--2!’ ..1 .4,1, Aii, I1111:1 IUrn] . .

.Im -m I : [ml : [m] (a) (b) Figure 5: Contribution of individua~ bubble Interaction mechanisms to total change in aj, (a) Run ]- 9:jx=0.702-m/s and j~3.49-m/s in a round pipe of 2.54-cm ID. (b) Run 2-3: jX=0,471-m/s and j~2.O 10-m/s in a round pipe of 5.08-cm ID.

5. SUMMARY AND CONCLUSIONS

The newly designed micro four-sensor conductivity probe and its signal processing scheme are presented. The new probe not only minimizes the bubble deformation and missing bubble phenomena, but also accommodates the capability of a double-sensor probe for small bubbles. This feature enables one to establish the database for the two-group bubble transport. The signal processing scheme accounts for the missing and non-effective signals and is constructed such that the two-phase flow parameters of the different types of bubbles can be separated and categorized accordingly. A good agreement is observed in the benchmark test employing the image analysis method, which assesses both the newly designed probe and the measurement principles in the signal processing,

The one-group interracial area transport equation applicable to the adiabatic air-water bubbly flow in round tubes is established. The development of the ai along the flow path predicted by the model agrees well with the data. Active fluid particle interactions are well demonstrated through the sensitivity analysis on individual source and sink terms, which reflects the dominant mechanisms at various flow conditions, Under the present experimental conditions, the RC mechanism plays a dominant role in bubble coalescence as a sink term, whereas the contribution from the TI mechanism varies depending on the Reynolds number and the particle Weber number. _.—

ACKNOWLEDGEMENTS

The authors wish to express their sincere appreciation to Drs. R. Goulard and R. Price of DOE/BES for their support. This study was performed at Purdue University under the auspices of the U.S. Department of Energy.

REFERENCES

1. M. lshii, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Co] lection de la Direction des Etudes et Recherches d’Electricity de France, Eyrolles, Paris (1975)

2. .Kocamustafaogullari and M. Ishii, Foundation of the interracial area transport equation and its closure relations, ht. J. Heat Mass Trans$er, 38, No. 3, pp. 481-493 (1995)

3. Q. Wu, S. Kim, M. Ishii, and S. G. Beus, One-group interracial area transport in vertical bubbly flow, Int. J. Heat Mass Transfer, 41, Nos. 8-9, pp. 1103-1112 (1998)

4. S. Kim, lnterfacial area transport equation and measurement of local interracial characteristics, Ph.D. Thesis, School of Nuclear Engineering, Purdue University, Dec. 1999 (1999)

5. L. G. Neal and S. G. Bankoff, A high resolution resistivity probe for determination of local void properties in gas-liquid flow, AIChE. J, 9, pp. 490-494 (1963)

6. 1. Kataoka., M. lshii, and A. Serizawa, Local formulation and measurements of interracial area concentration in two-phase flow, Inl. J. Multiphase Flow, 12, No. 4, pp. 505-529 (1986)

7. M. Ishii and S. T. Revankar, Measurement of interracial area using four-sensor probe in two- phase flow, Purdue University Technical Report, PU NE-91-1 (1991)

8. Wu, Q. and lshii, M., Sensitivity study on double-sensor conductivity probe for the measurement of interracial area concentration in bubbly flow, lnt. J Mzdtiphase Flow, 25, No. 1, pp. 155-173 (1999)

9. M. Ishii, One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes, Argonne National Laboratory Report, ANS- 77-47 (1 977)

10. M. Ishii and N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flOWS,AIChE J., 25, P 843 (1979)

11, Q. Wu, S. Kim, D. McCreary, M. Ishii, and S. G. Beus, Measurement of interracial area concentration in two-phase bubbly flow, ANS Transactions, 1997 ANS Winter Meeting, Albuquerque, NM, Nov. 10-20, TANSAO 77, p. 437 (1997)

12. G. Zhang and M. Ishii, Isokinetic sampling probe and image processing system for droplet size measurement in two-phase flow, InL J. Heat and Mass Transfer, 38, p. 2019 (1995)

13. M. J. Prince, and H. W. Blanch, Bubble coalescence and break-up in air-sparged bubble columns, AIChli J., 36, NO. 10, pp. 1485-1499 (1990)

14. M. lshii and T. C. Chawl% Local drag laws in dispersed two-phase flow, Argonne National Laboratory Report, ANL-79-105, NUREG/CR-1230 (1979)

124 THEORY OF SUBCOOLED BOILING

S. G, Bankoff[ and S. H. Davis2 Chemical Engineering Departrnentl Eng. Sci. and Applied Math. Department 2

Northwestern University Evanston, IL 60208 USA

ABSTRACT

A broad theoreticalattack has been made on all phases of subcooled boiling, as evidenced by the publication or submittal of five papers in leading journals in the 1999-2000 period. For details, the reader is referred to these publications. Here we give a broad outline. These have included nucleate, transition and film boiling. Nucleate boiling is perhaps the most interesting, because of the enormous steady heat fluxes attainable (>30 MW/m2), but also the most complex and difficult. An analogous, but somewhat simpler, problem is that of a vapor bubble confined between two parallel plates, one of which is heated and the other cooled. Simultaneous evaporation and condensation occurs. This latent heat transport is thought to be the dominant heat transfer mode in subcooled nucleate boiling. There is a transition region between the nearly- circular advancing bubble front in the parallel-plate (or thin capillary tube) problem, behind which an ultrathin liquid film is deposited, and thus evaporates on the heated wall. The initial thickness of this film depends on the bubble front velocity. By asymptotic matching of the transition region with the curved interface, it was established that this thickness is proportional to (Ca)m, where the capillary number, Ca, is a dimensionless bubble velocity. Previously, it had been thought that it was proportional to (Ca)’n. Another study showed that on imperfect (coated) surfaces, it was possible to obtain on a stable, microscopically-thin (1-3 nm) liquid film on the heated wall, owing to the combined presence of conjoining and disjoining presences in an apolar liquid. These arise from molecular dispersive forces from the top and bottom of the coating. This permits stable good wetting, resulting in complete utilization of the locally-available coolant. This may resolve a 50-year old puzzle as to how such enormous heat fluxes are possible. The stirring action of a growing and collapsing bubble while attached to the heating wall was simulated by considering a periodically-oscillating wedge with constant apex angle with a heated wall in a semi-infinite liquid. The linearized equation was solved by transform methods and Floquet analysis, and showed multiple vortices developing and migrating.

125 Film boiling, in which a thin vapor layer is interposed between the subcooled liquid and the hot solid, is also important for its negative aspects in nuclear reactor accidents and burnout of heat transfer equipment. The equilibrium base state has traditionally been taken to be a quiescent uniform vapor film. However, as the wall temperature is progressively reduced, a nonlinear bifurcation takes place, which may be supercritical (bounded) or subcritical (possibly unbounded). By integrating along the nonlinear branches, some fascinating phenomena are revealed, such as stable or unstable, steady states or traveling waves, and hysteresis loops. Convection in the film parallel to the plate leads to accumulation points for vapor, which are incipient bubbles. At a later stage liquid tongues penetrate the horizontal film, making contact with the solid surface. These contacts may grow or shrink, depending upon, among other things, the evaporation rate and the fiquid downflow rate. A wetting/dewetting map was thus constructed, giving the neutral stability line for the onset of transition boiling, and the minimum film boiling temperature.

INTRODUCTION

Significant new insights have been published in the past year on subcooled boiling, in which the bulk liquid is below the saturation temperature. Subcooled boiling can reach steady heat fluxes above 30 MW/m2 [1] in a relatively simple device, which makes it the heat transfer mode of choice in several high-heat-flux applications, A major barrier to the further densification, and hence miniaturization, of computer chips is the need for steady heat removal from concentrated sources. Plasma studies, leading towards eventual realization of fusion energy, and intense photon beams for material property studies (Argonne National Lab) are other sources of very large steady heat fluxes. On the other side of the coin, operation at such high fluxes implies that instabilities, leading to film boiling rather than nucleate boiling, are of concern because of possible equipment damage, melting and even vapor explosions, as in the Chernobyl accident. Despite a large number of investigations over the past half-century, knowledge of the mechanics of flow and heat transfer in boiling systems is based on small-scale experiments and phenomenological models. These have been useful, but our approach represents a new attack on the problem.

SUBCOOLED NUCLEATE BOILING

In highly-subcoo]ed nucleate boiling, enormous numbers of tiny bubbles grow and collapse while attached to the heating surface. Because they never detach, the bulk liquid remains free of vapor, in contrast to the usual situation in saturated boiling. Despite this important simplification, experimental information remains scarce, since the bubble maximum radii are of order 1-mm, with millions of bubbles with lifetimes of order 1 ms. There has therefore been a controversy for the past 50 years concerning the principal mechanism for this extraordinary heat transfer, One might suppose that it lies in the latent heat transport by the vapor, but this has been discounted on the basis of visual vapor volumetric generation rate, and calculation of evaporation rate from the thin liquid microlayer at the base of the growing bubble. Alternative possibilities include stirring of the liquid between the bubbles and quenching of the dry solid when the liquid returns after bubble collapse, The former mechanism has been studied by TNey, et al. [2] However, it is readily shown that neither of these possibilities can account for average surface heat transfer coefficients of the order of 1 MW/m2 K. On the other hand, condensation heat transfer rates of 60-80 MW/m2 were measured sby Bankoff and Mason [3] at the surface of an oscillating bubble resulting from the injection of steam in

126 ,t:,, f ..:-,

a turbulent water stream, with similardimensionsand cycle, so that the latent heat mechanismseems plausible. But how was the requiredvaporrate to be achieved? The assumptionhas been that the t.hh liquidmicrolayerat the base of the growing bubble remains immobile once it has been deposited by the advancing bubble front. A simpler analog to the bubble growing in an infinite sea of liquid is a bubble confined between two parallel plates, one of which is heated and the other cooled. If the microlayer remains locally immobile as it evaporates, the film can become discontinuous, since the local time of dryout depends on the film thickness that was deposited at that location when the bubble passed over it at some previous time. Wilson, Bankoff and Davis [4] found, by asymptotic matching of the transition region to the curved bubble front, that the local thickness at deposition was proportional to the capillary number (or dimensionless bubble wall velocity) to the 2/3 power, instead of square roo~ as previously assumed, Furthermore, in a long tube the bubble wall velocity can be discontinuous more than once. This was a first step towards the computation of a single bubble, and of an array of bubbles, growing and collapsing on a heated wall in subcooled nucleate boiling. The next clue was provided by a study by Bankoff and Oron [5] of the dryout of an evaporating ultrathin film on a coated hot surface. A model by Void [6] for a pure, apolar, isothermal liquid acting on a coated colloidal particle, was extended to the case of a thin film of non-isothermal apolar liquid acting on a coated (oxide, organic material or other contaminant) solid evaporating to dryness. This leads to a two-term van der Waals exponent pair in the evolution equation, corresponding to simultaneous conjoining/disjoining pressures resulting from attractions from the bottom and top of the coating for the vapor-liquid interface. This is in contrast to the [3,9] exponent pair usually used, which leads to attraction, but not repulsion until the solid surface is actually reached. With the [3,4] potential a stable liquid precursor film is produced, which maybe 1-3 nm in thickness. This would correspond to complete wetting, Furthermore, hydrodynamic, rather than adsorption/desorption, equations are appropriate for films of this thickness. The apparently dry areq which appears on the heated surface, grows and pushes the remaining liquid into drops surrounded by ultrathin film. Because of the enormous evaporation rates from the ultrathin film, the drops shrink, acting as reservoirs under the difference in conjoining pressures, until they disappear. All liquid quickly then evaporates. This is in contrast to the case considered by Burelbach, Bankoff and Davis [7] for a poorly-wetted surface, in which local dryout occurs as soon as the free-surface wave reaches the solid surface, Very little of the liquid has been evaporated at that point. With a wetted surface the process is efficient, in that all of the coolant is utilized. It appears that this may explain the 50- year old paradox, but more data are needed to test this theory.

Practical Significance Nettability of the heating surface thus maybe important in determining the efficiency of high-flux heat transfer. This may call for special surface treatment.

TRANSITION BOILING

Once film boiling is established a relatively quiet film of vapor separates the heated surface from the bulk liquid. However, close to the minimum film boiling temperature, tongues of liquid penetrate the film and touch the surface. The contact is generally unstable, and the tongues retract. However, a critical condition exists under which the contacts spread and cover the surface. This is known as transition boiling, leading to fill-fledged nucleate boiling. Joo, Davis and Bankoff [8] offered a simple hydrodynamic theory for this process, in which an inviscid liquid column flows downwards, being simultaneously evaporated at the solid surface. For the first time a phase diagram was produced which showed the critical condition for wetting/dewetting as a function of liquid downflow rate and solid thermal resistance, other factors being held constant. Extensions are intended which will take into account capillary effects in spreading and explore the parameter space more filly.

Practical Significance This is the first map which has been published for wetting/dewetting of hot dry surfaces under a vapor layer, which marks the onset of transition boiling and the minimum film boiling temperature. Long-range conjoining/disjoining pressures, as above (Oron and Bankoff [5,9], together with capillary effects, need to be brought in.

FILM BOILING

Before the stable film actually produces down-flowing tongues of liquid, there is a critical heat flux at which the smooth quiescent vapor film surface becomes unstable. At this point a bifurcation takes place, which may be supercritical or subcritical. Exploration by Panzarell~ Davis and Bankoff [1O]of these nonlinear branches reveals the existence of stable or unstable steady states or traveling waves, possible existence of hysteresis loops, and accumulations of vapor which are the precursors to bubble formation and removal. Weakly-nonlinear stability analyses of this type, leading at the third order to Landau-Ginsberg equations for the nonlinear growth of the wave amplitude are well-known, but have never been applied previously to film boiling. This is the first rigorous exploration into the nature of film dynamics in horizontal film boiling.

OTHER WORK

Other work published in the past year supported by this grant was a study of a slender dry patch on an inclined plate in a draining liquid film by Wilson, Duffy and Davis [11], relevant to the dewetting problem, spreading and imbibition of a viscous liquid on a porous base by Hocking and Davis [12], and the dewetting of hot coated surfaces by Bankoff and Oron [13].

ACKNOWLEDGMENT

Thiswork was supported by the Department of Energy.

REFERENCES

1. F. C. GUNTHER, “Photographic Study of Surface-Boiling Heat Transfer to Water with Forced Convection: Jet Propulsion Laboratory, Pasadena, CA, Progress Report No. 4-120 (1950).

2. **B. S. TILLEY, S. G. BANKOFF and S. H. DAVIS, “Unsteady Stokes Flow near an Oscillating Heated Contact Line”, J. Fluid Mech., submitted.

3. S. G. BANKOFF and J. P. MASON, “Heat Transfer from the Surface of a Steam Bubble in Turbulent Subcooled Stream”, AIChE J. 3,63-65 (1962).

4. S. K. WILSON, S. H. DAVIS, and S. G. BANKOFF, “The Unsteady Expansion and Contraction of a Long Two-dimensional Vapour Bubble Between Superheated or Subcooled Parallel Plates”, J Fluid Mech. ~, 1-27(1999).

5. *A. ORON and s. G. BANKOFF, “DeWetting of a Heated Surface by an Evaporating Liquid Film under Conjoining/Disjoining Pressures”, J Colloid and Interf Sci., ~ 152-166 (1999).

128 6. M. J, VOLD, “The Effect of Adsorption on the van der Waals Interaction of Spherical Colloidal Particles”, J ColloidSci., 16, 1-12 (1961).

7. J. P. BURELBACH,S, G. BANKOFFand S. H. DAVIS,“NonlinearStabilityof Evaporating/CondensingFilms”,J FluidMech. ~, 463-494 (1988).

8. S.W. JOO, S. H. DAVIS and S. G. BANKOFF, “Hydrodynamic Model for Transition Boiling”. J Fluid Mech, ~ 195-201 (2000).

9. *A. ORON and S. G. BANKOFF, “Dewetting of Coated Hot Surfaces” (2000). Proc. IUTAM Symposium on Nonlinear Wines in Multiphase Flow (in press),

10. C, H. PANZARELLA, S. H. DAVIS and S. G. BANKOFF, “Nonlinear Dynamics in Horizontal Film Boiling”. J FluidMech., (2000) 4@, 164-194.

11. S, K. WILSON, B. R. DUFFY and S. H. DAVIS, “On a Slender Dry Patch in a Liquid Film Draining under Gravity Down an Inclined Plane”, Euro. J Appl. Math (in press).

12. L,M. HOCKINGand S. H. DAVIS,“Spreadingand Imbibitionof a ViscousLiquidon a Porous Base. Part 11”(2000),Phys. Fluids (in press),

* Partial support from US-lsrael Binational Science Foundation **Partial support from National Science Foundation

129 COMPLEX DYNAMICS IN LARGE ARRAYS OF FLUID-ELASTIC OSCILLATORS

F.C. Moon, Cornell Universi~, Ithaca, New York USA M. Kuroda, Mechanical Engineering Laboratory, M..I, Tsukuba, Ibaraki, Japan

Abstract

New experiments on the dynamics of 90 and 300 elastic oscillators in a steady cross flow are described. Unlike the single row. dynamics, which lead to limit cycle behavior, multi-row arrays seem to exhibit chaotic though not necessarily, low dimensional dynamics, at a critical flow value. With increasing flow velocity however, organized wave-like structures appear to develop. Experimental models of tlds type may serve to help understand complex dynamics in large array heat exchange systems. It may also be a model to understand wind crop dynamics and damage.

INTRODUCTION

Fluid-elastic vibrations occur in heat exchanger systems, agricultural crop-wind interactions and bio-mechanical problems such as ciliated epithelia. Classic problems include the flow of fluid through tube structures and around tubes and have generally focused on linear dynamics. In this study we discuss experimental nonlinear dynamics of a large array of up to 300 cylinders in a cross flow. The rod-like structures are cantilevered at a base and free to vibrate at the top. (13gure 1) The coupling between rods consists of fluid forces and contact when the vibration amplitude becomes too large. The fluid forces are of two types; fluid-elastic nearest neighbor forces equivalent to springs and dampers, and non-nearest neighbor forces produced by vortices leaving the forward rows of cylinders and effecting the dynamics of the rearward rows of cylinders.

Observations of the tip vibration dynamics reveal complex patterns of motions of the rods, some of which appear nearly stationary, others vibrate in a straight-line motion in-line and at an angle to the upstream flow and others vibrate in elliptical patterns sometimes associated with rod to rod contact. While the rod frequencies lie close to their natural frequencies, the phases and types of motion, i.e., stationary, straight-line and elliptic show no regular pattern and change in time. It is important to emphasize that the linear theory would predict 2xNxM eigenmodes for a NxM array or rods. However, no

130 :.--,.,, ! ) ,.,;

clear modaI pattern emerges as the wind tunnel velocity is increased. Thus, we have sought to apply entropy measures of complexity to describe the dynamics.

The wind tunnel is a low turbulence system with a 25.6 cm x 25.6 cm cross section, The 17.1 cm long rods were steel with a diameter of 1.59 mm and a spacing between rod centers of 3.2 mm or a gap equal to the rod diameter. The lleynolds number based on the rod diameter ranges from 200-900. Although the base holes are precisely regular, the spacing of the ends of the rods varied slightly from a periodic spacing due to small initial curvature in the rods. The data reported in Figures 2,3 are for a 3 row by 30 rod array, as shown in Figure 1, However, another experiment involves 10 rows of 30 rods. Dynamic data are obtained by instrumenting one or two rods as well as video taping of the motion of the ends of the rods of the entire array. Also photographic images with a shutter speed on the order of the vibration period for 10 Hz were taken. The wind speeds ranged from 0-10 n-is, but no significant dynamics were observed below 2 m/s.

The 90 rod experiments were extended to 300 rods of the same diameter and spacing with 10 rows of 30 rods. In these experiments, the flow behind the 10 row array in a cross flow was measured with a pitot tube. The results are shown in Figure 4. The data shows that the array acts as a porous rigid object in the flow with most of the flow directed around the sides and over the top of the rods. There still is significant flow through the array however. In addition an accelerometer was fixed to the middle rod in the last row. Power spectra and probability distribution of accelerations were also measured. Video data was recorded to show the wave-like structures in the flow.

RESULTS

To describe the vibration patterns in the 90 rod array photographs were taken at different wind speeds from the onset of vibrations, around 2 m/s to 9 rrds. We use an entropy measure based on three symbols corresponding to the three types of motion; stationary, straight-line and elliptical orbits. A typical pattern is shown in Figure 3. Although the states of each rod varied in time, it was found by observation of the video records that the photographic pattern gave a good sample of the average patterns.

In Figure 2, we show the number of rods in straight-line and elliptical orbits as a function of wind speed. Clearly, one can see an onset of motion at a critical speed and the growth of the number of rods in elliptical motions. This may be related to the greater

131 incidence of rod impact at the higher wind velocities. The data also shows hysteresis for increasing and decreasing flow,

Data was also taken for the array at an angle to the flow direction. The same phenomena occurs as in the head-on flow case except near the 90 degree flow case where there are 30 rows of 3 rods each. In this case, there is very little motion as the array seems to act as an airfoil and directs the flow around the array instead of through it.

For the 300 rod array, velocity measurements (Figure 4) show that the collective action of the rods screens the flow, forcing a large fraction around the sides and over the top. However there is no indication that the edge rods experience more or less vibration. Video pictures clearly show that all the rods participate, sometimes in wave-like motion transverse to the flow direction. Also the accelerometer data on one of the rods, (Figure 5) shows bursting phenomena probably related to impact between the rods as the flow velocity is increased. We are trying to be able to take data from the video records in order to obtain more collective dynamic measurements.

ENTROPY MEASURES

Several pattern entropy measures were used, based on the entropy measure

where p~ is a probability measure of a certain spatial pattern occurring. These measures of local cluster pattern show an increase in entropy with flow velocity.

REFERENCES

1. Coutts, M.P., Grace, J. (1995) Editors. Wind and Trees Cambridge University Press, Cambridge, U.K.

2. Finnigan, J.J. (1979) “Turbulence in Waving Wheat” Boundary Luyer Meteorology 16, 181-211.

3. Finnigan, J.J., Mulheam, P.J. (1978), “Modeling Waving Crops in a Wind Tunnel”, Brendary-Luyer Meteorology 14,253-277

4. Grace, J. (1977) Plant Response to Wind Academic Press, London

132 .,

5. Inoue, E,, 1955, Studies of Phenomena of Waving Plants (“HONAMI”) Caused by Wind”. .Agric. MeteroL (Japan) 11,18-22,

6. Lunley, J.L. & Panofsky, H.A. 1964, The Structure of Atmospheric Turbulence, Wiley-Interscience, NY 239.

7. Moon, F.C. (1992) Chaotic and Fractal Dynamics J. Wiley& Sons, N.Y.

8. Moon, F.C., Kuroda, M. (2000), “Complexity Measures in Large Arrays of Fluid Elastic Oscillators” Chinese J. mechanics (to appear).

9. Niklas, K.J. (1992), Plant Bionzechanics, Chapters 7,9. University of Chicago Press.

10. Williams, G. P. (1999), Chaos Theory Treed, Joseph Henry Press, Washington, D.C.

11. Raynor, G.S. “Wind and Temperature S&ucture in a Coniferous Forest in a Contiguous Field”, Forest Science 17(3), 351-363.

12. Thothadri, M., Moon, F.C. (1998) “Helical Wave Oscillations in a Row of Cylinders in a Cross-Flow” J. Fluids and Structures 12,591-613.

13. Thothadri, M., Moon, F.C. (1999) “An Investigation of Nonlinear Models for a Cylinder Row in a Cross Flow” J. Pressure Vessel Technology ASME 121, 133- 141.

133

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136 ROBUST FOREWARNING OF DYNWICAL CHANGE FROM SINGLE-CHANNEL SCALP EEG DATA

V. Protopopescu, L. M, Hively, and P. C. Gailey

Oak Ridge National Laboratory Oak Ridge, TN 37831, USA

ABSTRACT

We present a robust, model-independent technique for measuring changes in the dynamics underlying nonlinear time-serial data. We define indicators of dynamical change by comparing distribution functions on the attractor via L1-distanceand ~2 statistics. We validate these measures against model data and then we apply them to clinical single- channel, scalp EEG data with the objective of capturing the transition between non-seizure and epileptic brain activity in a timely, accurate, and non-invasivemanner. We find a clear superiority of the new metrics in comparison to traditional nonlinear measures as discriminatorsof dynamical change.

INTRODUCTION

Nonlinear processesare ubiquitous. Examples include:brain and heartwaves; electrical transients in power systems; fluid (air or water) flow over the surfaces of automobiles, airplanes, or submarines; weather and climate dynamics; machine tool chatter; nuclear reactor instabilities; fusion plasma instabilities; earthquakes; turbulent flow in conduits; fatigue and stress crack growth; and planetary or satellite motion. Typically, nonlinear data arise from a virtual “black box”with little or no knowledgeof the underlying system, its dimensionality, or noise contamination. More ofien than not, traditional nonlinearanalysisrequires some assumptionsaboutthe underlyingdynamics.Forexample, calculationof Lyapunovexponentsor Kohnogoroventropy implicitly assumesthat the process can at least be modeled as a (low dimensional) dynamical system. At a more fundamental level, one may ask whether the data arises from a stationary process. It is very likely that complex systems, such as the weather or the brain, could not be well modeled by low dimensional, stationary dynamics over long times.

137 The technologist must frequently distinguish or quantifi differences between nonlinear states that are apparently similar, but actually different. Inherent nonlinearity and high levels of noise in most real-life systems make condition or state comparisons extremely difficult or even impossible with linear or traditional nonlinear analyses. New measures are needed that are less affected by noise and at the same time are more sensitive to structural or parametric changes in the underlying dynamics.

We describe a new model-independent method for measuring dynamical change in nonlinear, possibly nonstationary data. The dynamics of reference and test cases are represented as discrete distributions of the density of points in reconstructed phase space during different time windows. Variability is captured by the visitation frequency at various regions of phase space as described by the distribution function. The method quantifies differences in these reconstructed dynamics by comparing the distribution functions. We make no specific assumption about stationarity, because no dynamical properties are inferred from the reconstructed attractor. The system dynamics may change within the time window, but such variability presents no problem for our technique, which measures dynamical change over a variety of length scales, and over a wide range of time scales. Moreover, our method allows measurement of dynamical change that that occurs continuously or intermittently.

Recently, Moeckel and Murray [1] discussed similar concepts for measuring the “distance” between attractors from time-delay reconstructions. In this context, our method provides continuous measuresof change, in contrastto stationaritytests forwhetheror not any statistically significant change has occurred. Due to their continuous nature and their independence from assumptions about stationarity, our measures are particularly useful for analysis of physiological data. We illustrate the practical use of the technique for such data, namely analysis of single-channel, scalp EEG for forewarning of epileptic seizures.

TRADITIONAL NONLINEAR MEASURES

We assume that an unknown scalar signal, x, is sampled at equal time intervals, ~, starting at time, to, yielding a sequence of N points, x = x(to + iz). Dynamical process reconstruction [2] uses d-dimensional time-delay vectors, y(i)=[xi, xj+l , .... N+(&I)~], for a system with d active variables and time lag, L. The choices of lag and embedding dimension, d, determine how well the reconstruction unfolds the dynamics for a finite amount of noisy data. A proper reconstruction allows calculation of nonlinear measures that are consistent with the original dynamics. Below, we use three traditional measures, for comparison to our phase-space indicators of dissimilarity.

The mutual information function is a nonlinear form of auto-correlation function. Mutual information was devised by Shannon and Weaver [3], and applied to time series by Fraser and Swinney [4]. Mutual information measures the information (in bits) that can be inferred from one signal about a second signal, and is a function of the time delay between the measurements. Univariate (bivariate) mutual information measures information within the same (different) data stream(s) at different times. Here, we use the first minimum, MI, in the univariate mutual information function. Ml measures the averagetime separation(in time-steps)that decorrelatestwo points in the time series.

The correlation dimension, D, measures process complexity and is a function of scale length, & in the data. Here we use the maximum-likelihood correlation dimension developed by Takens with modifications for noise by Schouten et al. [5,6].

The Kolmogorov entropy, K, measures the rate of information loss (bits/s). Positive, finite entropy generalIy is considered to clearly indicate chaotic features. Large entropy implies a stochastic, totally

138 >,.

unpredictableprocess. Entropy measures the average time for two points on an attractor to evolve from a small initial separation to more than a specific (large) distance, 8>60. We use maximum-likelihood entropy by Schouten et al. [7].

Noise corrupts all real data. In addition, finite precision computer arithmetic truncates model data. Thus, we choose a finite-scale length that is larger than the noise, tio = 2a, at which to report K and D, corresponding to finite-scale dynamical structure. Our choice of length scale balances local dynamics (typically at 3< 3a) against avoidance of excessive noise (ty ically at 8s a). The symbol, a, denotes the absolute average deviation as a robust indicator of variabili d in the time serial data:

ti=(l/N); ]Xi-~l. (1) i=I where symbol x denotes the mean of xi. Thus, our values of K and D have smaller values than expected for the zero-scale-length limit.

NEW MEASURES OF DYNAMICAL CHANGE

Traditional nonlinear measures characterize global features by averaging or integrating over the data. Such measures describe the long-term behavior but poorly indicate dynamical change. Greater discrimination is possible by more detailed analysis of the reconstructed dynamics. The natural (or invariant) measure on the attractor provides a more refined representation of the reconstruction, describing the visitation frequency of the system dynamics over the phase space, We begin by converting each signal value, W,to one of S different integers, {O,1, .... S-1}:

Here, xlnilland xl~mdenote the minimum and maximum values of xi, respectively, over the reference case . . . only and INT ISa function that rounds a decimal number to the closest lower integer. For x~in< xi < x,n~X, the inequality 0< q < S-1 holds trivially. We take q(x = x~u)= S-1 in order to maintain exactly S distinct symbols and to partition the phase space into S~ hypercubes or bins. We then discretize the distribution fimction on the attractor, by counting the number of phase-space points occurring in each bin. We denote the population of the i-th bin of the distribution function, Pi, for the base case, and Qi for a test case, respectively. For this work, we iteratively vary each parameter (S, d, N, etc.) with the others fixed, to obtain optimum sensitivity of the measures to changes in process dynamics. A systematic method to determine optimal values for these parameters is the subject of future work.

We use an embedding window, Ml = (d – l)A, Here, the first minimum in the mutual information function, Ml, is measured in timesteps. We obtain an integer value for the lag from the previous equation by L = INT[0,5 i- Ml/(d-l)] 21, thus constraining the largest value of dimensionality to ds 2M, + 1.

We compare the distribution function of a test state to the reference state, by measuring the dissimilarity between Pi with ~ via the X2statistics and LI distance:

X2= ~ (Pi - Qi)2/(Pi+ ~ ), and (3)

L = ~lPi - Q1. (4) ——

The summations include all of the populated cells in the phase space. The sum in the denominatorof Eq. 3 is based on a test for equality of IWOmultinominaldistributions. Proper application of these measures requires a resealing so that the total population of the test case distribution function is the same as the total population of the base case.

By connecting successive phase-space points as indicated by the dynamics, y(i) + y(i+l ), we construct a 2d-dimensional phase-space vector, Y(i)= [y(i), y(i+l)]. Thus, we obtain a discrete representation of the process flow [8]. This approach extends the method to capture more dynamical information using pair-wise connectivity between successive d-dimensional states. We use base-S arithmetic to assign an integer identifier j = Ii for the i-th phase-space state, using Ii = Ed’n-’si(m). The sum runs from m=l to m=d, corresponding to successive components of the d-dimensional phase-space vector. The symbol, si(m), denotes the m-th component of the i-th phase-space vector. The numeric identifier for the sequel phase-space point is k = Ii+].Then, we can define the measure of the dissimilarity between these two connected phase-space states, as before, via the L1-distance and X2 statistics:

(5)

J-w=,: ]Pjk – Qjk]. (6) pjkand Qjkdenote the distribution functions for the base case and test case, respectively, in the connected phase space. The summations in both equations run over all of the populated cells in the connected phase space. The subscript, c, denotes the connected measures, which are stronger metrics than the non- connected versions, according to the following inequalities [9-10]: X2

VALIDATION

We test the discriminating power of our measures on chaotic regimes of the Lorenz system [9] and of the Bondarenko model [11]. The latter model mimics high-dimensional EEG dynamics via a system of delay-differential equations. The Lorenz model reads [12]:

dx/dt = a(y - x) dyldt=rx-y-xz (7) dzidt = Xy- bz.

As stated before, some traditional nonlinear measures are good indicators of a bifurcation or transition to chaos. However, transitions between two chaotic regimes are poorly detected by these measures, especially for relatively small changes in the parameter that underlies the transition. Therefore we focus on detecting dynamical changes within a region where the Lorenz system is known to behave chaotically, namely [13]: a = 10, b = 8/3, and 25s rs 90. We compute various nonlinear measures versus r, by analyzing only the time serial values of z. The results of this analysis are as follows [9]. The correlation dimension, D, varies erratically from 1.7 to 2.15 over the whole range of r. The Kohnogorov entropy, K, also varies irregularly from 0.03 to 0.05. The value of Ml, increases somewhat monotonically, but step-wise as r rises, so that relatively large variations in r are poorly indicated (e.g., constant for 60< r < 72). In sharp contrast, as r rises from 25 to 90, the PS and CPS measures increase almost monotonically from zero to rather large values. The values of L and X2essentially coincide over the whole range because the measures are dominated by (C)PS domains that are populated only for the base case (Qi >0 for Ri = O)and only for the unknown (Ri >0 for Qi = O), for which the two measures become analytically equivalent.

140 We also assess the phase-space measuresby testing them on the Bondarenkoneuron model [11], which is a coupled set of time-delayed ordinary differential equations: M ,,

d~fdt = +%(t)‘j~i aij f(uj(t - ‘j)), (8)

The signal from the i-th neuron is uj(t). The indices, i and j, run from 1 to M=] O for ten neurons. The matri~ ~j, is a set of coupling coefficients having uniformly random values, -2s aijs z. The time delay is a constant, Tj = 10. The function, f(x)= c tanh(x), simulates nonlinear neural response to signals from neighboring neurons. We concentrate on measuring dissimilarity within a region where the Bondarenko system is known to behave chaotically [11]: 5 < c s 16. We use one of the ten neuron signals for dissimilarity detection, The results of this analysis areas follows [10]. The correlation dimension varies erratically between 3.5 and 8.5 as c increases from 5 to 16. Over the same range of c, the Kolmogorov entropy rises almost monotonically from 0.025 to 0.16. The location of the first minimum in the mutual information function, Ml, also varies erratically as c increases. In sharp contrast, as c rises from 5 to 16, the (connected) phase space measures increase almost monotonically over several orders of magnitude, As before, the values of L and X2essentially coincide over the whole range because the measures are dominated by phase space bins that are populated only for the base case Pi >0 for Qi = Oand only the test case Pi> Ofor Q, = O,for which the two measures become analytically equivalent.

Analysis of these two analytical models of chaotic dynamics shows continuous change in the phase- space measures, which increase monotonically by four orders of magnitude over a reasonable parameter range. Over this same parameter range, the phase-space measures of condition change consistently outperform the traditional nonlinear measures, which are indistinguishable from noise or vary erratically by a factor of two, These results provide confidence that the phase-space measures are useful for noisy clinical EEG data.

EEG DATA ANALYSIS AND RESULTS

We analyze a fixed channel of scalp EEG with 12-bit precision at a sampling rate of 512 Hz. Table 1 summarizes these nine datasets with monitoring periods of 1380-3115 seconds. The clinical seizures begin at 966-2775 seconds. We also analyze digital scalp EEG from other clinical sites, sampled at 200 Hz with 10-11 bits of precision, These data have 23-32 channels with monitoring periods of 2,217-20,000 seconds. The clinical seizures begin at times that range over 1,930-15,750 seconds. Only one clinically designated channel was examined in each of these eleven datasets, as shown in Table 1.

We choose N=22,000 data points for each cutset to balance better time discrimination (smaller N) against higher statistical power (larger N). We next remove muscular artifacts (e.g., eye blinks) with a zero-phase quadratic fiIter [9-10]. We designate the first ten non-overlapping time windows (cutsets) as base cases. We then compare each base case cutset to every test case cutset to obtain average values for XZ and L (and a corresponding standard deviation of the mean). We find that d=3 and S=22 are adequate for this data. The value of Ml comes from the base case period of (nonseizure) data.

The substantial disparity in range and variability of the conventional and phase-space measures makes them difficutt to compare and interpret. To remove this disparity and compare all the measures on a consistent basis, we renormalize the nonlinear measures as follows. For each nonlinear measure, V, we define Vi as the value of nonlinear measure for the i-th cutset. The variable, V, is in turn D, K, Ml, X2,etc. We obtain the mean, ~, of Vi over the ten non-overlapping base case cutsets. The corresponding sample

141 standarddeviation is denoted by O.Then,the renormalizedform is U(W = ]Vi – Yb. For an indication of change, we use U > UC= 3.09, corresponding to a false positive probability of <10-3 in Gaussian random data. We require two or more consecutive occurrences of a positive indication to avoid spurious false positives, corresponding to a joint false positive probabilityof<104 in Gaussian data.

Table 1: Summary of EEG datasets .— .— . ..- DataSet # # Channels Seizure (s) Tot Time (s) Channel Sample Rate (Hz) -— . ...- ..-—— 109310 16 2775 3115.3 13 512 109314 16 2480 2742.4 13 512 119230 16 2491 2917.4 13 512 119234 16 2560 2649.6 13 512 62723t 16 2620 3060.8 13 512 69212 16 2356 2547.8 13 512 73305d 16 1245 1380 13 512 c8492d 16 966 1603.6 13 512 wm12sd 16 1041 1428,6 13 512 Szproo 23 5236 5401 Fp2 200 szprec 32 1930 2217 F7 200 szpr03 32 1932 2217 T4 200 szpr04 23 3794 3963 T4 200 ezpr05 23 4888 6000.2 T4 200 emu02 27 4320 15,006 F4 200 emu03 27 13,200 16,228 C3 200 emu04 27 15,750 18,423 C4 200 emu14 27 4080 20,000.2 F4 200 emu 18 27 4200 18,000.2 T3 200 emu26 27 13,987 16,224 Fp 1 200

Table 2 summarizes the forewarning times for each renormalized nonlinear measure over the twenty EEG datasets. A negative value of forewarning time corresponds to an indication after seizure onset. Starred (*) values indicate that no condition change was detected by this measure. Bold entries denote the earliest time of change. These results are assessed as follows. The phase space measures provide the earliest seizure forewarning in 11, 10, 14, and 13 datasets for L, LC,XC*,and X2,respectively. Moreover, the phase-space measures provide preseizure indications in all twenty cases. in sharp contrast, the traditional nonlinear measures only give the earliest forewarning of a seizure in 1, 1, and 3 instances for K, Ml, and D, respectively. These same traditional measures provide no forewarning of a seizure in 7, 8, and 6 cases, respectively. The total number of instances of earliest-forewarning times exceeds twenty, because more than one measure can simultaneously detect condition change. We note that the forewarning time (1O seconds) for dataset #wm 12sd is too short to be clinically useful. In addition, the forewarnings of more than one hour (datasets # emuO03, emuO04, emu026) are too long to be clinically useful. These results show that the phase space measures are much superior to the conventional nonlinear

142 .,, , -.

measures as preseizure indicators of condition change for a single channel of scalp EEG. Analysis of normal EEG shows no positive indication of change. Table 2: Times (seconds prior to seizure) when change is detected —. Dataset # D K Ml L, L X$ X2

109310 1099 * * -61 -61 1142 -61 109314 1921 1406 1835 1878 1921 1921 1921 119230 901 386 -216 471 -44 471 514 119234 1915 * * 1915 1915 1915 1915 62723t 1374 * -44 2233 1675 2233 2233 69212 * 165 637 1626 1497 1626 1626 73305d 600 600 * 343 772 -87 772 c8492d -22 321 364 193 193 193 193 wm12sd * * * -76 10 10 10 szprec 500 -160 500 610 610 610 610 szprOO * * 1496 726 -154 836 1716 szpr03 -158 -158 172 502 502 502 502 szpr04 -166 * -166 384 384 384 384 szpr05 3568 3348 3568 3678 3568 3678 3568 emuO02 * -190 -410 2230 2780 1900 2780 emuO03 * * * 1276012760 12760 12760 emuO04 * 6950 * 1366013550 14540 13660 emuO14 * * -540 670 670 -210 670 emuO18 -90 -1630 -310 3650 2220 3650 2220 emu026 11127 11237 4747 1123711237 1123711237

Figure 1 shows changes in various metrics as functions oftime, fordataset#c8492d. The first 300 seconds ofdata displays modest variability in all oftherneasures,representing the dynamics ofnortnal brain activity. The clinical seizure occurs at 966-1035 seconds, as indicated bythe vertica] bars atthese times; al[ofthe measures clearly showthe seizure. Maxima andminimainthe raw EEG(Fig. la) provide nopreseizure indications, nordoes thecorrelation dimension, D, (Fig. lb). Boththe Kolmogorov entropy, K, (Fig, lc) and mutual information, Ml, (Fig. ld)show preseizure change, beginning at750 seconds, Connected (solid lines) and non-connected (dashed lines) phase-space measures for the LI– distance (Fig. Ie) and %2statistic (Fig lf) exhibit significant dissimilarity, starting at around 600 seconds, The ordinate value of the respective metric change, U(. ), are in units of standard deviation from the mean.

DISCUSS1ON

The present results differ markedly from previous work, which used conventional nonlinear measures, such as correlation dimension [14], largest Lyapunov exponent [15], and correlation integral [16]. First, previous investigations used multichannel data from subdural and depth electrodes. The present work uses single-channel scalp EEG data, which allows non-invasive, ambulatory, long-term, non-clinical monitoring. The use of scalp data is made possible by the combined effect of sensitive measures and

143 —-—. .

effective low frequency artifact filtering [17]. The robustness of the methodology has been tested over a variety of clinical conditions: digital and analog EEG data from several clinical sites; data sampled at 200 and 512 Hz; raw EEG data precision between 10-12 bits; presence of substantial noise in the raw EEG; various types of seizure; use of a fixed channel in the bipolar montage (channel 13 which lies over the patient’s right eye and has a large eye-blink artifact) as well as various clinically designated channels in the 10-20 montage. We intend to develop the methodology to include: (i) consistent use of multi-channel data for improved monitoring and forewarning (ii) analysis of surrogate dat~ (iii) more robust renormalization techniques to facilitate broad comparisons; and (iv) other medical, engineering, and geophysical applications.

ACKNOWLEDGMENT

This article has been authored by a contractor of the U. S Government under Contract No. DE-AC05- OOOR22725, Accordingly, the Government retains a nonexclusive, royalty free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Research sponsored in part by the Engineering Research Program of the Office of Basic Energy Sciences, U.S. Department of Energy. The Oak Ridge National Laboratory is managed for the U. S. Department of Energy BY UT-Battelle, LLC under contract DE-AC05-OOOR22725.

REFERENCES

1. B. R. MOECKEL and B. MURRAY, Physics D ~, 187 (1997). 2. J.-P. ECKMANN and D. RUELLE, Rev. ModPhys.~617 (1985). 3. C. E. SHANNON and W. WEAVER, T%e Mathematical Theory of Communication, University of Illinois Press, Urbana (1949). 4. A.M. FRASER and H. L. SWINNEY, Fhys. RevA 33_ 1134 (1986), 5. J. C. SCHOUTEN, F. TAKENS, and C. M. van den BLEEK, Phys. Rev. E 50, 1851 (1994). 6. F. TAKENS, Lecture Notes in Mathematics ~ (1984) 99, Springer-Verlag, Berlin. 7. J. C. SCHOUTEN, F. TAKENS, and C. M. van den BLEEK, Phys. Rev. E @ 126 (1994), 8. H. D. I. ABARBANEL, Analysis of Observed Chaotic Data, Springer Publ,, New York (1996). 9. L. M. HIVELY, P.C. GAILEY, and V.A. PROTOPOPESCU, Phys. Lett. A ~, 103 (1999). 10. L. M. HIVELY, V.A. PROTOPOPESCU, and P. C. GAILEY, submitted to Chaos (2000). 11. V. E. BONDARENKO, ht. J Bifur. Chaos ~, 1133 (1997). 12. E. N. LORENZ, J Atmos. Sci. 30_ 130 (1963). 13. E. A. JACKSON, Perspectives of Nonlinear Dynamics, Vol. 2, Cambridge University Press, Cambridge (1990). 14. K. LEHNERTZ and C. E. ELGER, Phys. Rev. Lett. SO, 5019 (1998). 15. L. D. IASEMIDIS and J.C. SACKELLARES, Neuroscientist ~, 118 (1996). 16. M. Le VAN QUYEN, J. MARTINERIE, M. BAULAE, and F. VARELA, NeuroReport 10, 2149 (1999). 17. L. M. HIVELY, N. E. CLAPP, C. S. DAW, W. F. LAWKINS, and M. L. EISENSTADT, ORNL/TM-12961 (Oak Ridge National Laboratory, Oak Ridge, TN) 1995.

144 . ~,,,,, .,,:

n L I n I t 8 8 # 1 i3q 3 -o s-o - g’ -1

Cl L I # n 1 I 1 I 1 g’ ‘1 - (d) 3 A n, ~-nn -~ o 1’ g -1 I t t t I # I 3 1 1 1 8 1 1 I =2 - ~ (e)- 2. 1 - A m- o - \y – - ~ +- y u -1 I I I t I I

3 I I I 1 1 N: 2 - A (9 - ~1 - -o A x, v’ A v w/ .E ‘1 L- -1 \ I t 1 t 0 200 400 600 800 1000 1200 1400 1600 TIME(SECONDS)

Figure 1:Various metrics for dataset #c8492D versus time (see text for complete explanation)

145 ENERGY LOCALIZATION, ENERGY PROPAGATION, AND THERMAL RESONANCE IN NONLINEAR ARRAYS

K. Lindenberg, R. Reigada, and A. Sarmiento Department of Chemistry and Biochemistry and Institute for Nonlinear Science University of California, San Diego La Jolla, CA 92093-0340, U.S.A.

ABSTRACT

Signal propagation in discrete nonlinear noisy media has been connected to dynamical processes in systems as diverse as chemical excitable media, arrays of coupled electronic resonators, dislocations in crystals, adsorbed atomic layers, and cardiac tissue. We highlight a number of interesting properties of nonlinear arrays consisting of masses connected by enharmonic springs. In particular, we focus on the effects of a thermal environment and on the role that thermal fluctuations may play in energy localization and propagation in these chains. We show that it is possible to tune the temperature to obtain optimal response, and that the optimal temperature depends on the desired response. Wc also show that the dynamics of activated processes depend sensitively on the nature of the thermal environment.

In the past few years it has become abundantly clear that the presence of noise in nonlinear systems may lead to an enhancement of a number of desirable features such as energy localization (and mobility and the detection and propagation of weak sigmals. The interplay of stochasticity and nonlinearity that amplifies the system response is a cooperative phenomenon whose detailed nature depends on the particular structure of the system and the forces acting upon it. Recent literature, including our own work [1--3], has focused on spatially extended systems [4] including noise-enhanced propagation in coupled arrays of bistable units [5, 6], excitable media [7–9], reaction-diffusion systems [10], and dynamics and signal propagation in cardiac tissue [11, 12]. It has been repeatedly noted that discrete extended systems pose particular mathematical challenges that have barely been explored in spite of the fact that many physical systems are intrinsically discrete [13–17]. We focus on some of the simplest nonlinear arrays, namely, chains of masses connected by enharmonic springs, thereby isolating some of the most generic features responsible for these cooperative phenomena. In this report we highlight some of our results concerning four sets of questions: 1) What is the texture (magnitude, spatial distribution, persistence) of thermal fluctuations in various discrete enharmonic arrays [1,3]? 2) How does a pulse travel and disperse along these arrays and how are these properties affected by temperature [2]? 3) How do various chains transmit a persistent signal applied at one end (amplitude and distance of travel) and how are these properties affected by

146 ternperaturc? 4) If a bistable impurity is embedded in a thermalized discrete medium, how does the nature of the medium affect the transition rate of the impurity [3]? The equations of motion for chains of N unit masses are

N tin= - ~ V’(.n,zm) -@n +qn(t) (1) m=l wheren= 17. .” , N, ~ is a dissipation parameter, and the q’s are zero-centered Gaussizm thermal fluctuations that obey the fluctuation-dissipation relation at temperature 2’, (qn(t)~m(~)) = 2@BT&m/i(t - T). Dots denote time derivatives and the prime a derivative with respect to Xn. The potential of interaction V(Zn, Zm) connects only nearest neighbors. We consider three prototype potentials (here z s xn – X,n):

12 1,4 v(x) = ~kx -1-~k X hard (2)

12 = ~kx harmonic (3)

= # 1x1- # In(l + k’lzl) soft (4) [ 1 The numerical integration of the stochastic equations is performed using the second order Heun’s method (equivalent to a second order Runge Kutta integration) [18,19]. In Fig. 1 wc display a typical set of equilibrium energy landscapes for the three chains with periodic boundary conditions [1,3], all at the same temperature and subject to the same damping parameter. Darker regions represent higher energies. The horizontal axis indicates the location along the chain and the vertical axis is time evolving upward. Noteworthy features (robust over broad ranges of parameter values) are 1) The magnitude of the fluctuations is greatest in the soft chain. This can be explained straightforwardly using the virial theorem [20]; 2) The fluctuations are mobile in the harmonic and hard chains but not in the soft; 3) The thermal fluctuations travel most rapidly and remain localized over considerably greater distances in the hard chain. Now suppose that a strong (relative to thermal motions) kinetic energy pulse is applied to a particular site on the chain. The pulse then propagates and disperses. We obtain the following results, not all of whkh can be illustrated here [2]. The pulse in the hard chain propagates more rapidl~ ss one incresses its intensity, decreases the daping, or increases the temperature. The pulse in the soft chain propagates more S1OWZYwith these same variations, and the pulse velocity in the harmonic chain is independent of these variations. The dispersion increases in all cases with increasing temperature, but most slowly in the hard chain. A rather dramatic illustration of the different effects of damping on the different chains is shown in the left panel of Fig. 2. The effect of a temperature increase is illustrated in the right panel of the figure. The quantities displayed are the local energy E(n) defined as

1 1 E(n) = ; + jwn+l, %) + $%> %-–1) (5)

(here illustrated for n = 5), and the average distance (z) traveled by the pulse, defined as

(6)

147 .. _—. .

Figure 1: kDT = 0.08, ~ = 0.005, IV = 71, tn,ti. = 160. Hard (top): k = 0.1, k’ = 1. Harmonic (middle): k = ().1. Soft (bottom): k = 0.1, k’= 5.

These results, some of them perhaps cwunterintuitive, all follow from the observation that pulse velocity increases with average array frequency while pulse dispersion decreases with increasing frequency. Increased pulse intensity, decreased damping and higher temperature are all associated with higher energy; in turn, a higher energy in a hard chain leads to a higher average frequency. In a soft chain higher energies are associated with lower frequencies, and in a harmonic chain the average frequency is independent of energy [2J. The connection between pulse velocity and dispersion and the average array frequency can be established analytically for a periodic chain, but is at this point only a numerical observation for the enharmonic arrays. The tendencies of the hard array to keep the energy “together” and to transport it more quickly may conflict under certain conditions. For example, in a two-dimensional hard array a front travels more rapidly with increasing temperature, but a local pulse that would have to travel out radially tends to remain localized because outward motion along the bonds of the lattice as required by symmetry would disperse the crwrgy [2] (see Fig. 3. Next suppose that a sustained sinusoidal signal i(t) = A sin(uOt) is applied at one site of an otherwise free chain. We observe the propagation of the signal along the chain and, in particular, its temperature dependence. We observe that in a hwd chain increasing the temperature can lead to enhanced signal propagation (whereas this does not occur for the other chains). Of course if

148 ,:)-. ,,;,.4 ,7. ,,4,, , ,,’

60 / 5 — hannonlc, y=O.O I :% I — harmonic, yo.2 ,/” 50 --- hard, “#Jo ,/ 4 --- hard, y==.2 ,,/ ,, ~ . ----- soft, y==o.o ----- soft, y=o.z /“ 3

0: - ,~” / / 2 / 20 / /’/~ 1 10

0 o 10 20 30 40 50 t t

Figure 2: Left panel: Mean distance traveled by the pulse as a function of time for hard (k = o, k’ ‘= 1), harmonic (k = 1), and soft (k = k’ = 1) chains of 151 sites at zero temperature &d for different damping coefficients. Initial momentum at the middle site is &(t = O) = 8. Right panek Energy profile vs time at the 5t]’ site horn the initial pulse at different temperatures with damping parameter ~ = 0.2.

Figure 3: Left panel: energy distribution at a subsequent time for an initial front in a harmonic (upper) and hard lattice (lower). Right panel: energy distribution at a subsequent time for an initial pulse at the center of a harmonic (first) and hard (second) array. the temperature is too high the signal is buried in the fluctuations and transmission ceases to be effective. Thus we conclude that the temperature can be tuned to achieve optimal transmission properties, with a specific temperature leading to optimization of a specific property. For example, there is an optimal temperature to maximize the signal-to-noise ratio (SiV@

signal power (j) Slw(j) 5 log~” (7) ( thermal power (j) ) ‘ at a given distance from the forced site, or one can choose a temperature to optimize the transmission distance. These effects are illustrated in Fig. 4. The SNR at site j is expressed in terms of the power spectral density 5’j(w) at each site j defined as a Fourier transform of the velocity autocorreliition function; the thermal power is estimated by performing a polynomial fit to Sj(w) around - but not including -- the forcing iiequency Wo,and the signal power is just the value Sj (wo). The SNR at different distances from the forced site as a fimction of temperature for a hard chain is shown in the left panel (in the other chains the dependence are monotonically decreasing at all sites). The propagMion length is defined as the maximum distance at which the SNR exceeds

149 ...—— —

-0.5 15 –J’ .-,“. \ \ N I \\ -.+ \ a N ~ -0.75 < 10 . “\\\ II ------

-1 5

-1.25 0 0 5 15 20 k?

Figure 4: Left panel: SIVR curves as a function of temperature for different sites from n = 6 (highest curve) ton = 15 (Iowcst curve) along the hard chain with k = O, k’ = 5, -y= 0.2, A = 0.5, and W. = 1. Right panel: propagation length as a function of temperature for the hard chain (dashed curve) and for a harmonic chain (solid curve) (k= 1). a threshold value. The propagation length as a function of temperature with the threshold value arbitrarily picked as 0.4 is shown in the right panel. We have identified the maxima in the curves as thermal resonances, and point to this as one of the few cases in which such resonances are achieved by thermal (as opposed to external noise) tuning. Finally, consider a bistable system embedded in our various thermal environments. Bistable systems are ubiquitously invoked as models for chemical pmccsses. One well represents the ‘kc- actant” state, the other the “product” state, and separating thcm is the “activation barrier”. A thermal environment may induce transitions from one state to the other, and one studies the associated transition rate or “reaction rate”. This rate of course depends on the nature of the thermal environment and the way in which the bistablc system is coupled to it. For example, one of the most extensively studied problems is that of the dependence of the transition rate on the damping [21]: at low damping the system is in the “energy-limited” regime where the transition rate increases with increasing damping. In this regime it is difficult for the system to gain or lose energy. Therefore the system tends to move periodically within one well, rarely gaining enough energy to move over the barrier. When it does so, it tends to recross the barrier many times within this single event before losing energy and becoming trapped again in one of the wells, where it again performs periodic motion. With increasing damping the transition eventually becomes Wiffusion-limited.’) Here the system tends to move erratically within one well. The system can easily gain energy from large fluctuations, but it can also lose energy rather easily. Therefore the independent barrier crossing events are more frequent, but recrossing are rare and the system immediately gets trapped in a well where it moves erratically until another large fluctuation causes another barrier crossing event. If a bistable system is embedded in a chain which is in turn connected to a thermal environment, how does the nature of the chain affect the transition rate [3]? A sample of behaviors can be seen in Fig. 5, which shows the trajectory of the coordinate g of a bistable system connected to the three types of chtina. When the bistable system is in the right (left) well the coordinate is y = 1 (y= –l). The thermal fluctuations and crossings over the barrier at y = Oare apparent. Note that these three sample trajectories involve the same damping and temperature - the only difference

150 2.0 [ 1 1 ) 8 I 1.0

% 0.0

--1.0

_2.o ~~~ 1 , I 0.0 2000.0 4000.0 6000.0 8000.0 10000.0 2.0 I I 1 I I I -1.0

h 0.0

–1 .0

_pJ’J 1- 1 1 I I I 0.0 2000.0 4000.0 6000.0 8000.0 10000.0 2.0 I 1 1 1 I I 1.0 % 0.0

–1 .0

–2.0 1 # 1 I I J 0.0 2000.0 4000.0 6000.0 8000.0 10000.0 t

Figure 5: Trajectory of a bistable impurity with barrier height of 0.25 embedded in a chain of 30 oscillators with kDT = 0.08, and Y = 0.005. Top panel: hard chain with k = 0.1 and k’ = 1. Middle panel: harmonic chain with k = 0.1. 130ttom panel: soft chain with k = 0.1 and k’ = 5. lies in the nature of each chain. Nevertheless the trajectories are entirely different; in particular, in the hard chain the trajcctor y is typical of the cWfusion-liiited regime, while in the soft chain it is that of the energy-limited regime. This is a direct reflection of the behavior seen in Fig. 1, that is, of the fact that in the hard chain the thermal fluctuations createcl elsewhere along the chain have a good chance of reaching the bistable impurity and hence causing a transition, but the same energy mobility also makes it easy for the impurity to then lose its energy back to the chain. In the soft chain, on the other hand, only fluctuations that occur in the sites immediately adjacent to the impurity can excite the impurity - fluctuations originating elsewhere do not travel to the impurity. These neighboring fluctuations arc rarer but stronger and more persistent. A useful characterization of these trajectories is the correlation function

(8) where the brackets indicate an average over t. The correlation functions for the three trajectories of Fig. 5 are shown in Fig. 6. The oscillations apparent in the soft and hmmonic chain at short times are the direct result of oscillatory motion characteristic of energy-limited behavior. The alternation of amplitudes of the oscillations in the soft chain correlation function is a direct consequence of the correlated periodic motion above the barrier that is associated with the prolonged bursts that often accompany the barrier crossing event. Such bursts are not nearly as prevalent in the harmonic systcm, The hard chain correlation function decays essentially monotonically the suppression of oscillations is indicative of the erratic motion withb the wells that is characteristic of higher

151 ._.—.

1.0

\ “-....+...... 0.8 ...... -0.5 ‘! \\ \ \ \ \ ‘x \ ~ 0,6 \ ‘\\ -1.0 c1 \ N ‘\ ‘\\ ‘. \ ~. \ 0.4 ‘. -1.5 \ -.. \ \ -.~~ \ --- \ \ \ 02 -2.0 0.0 20.0 40.0 60.0 80.0 100.0 0.0 200.0 400.0 Ono.o T

Figure 6: Correlation functions associated with the trajectories of Fig. 5. Dashed curves: hard chain; solid curves: harmonic chain; dotted curves: soft chain. Left panel: short-time behavior. Right panel: correlation function on a, logarithmic scale. effective damping. The slopes in the logarithmic rendition can be associated with the inverse of the transition rate from one well to the other. The transition rate is highest for the hard chain and lowest for the soft. The hard chain clearly provides the most favorable environment for transitions to occur at a given temperature. More detailed explanations, comparisons, and parameter variation effects can be found in Ref. [3].

ACKNOWLEDGEMENT

This work was performed under the auspices of the Engineering Research Program of the Office of Basic Energy Sciences at the U. S. Department of Energy. Portions of thk work were carried out in collaboration with J. M. Sancho and A. H. Romero.

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[15] T. PROSEN and D. K. CAMPBELL, “Momentum Conservation Implies Anomalous Energy Transport in ID Classical Lattices,” chao-dyn/9908021.

[16] P. .J. MARTINEZ, L. M. FLORIA, F. FALO and J. J. MAZO, “Intrinsically Localized Chaos in Discrete Nonlinear Extended Systems,” Burophys. Lctt. 45, 444 (1999).

[17] C. GIARDINA, R. LIVI, A. POLITI and M. VASSALLI, “Finite Thermal Conductivity in ID Lattices,” l%ys. .Ekw.Letters 84,2144 (2000).

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Seth Putterman and Raffi Budakian

Physics Department,University of California, Los Angeles, CA 90095

ABSTRACT

Friction, triboelectrification and sonoluminescence are phenomena which indicate nature’s propensity to focus energy and stress is continuous media driven into off-equilibrium motion. In cavitation luminescence sound energy can focus by 12 orders of magnitude to make light. In tribological processes quantum mechanics focuses applied stress by over a factor of 1 million to account for stick-slip friction. Observation of these effects makes use of new techniques that have been developed to measure charge transfer and bonding between sliding surfaces.

INTRODUCTION

The tendency of nature to spontaneously focus energy in the off-equilibrium motion of continuous media is spectacular. Figure 1 shows the spectrum of light that is emitted from a fluid as it is forced to flow through a Venturi tube at speeds which lead to a pressure drop of about an atmosphere[l ]. Although the velocity of the room temperature water is measured in meters/second the emitted light is broad band out to energies of 6eV which means that the light is emitted from hot spots with temperatures of about 50,000K or higher. This light is due to the formation of bubbles which focus energy as they collapse supersonically[2]. A single such bubble can be trapped in a resonant sound field so as to emit one flash of light with each cycle of sound and as shown in Figure 1 its spectrum is similar to that of the Venturi tube flow. The pulsating motion of the bubble focuses the difhse sound energy density by 12 orders of magnitude to make flashes of light whose width is measured in picosecond. Cavitating bubbles have actually found use in surgical procedures where they form on the end of a vibrating tip. The energy focused by this cloud of bubbles can effectively cut through tissue[3]. The spectrum of a cloud of transient bubbles is also displayed in Figure 1. At high frequencies [over lMHz] the bubbles formed in a high amplitude sound field collapse down to radii on the order of tens of nanometers[4] at which point light is emitted. This can be called nanoluminescence.

154 Transient Sonoluminescence

Venturi Tube

i 1 200 400 600 800 Wavelength (rim)

I?IGURE1: SPECTRA OF VARIOUS OFF-EQUILIBRIUM MOTIONS

Energy focusing is not limited to cavitation. One of the earliest ~icard 1676] investigations of luminescence dealt with the light emitted by mercury sloshing around inside of a barometer. In a controlled laboratory experiment[5] one can rotate a container of mercury around a horizontal axis and observe light emission from the region of the meniscus with the unaided eye. For the purpose of taking the spectrum shown in Figure 1 neon gas was added to the system. In the case of “rubbing electricity” the spectrum appears to come out as lines. But excitation of the neon line requires electrons with energies above 20ev. So the relative motion of mercury against glass at about 1mrdsecond leads to the repetitive acceleration of electrons to about 1% the speed of light. These fast electrons collide with the neon atoms to make the light. The mechanism of this effect is still unclear[6].

EXPERIMENTS AND DATA

In the experiments where mercury rubs against glass one observes that the mercury sticks to the glass between discharges. It thus undergoes a kind of stick-slip motion. In order to determine whether these observations can be generalized so as to gain insight into the long standing problem of friction[7], the charge transfer between rubbing surfaces has been measured[8], Figures 2A,B show the apparatus used to measure the force of friction between surfaces in relative motion as well as the charge transfer. In this case the tip is gold and the ——. —

substrate is a dielectric [PMMA]. Charge deposited onto the substrate as a result of a stick slip friction event will lead to a time varying voltage when chopped with a conductor as shown the figure. xz - cantilever normal -7 scan direction! capacitor 4-I! !

,~mc$:’or ii ,Z ‘s n , C,oppcr ~i __ -__!~~__m_etaltip ~~/,.” /~, dielectric surfllce ,~——-—r-----—-—------..----—..-----—-.---—, ~ chopper —-——-.I .— —-—--.--.-1-.———...——----\

back plate d

‘—-—------clock-in amplifler input

FIGURE 2A - APPARATUS TO MEASURE STICK-SLIP FRICTION AND CHARGE TRANSFER

Figure 3 shows the force of friction as a function of distance scanned as well as the total charge laid down by the gold tip. Note that each slip event in Figure 3 reveals a jump in the accumulated charge and furthermore there exists a scale factor .48eV/A which can be used to collapse these two measurements onto one curve as shown in Figure 3B. To calculate the scaled curves we introduce the displacement Axi of the tip on the i’1’ slip event which is resisted by a force, ~. = hkr, where k is the lateral spring constant of the cantilever [47N/m]. The total distance x,$ scanned by the stage obeys:

x.$ = Axj + AX(XY) (1) i

~~156 quadrant photodiodcdetector~~

~~,. single mode m;i ------fiberoptic - =~— [ SLID m I I 1$ z-axis piezo~~

~~positionsensing RF lock-in photodiode !.%“.Y&=?l&~g.,.<$&~~

~~modulation Y/L x-axis piezo scandircctio: fiberdeflection rcfemnce 5’ //7 goldtip -.1 Bar goldsurface ?nacro current ,r r-l~~

~~TODView~~

~~~bonds -—-- . ‘13iJ’—— highbandwidth di itizcr Surfiace fL!3 acoustic~? 7 transducer ● J \ P - N - MBar BONDS ~ T-~~

~~FIGURE2B- APPARATUSTOMEASUREBONDSTRENGTH~~

J%(X$– Ax(xY)) = CxN(x,$) (2) where ANj is the charge transferred on the i’h event, N(x,, ) is the total charge deposited in scanning x.$and ~ is the average lateral force per charge. The force curve in Fig. 3A, which is equal to klw(x$, ), has been combined with the imposed x, to obtain a scaled force curve equal to the left hand side of Equation (2). This is plotted in Figure 3B along with ti(x~) , using the value 0.48 eV/ ~ for ~. The energy and length scale that combine to determine ~ are characteristic of a single molecular bond, which suggests that in these experiments friction arises from bunches of bonds that form between and grab to rest two surfaces in relative motion. The charge transfer is a marker for the number of bonds ruptured at a particular slip event. The force of a single bond is remarkably large as an eV/~ (the natural scale for ~ ) is 1 nN so that 108bonds/mrn2, which is typical of our findings, corresponds to a force of 1 mN. This corresponds to an average macroscopic stress of about an atmosphere, and a focused stress at each bond of a Mbar (ule V /~3 ). By use of a liquid crystal film under the substrate the location of the charges can be instantaneously imaged with a resolution of 1()-12Coulomb/ mmz. Future generations of this charge microscope should reach resolutions of 10-14Coulomb/ mmz . This device shows that the charge transfer is indeed concentrated at the slip locations [8].

~~157 t I I 1 I I I I I I I I I t 1 I I I I 1,,,,1,,,,1,,,,1, I t 1 40~~

~~0 l“’’I’’ ’’1’ ’’’1 ’’”1’ “’I’J’’I’’’IIJIJI o 1000 2000 3000 4000 i I I I i 1 i I I 1 I I 1 I 1 I 1 1 I i i I I I 1 i I 1 <0.8 r~~

~~0.4 : RHsof(1)~~

~~LHS of(l) / --- k (X, - X(X,)) 0.2 g.. .p / N(x,) ‘ /~~

~~0.0 1 I I 1 f I 1 I I t I I I 1 I I ! I 1 t I t I I I 1 I 1 t I o 1000 2000 3000 4000 clislancescanned[x,1( m)~~

~~FIGURE 3- STICK-SLIP FORCES AND CHARGE TRANSFER~~

158 ...... -. For a metal surface sliding over ahother metaI_stiace it ii not”obvious how io””rnias~e-~ the charge transferred as a result of stick-slip events. In this case one can measure the elasticity of the bonds which form when the surfaces come into contact. The apparatus is ~ I shown in Figure 2. A 100micron gold ball han’s from the end of a fiber optic which also I serves as cantilever. The natural frequency of oscillation~ of the ball on the fiber is 1,600Hz. I~- As a lmm gold ball is brought into contact with the suspended 100micron ball one observes ! that the resonant fkequency for motion parallel lo the interface stiffens and that the balls I attract each other. This behavior is shown in Figure 4. Attraction between the surfaces is a L process that can take off on its own[9]. For the parameters presented here the centers of the spheres can approach by an additional 40nm. This behavior can also be interpreted ii terms of bonds that form between surfaces in contact. As some bonds form the local attractive stresses increase so as to favor the formation I of additional bonds until the elastic forces setup by the distortion of the stiace balance the process. The observed forces of stick-slip friction for gold on gold agree with the bonding forces documented in Figure 4. f

‘~ (transversechannel) ., -: mlBUVBdh?placement .-. duringeppmaoh 2600 .. . (compreeafon) .:. --- . .. . .- - -. .i ~ L ..:. -- — .— — --- —_ ...... --:....,. 2000 ...... ,.- ,.. ~,- .4? ...,. .: .. , . . ... i .“. iv) 1500 .,,.... . - .. . . . “.. . .,----; :...,- ,.:...... -. \- kioo ...... -1 ..” .;: / ,{ . .. , ... .: .,< .,. .- . . . . . “~j ,-. ” “- :-. .,--,; . . ,...... ’ .2 , .,.. 1000 .’ . . 1000 .. 1 ...... 500 .. ‘%9 600 .. .+ -9. o- L ‘“ ‘“”:- ‘“-” .“ . &d&kuLAo 0 2 4 6 8 PO Ii -20 -10 Q Idiz t dhplacemant(rim) Fundamental Mode (1.606 Id-tz) PIGURE 4- STRBNGTH OF SPON’MNEOUS BONDING - \ i I

~~IxiN~~

~~-—-. ..—.. .. -..~~

~~‘ ,:~~

~~CONCLUSION~~

In conclusion macroscopic measurements of surfaces in relative motion suggest that triboelectrification and friction have a common origin namely bond formation and rupture. , The quantum processes that lead to bonding also lead to highly focused local stresses that constitute an essentiaI consideration for engineering at the nanoscale.

~~ACKNOWLEDGMENT~~

~~Research supported by the U.S. Department of Energy.~~

~~REFERENCES~~

1. K.R. WENINGER, C,G. CAMARA and S.J.PUTTERMAN ‘Energy Focusing in a Converging Flow’ Phys. Rev. Lett. 83,2081 (1999). 2. S.J. PUITERMAN and K.R. WENINGER ‘Sonoluminescence’ Ann. Rev. Fluid Mech. 32, 445 (2000). 3. K.R. WENINGER, C.G. CAMARA and S.J.PUTTERMAN ‘Physical Acoustics of Ultrasound Assisted Lipoplasty’ Clinics in Plastic Surgery 26,463 (1999). 4. K.R. WENINGER, C.G. CAMARA and S.J.PUTTERMAN, Unpublished. 5. R. BUDAKIAN, K. WENINGE~ R.A. HILLER, S.J. PUTTERMAN ‘Picosecond Discharges and Stick-Slip Friction at a Moving Meniscus of Mercury on Glass’ 391,266 (1998). 6. B.D. TERIUS, et al ‘Contact Electrification Using Force Microscopy’ Phys, Rev. Lett. 63, 2669 (1989). 7. B.N.J. PERSSON, ‘Sliding Friction’ (Springer, Berlin 1998). 8. R. BUDAKIAN and S.J. PUTTERMAN ‘Correlation between Charge Transfer and Stick- Slip Friction at a Metal-Insulator Interface’ to appear Phys. Rev, Lett.; ‘Real Time Imaging of Two-Dimensional Charge on Dielectric Surfaces’ Rev. Sci. Inst. 71,444 (2000). 9. K.L. JOHNSON ‘Contact Mechanics’ (Cambridge University press, Cambridge, 1977).

~~160 “. Instabilities and Defect Chaos in Models for Rotating Non-Boussinesq Convection~~

Hermann Rieckej Bias Echebarria, Vadim Moroz, and Filip Sain*

~~Department of Engineering Sciences and Applied Mathematics Northwestern University, Evanston, IL 60208, USA~~

Abstract We are interested in the types of spatially and temporally complex dynamics that may arise in systems in which patterns with hezagomd planform become unstable. Motivated by the Kiippers-Lortz instability of rotating Rayleigh-B&mrd convection, whkh leads to persistent domain chaos, we study the effect of rotation on convection with a hexagonal planform ss it arises for sufficiently strongly temperature- dependent fluid parameters. Using coupled Ginzburg-Landau equations and order-parameter models of the Swift-Hohenberg type, we find that the steady hexagons that arise near onset can become unstable via steady and oscilla~ory,short- and long-wave instabilities. There are regimes in which the instability gives rise to persistent dynamics in which the Fourier spectrum of the disordered pattern effectively rotates with time, Within weakly nonlinear theory, the oscillating hexagons that arise farther away from threshold are described by the single complex Ginzburg-Landau equation (CGLE) and generically exhibit bktability between periodic oscillations and defect chuos. They appear to be the first system that should allow detailed quantitative comparison between experiments and the CGLE in one of its regimes I of complex dynamics. As a first step towards a quantitative comparison we derive the relevant coupled Ginzburg-Landau equations directly from the Navier-Stokes equations.

~~1 Introduction~~

Among the current challenges in the understanding of chaotic systems are systems that behave chaotically in time but are also disordered in space. Such spatio-temporal chaos can arise in systems ranging from waveson fluid surfaces to electrical excitation waves in hearts undergoing fibrillation, a serious heart condition. The understanding of Iow-dimensional chaos of systems with few active degrees of freedom has reached a high level and has allowed substantial progress in its control as well as in harnessing its features for applications, e,g, in communications or in mixing. High-dimensional chaos is far less well understood. Spatio-temporal chaos in spatially extended dynamical systems falls into this category. One of its characteristic features is the extensivity of the chaotic attractor, i.e. the number of active modes grows linearly with the size of the system. This suggests that these systems may be thought of as interacting dynamical, possibly chaotic units. The identification of the relevant units is, however, far from obvious. In many pattern-forming systems, e.g. in R,ayleigh-B&mrd convection, natural candidates for building blocks of the chaotic dynamics are defects in the pattern. These can be point defects like holes or dips in the wave amplitude in one dimension [1, 2], or disclinations and dislocations in two dimensions [3, 4, 5, 6], or they can be line defects like domain walls separating, for instance, stripe patterns of different orientation [7, 8]. Whether the defects play in fact an active role in the overall dynamics has not been clarified in most systems. In simulations of the single complex Ginzburg-Landau equation (CGLE) it has been established that a certain fraction of the total fractal dimension of the attractor can be attributed “Current address: The CNACorporation,4401Ford. Ave,Alexandria,VA22302

161.’ to the dislocations in the wave pattern with the remainder being due to the wave field between the defects [4]. In simulations of coupled Ginzburg-Landau equations the dynamics of the dislocations have been found to provide an intuitive understanding of the transition between a spatially ordered and a spatially disordered state, both of which are chaotic in time [6]. In experiments on waves in binary-mixture convection progress has been made in reconstructing the complete wave field from the field generated by the dislocations alone [5]. Experimentally, spatio-temporal chaos has been investigated in a number of systems, in particular in various fluid flows in layers with large-aspect ratio. In Rayleigh-B6nard convection at low Prandtl numbers quite complex textures have been found that are characterized by stripe patches of various orientations, spirals, disclinations, and dislocations [3]. This state does not arise very close to threshold and is therefore not a good candidate for theoretical approaches using weakly nonlinear reductions of the full Navier-Stokes equations. In the presence of rotation, roll convection can become unstable and chaotic immediately above threshold due to the Kiippers-Lortz instability [9]. In thk system the dynamics are characterized by domain walls separating stripes (rolls) or different orientation. The success of a description using Ginzburg-Landau equations is, however, limited since these equations break the isotropy of the system. In electroconvection of nematic liquid crystals a regime is found in which spatio-temporal chaos arises immediately above onset [10]. Since the system is anisotropic, coupled Ginzburg-Landau equations should be able to describe the dynamics quantitatively. Unfortunately, while most of the coefficients in these equations have been derived from the underlying fluid equations [11], one coupling coefficient is still missing. On the theoretical side, spiral-defect chaos in convection has been treated by full numerical simulations of the Navier-Stokes equations [12] as well as model equations of the Swift-Hohenberg type [13]. The latter approach has also been used for the study of the domain chaos arising from the Kuppers-Lortz instability [7]. Most theoretical investigations of spatio-temporal chaos have been concerned, however, with the complex Ginzburg-Landau equation (CGLE) which applies quite generally to systems undergoing an instability to homogeneous oscillations. Despite its simplicity the CGLE exhibits a number of different chaotic and ordered regimes [14, 15, 16]. Surprisingly, however, up to recently no system appears to have been identified that exhibits one of the complex regimes found theoretically in the two-dimensional CGLE and that is suitable for detailed quantitative comparison with experiments. In this communication we enlarge on recent results on the dynamics of hexagonal patterns in the presence of rotation [17, 18, 19, 20, 21]. The motivation for thk work is two-fold. Most of the previous studies of spatio- tcrnporal chaos have been addressing regimes that arise from stripe-like states and therefore inherit some of their characteristics. It is to be expected that chaotic states that arise from instabilities of a hexagonal planform will differ in a qualitative way. Motivated by the results on the Kiippers-Lortz instability, we conjectured that rotation may also trigger persistent dynamics in the hexagonal planform. This is indeed the case, albeit in a quite different way. In addition to inducing instabilities of the steady hexagons, the rotation introduces a completely new state, oscillating hexagons, that arises in a secondary Hopf bifurcation off the steady hexagons. Strikingly, these oscillating hexagons are to leading order described by the single CGLE and within the weakly nonlinear theory they are always in a regime of bistability of stable oscillations and deject chaos [19]. Thus, rotating non-Boussinesq convection appears to be the first system that should allow a detailed comparison of one of the non-trivial regimes of the two-dimensional CGLE with precise experiments.

~~2 Weakly Nonlinear Description of Hexagons with Rotation~~

We are interested in a weakly nodinear description of hexagon patterns in the presence of rotation. One of the best known systems exhibiting such patterns is non-Boussinesq convection, i.e. fluid convection in regimes in whkh the temperature dependence of the fluid parameters is of importance. In the weakly nonlinear regime the full fluid equations can be reduced to simpler equations for the overall amplitude of the convective pattqn. We discuss two complementary approaches.

~~162 ●.” , ‘. ‘i’””= ‘‘O’O;? ‘ ,s ,’ ,. ‘.. Hexagons .’ \. #’ ‘. ------,’ .. ,’ --.+ ,’ . #’ -t- ‘~~

~~1’ Mix~~J’bde 1’ Solution s8 : . Solution - . ..‘.. *T----’ -.-..-,------... ———-... —-—.—— ..- R - ‘“: k:- R R ------R r RH R , ‘--.---.~~~ R, sn: = 1 -. I I I 1, .~~

~~Figure 1: Bifurcation diagrams for weakly non-Boussinesq convection without imd with rotation.~~

~~For small convection amplitudes the fluid equations can be reduced systematically to three coupled Ginzburg-Landau equations for the three Fourier modes making up the hexagonal pattern [17],~~

~~6jA = RA + (nA. v)2A+ 7X7– AIA12 – (~+ fi)Ap312– (~ – ti)A\c12. (1)~~

~~In terms of the amplitudes A, B, and C, typical fluid quantities like the temperature in the midplane are given by~~

~~fj = Aeif’m + fjei(-f?z/z’-!-fi9v/2) + &G17d2-d%/2) + ~.~. + ~.oj. (2)~~

The form of (1) can be derived using symmetry arguments. The bifurcation parameter in the amplitude equations is R. The breaking of the chiral symmetry by the rotation introduces a difference between the two cross-coupling coefficients as expressed by U . In the absence of spatial gradients these equations yield typically the bifurcation diagrams shown in fig.1 [22, 23]. The main new feature introduced by the rotation is the branch of oscillating hexagons arising at RH in a Hopf bifurcation and ending on the mixed-mode solution in a heteroclinic cycle at R~ . To achieve a quantitative comparison with experiments we have also derived the coupled Ginzburg- Landau equations (1) for weakly non-Boussinesq convection directly from the fluid equations. A typical phase diagram obtained from ‘:at analysis is shown in fig.2. Since currently available experimental set-ups allow rotation rates up to lHz the regime of oscillating hexagons should be easily accessible in these systems. It turns out that due to the rotation the steady hexagons can undergo an instability to a spatially disordered state with an isotropic Fourier spectrum. Since the coupled Ginzburg-Landau equations (1) only allow small deviations in the wavevector from the three preferred wavevectors they cannot capture such a state, We have therefore also made use of a phenomenological model of the Swift-Hohenberg type [20],

@J = R@-(V2+l)2@–163+a~2+72= . (VV X V(V2@)), (3) which preserves the isotropy of the system. Here R is the control parameter, ~ is a measure for the rotation, and v is the order parameter, which gives, e.g., the temperature of the layer in the mid-plane.

~~3 Instabilities of Steady Hexagons~~

The stability analysis of the steady hexagons within coupled Ginzburg-Landau equations as well as within Swift-Hohenberg-type equations reveals steady and oscillatory instabilities that can arise at long wavelengths or at finite wavelengths [20, 17]. A typical result from the Swift-Hohenberg-type equation (3) is shown in

~~163 ——.. .~~

~~1 0.9- 00.8 - a > g 0.7- d T 0.6- u $0.5 - E g 0.4 n Rolls F 0.3 :1 E 80.2~~

~~0.1 ‘F o~ 0 Taylor number T; 1 Hz cwresponds to ‘c = 24.0~~

~~Figure 2: Phase diagram for non-Boussinesq convection in a layer of water of height d = 0.106cmwith mean temperature To = 47.5”C.~~

~~r 1 ““Wi unstable ~ ‘“ 00’5~ 00s t % 004 R 003 .g~ 00’0 002 .:0.025 001 6~~

~~.—— ..—-. I [// 083 105 “’%2.3 0 U25 0.040 Hex~~on Wavenu’r%er k f3ifurcatior%ramet#% ‘~~

Figure 3: a) Stability region for steady hexagons in (3). Modulated hexagons arise between the lines marked by-crosses and solid diamonds. Chaotic hexagons appear to the right of the solid diamonds (see fig.4). b) Contour lines of modulated hexagons. c) Bifurcation diagram for the oscillation amplitude of the modulated hexagons.

fig.3a. The stability limit for wavenumbers larger than the critical wavenumber is due to an oscillatory instability, which leads to spatially and temporally periodic modzdated hexagons. A snapshot of this state is shown in fig.3b. The modulation is in the form of a standing wave: after half a period the contour lines will be disconnected in the center of the pattern and connected in the top and the bottom part. The bifurcation t,o the modulated hexa~ons is supercritical as shown in the bifurcation diagram fig.3c. The modulated hexagons persist up to the line marked by solid diamonds. There, additional sideband modes come into play and destroy the order as illustrated in the time dependence of the dominant Fourier modes shown in fig.4a. The modes A, B, and C make up the hexagon pattern, while the mode POOO is responsible for the spatial modulation of the hexagons. Around t = 4000 additional modes become important and the modulated hexagons are supplanted by a spatio-temporally chaotic state. Two snapshots of that state are depicted in fig.4b,c. Strikingly, the hexagonal symmetry of the pattern does not break down completely. Thus, the Fourier spectrum still exhibits 6 peaks, which are, however, quite broad due to the

~~164 0.0+3 ,, -8 !OO’ 002~~

~~O,co o !xcoacoemoaca Time~~

Figure 4 a) Crossing the solid diamonds in fig.4a the order of the modulated hexagons breaks down. Modes A, l?, and C correspond to the modes making up the initial hexagon pattern. Mode Pooois the mode modulating the hexagons. b) and c) Successivesnapshots indicating the rotation of the dominant orientation of the disordered patterns disorder in the pattern. With time, the spectrum evolves and effectivelyrotates at a quite steady rate 120]. The rotation can be seen by comparing the two snapshots in fig.4b,c. In fig.4c the dominant orientation has rotated by about 30° compared to fig.4b. The rotation is also visible in the time-dependence of the dominant Fourier modes shown in fig.4a. Beyond t = 6000, the growth and decay of the modes A, B, and C representing the initial hexagon pattern shows the variation of the dominant orientation of the pattern relative to these modes. “

~~4 Defect Chaos in Oscillating Hexagons~~

The oscillating hexagons arise in a secondary Hopf bifurcation offthe steady hexagons. Near that bifurcation they can be described by a CGLE for the oscillation amplitude H coupled to the phase vector ~s (@Z,@v) that characterizes the two wave vectors of the hexagons [18],

Two aspects of these equations are particularly noteworthy. First, to the cubic order considered in (1) the CGLE (4) decouples from the equation (5) “for the phase vector if the hexagon wavenumber is at the bandcenter. Second, although the coefficients & and p in the CGLE depend on the values of v and U their variation turns out always to be restricted to a range in which there is bktability of ordered oscillations and defect chaos, Thus, if the non-Boussinesq effects in the fluid are sufficiently weak to allow a description of the oscillating hexagons by the coupled Ginzburg-Landau equations (1), then independent of the values of v and fi the oscillating hexagons are predicted to exhibit defect chaos of the type studied theoretically in the CGLE [14]. Two snapshots of simulations of the coupled Ginzburg-Landau equations in that regime are shown in fig.5a,b. The dkordered pattern shows domains in which the hexagons oscillate. Thus, they have a slight roll-like character with an orientation that ‘rotates’ in time. The time interval between fig.5a and fig,5b corresponds to half a period of the oscillation. In addition, there are also localized regions in which the hexagons are quite unperturbed and steady, e.g. in the bottom left corner of fig.5a,b. The latter positions correspond to locations of vanishing oscillation amplitude, i.e. dislocations (spirals) in the complex amplitude 7f, This is made more clear in fig.5c in which the zero-lines of the real and of the imaginary part of 74 are plotted for the same time as in fig.5a. The dislocations correspond to the points of intersection of these lines. Comparison with fig.5a,b shows that whereever two defects are close to each other the oscillation

165 +“’’@).s I 1! Ii \ \ \ ,’ ‘. -----~ /’ ~--. /’ \ , 1’ t, ‘, @ \ \ \ 1’ ‘t \ \ ‘. 1’ 1’ ‘. \ ‘..--~.’ [ , -. i I ,- ‘. i, , /’ . ‘. --, . \ .. % : ------/-.---

Figure 5: Snapshot of defect chaos in oscillating hexagons. a) and b) contour-lines of hexagon pattern half a oscillation period apart. c) zero-lines of the real and imaginary part of the oscillation amplitude. Intersections identify defects. amplitude is strongly suppressed and the hexagon pattern is quite regular. For these parameters the spiral character of the dislocations is not very strong; the spirals do not persist long enough to develop into a clear spiral structure. Away from the band center the CGLE (4) becomes coupled to the phase equation (5). At the same time the values of the other coefficients in the CGLE change as well. The resulting dynamics are found to be very similar to that obtained in the CGLE alone. As the wavenumber of the underlying hexagons is increased the chaotic activity becomes weaker and the average number of defects decreases. A comparison of the density of dislocations in simulations of the coupled Ginzburg-Landau equations (l), of the phase-amplitude equations (4,5), and of the CGLE alone shows that even away from the band center the effect of the coupling to the phase is small. Specifically, we find a decrease in the chaotic activity and eventually a transition to a state like the frozen-vortex state found in the CGLE [16].

~~5 Conclusion~~

We have performed a weakly nonlinear analysis of hexagon patterns in systems with broken chiral symmetry. For the steady hexagons various regimes of interesting complex dynamics are possible, including the stable coexistence of steady hexagons, modulated hexagons, and spatio-temporally chaotic hexagons. The oscillating hexagons arising at slightly larger amplitudes are predicted to be described by the complex Ginzburg-Landau equation. The coefficients are found to be such that the oscillating hexagons should exhibit defect chaos that is bistable with the ordered oscillations. Calculations based on the fluid equations for weakly non-Boussinmq convection predict that this regime should be accessible in current experiments [24].

~~Acknowledgments~~

We have benefitted from discussions with M. Silber and gratefully acknowledge the support by the Engineering Research Program of the Office of Basic Energy Sciences at the Department of Energy (DE FG02-92ER14303).

~~166 ,.~~

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~~[18] B. Echebarria and H. Riecke. Defect chans of oscillating hexagons in rotating convection. Phys. Rev. Lett., 84:4838,2000.~~

[19] B. Echebarria and H. Riecke. Stability of oscillating hexagons in rotating convection. Physics D, to appear. [20] F. Sain and H. Riecke. Instabilities and spatio-temporal chaos of hexagonal patterns with broken chiral symmetry. Ph~sica D, accepted.

~~[21] F. Sain. Instabilities and Spatio-Temporal chaos ofhezagons inthepresence of rotation. PhD thesis, Northwestern University, 2000.~~

~~[22] J.W. Swift. Convection inarotating fluid layer. In Contemporary A4athematics Vol. 28, page 435, Providence, 1984. American Mathematical Society.~~

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~~168 COMPLEX INTELLIGENT MACHINES~~

~~Herschel B. Smartt, Ph.D., Charles R. Tone, Ph.D.,~~

~~Kevin L. Kenney~~

~~Idaho Ndtional Engineering and Environmental Laboratory P.O. BOX1625 Idaho ~d]k, ID 83415-2210~~

~~ABSTRACT~~

The machine control problem is normally approached from the perspective of having a central body of intelligence (and control) in the machine [Albus, 1991 ]. However, we present a conceptual design of a machine using distributed learning and intelligence. This new design is loosely based on biological models of social insects. For example, in an ant colony each ant functions according to local rules of behavior [Holldobler and Wilson, 1990, see chdpters 8 and 9]. There is no “king” or “queen”, although the latter name has been given to the reproducing ant. Following a similar approach, we present a modular machine architecture in which each machine element has local rules of behavior (and local learning) along with a global element that influences local behavior (but does not dictate actions). A prime goal is to develop methods of learning and behavior modification that ensure global stability and optimization of the total machine; we discuss the theoretical aspects of ensuring such optimal performance.

~~INTRODUCTION~~

James Albus [1991] at NIST has defined machine intelligence as “the ability of a system to act appropriately in an uncertain environment, where appropriate action is that which increases the probability of success, and success is the achievement of behavioral subgoals that supports the system’s ultimate goaL” Following Albus’ intent, we can say that intelligent machines are those that either know or can learn everything they need to know to perform a process or task. Such machines may be able to perform a processor task autonomously (without opemtor intervention) or semi-autonomously (with operator intervention).

~~In this paper, we present a conceptual design of a machine using distributed learning and intelligence. Related work has been conducted, for example, by Dorigo and Colorni [1996] using ant- ,,~~

~~!8 @@.\ml A cd row= rqtih Sq>pl, ,igent 00.@ull a Ctmlm Tip III Work-P&c Dixlmcc And VOIIWC “’’”C’\-“ rT \ Wckl NULWCIVoluIIw~~

Figure 1. Arc spot welding machine with agents for the power supply, electrode wire feeder, positioner axes, sensor, and operator interface. based local behaviorof multiple agentsto solvethe TrdveilingSalesmanProblemand other classical hard problems. Schatz et al. [1999]formulateda model for route learning in ants. Lambrinos et al. [2000] used a similar model for navigation of a mobile robot. Overgaard, Petersen, and Perram [1995, 1996] used local agent control of dynamic motion and pdth planning in multiple link robot arms.

Consider an intelligent machine in which various machine functions are carried out in a distributed manner. A schematic of such a machine for arc spot welding is shown in F@re 1. In addition to the machine hardware required (most of which is not shown) there are seveml “agents”. These agents have local control of various machine functions and are able to communicate with each other and with an operator agent, see Figure 2. The operator agent may be a human or may be an interface to a hurndn (or even an interface to another rn~chine). (Although it would be possible to focus on autonomous machines, we chose not to do so; our machines will interact with humans who have supervisory control authority.)

~~analog~~

~~dead man digital~~

~~mid-level motion control~~

~~Figure 2. Agent block diagram.~~

~~170 .~~

~~‘OWER UPPLY~~

~~Cv 20-20 VOns l-low S.* 1cc LW.500amperes I / 101o “’”’~ I~~

~~4 5.50 mmh Figure 3. Schematic of gas metal arc weldingprocessshowingtypical values of parameters.~~

The various agents will incorporate knowledge of how to perform tasks, the ability to learn from experience, and memory of past performance. The agents will also be able to optimize both their local behavior and the global behavior of the total machine.

To formulate such a machine, we need a variety of methods. In addition to distributed learning and control, we also chose to have our machines learn rules of behavior. This is distinct from learning control trajectories, a method frequently employed for machine learning. Our rules will be embodied using a variant of tizzy logic [Johnson and Smartt, 1995] that allows the system to learn by back propagation [Rumelhart, 1986]. However, we discuss the application of iterative learning control’ to distributed intelligence. Iterative learning control is a recent set of methods for learning control trajectories that is well suited to iterative processes. However, iterative learning control methods may also be used to learn the weighting of rules for local optimization. We also discuss a new method of global optimization that uses artificial neural networks that learn the contribution of local behaviors to global cost.

~~SIMPLE INTELLIGENT WELDING MACHINE~~

Now consider the welding machine control problem. This is a much more complicated problem than two-dimensional motion control. First, there is a motion control problem involved. Even simple automated welding machines may have three degrees of motion. Consider welding in the flat position (e.g. joining two flat plates edge to edge with the plates in the horizontal plane). The welding torch must move along the weld joint. It also needs to be able to move at right angles to the weld joint (in the horizontal plane) to track misalignment of the joint with the axis of primary motion. Finally, it needs to move in a vertical direction to obtain changes in the contact tube to weldment distance. In addition, the weld torch may be mounted with a lead or lag angle relative to the weld joint. That is, the torch maybe nominally vertical to the plates, but tilted backwards or forwards, respectively, with respect to the welding direction. For other weldment configurations, the torch maybe leaned to one side or the other. Finally, the torch may be moved laterally with respect to the weld joint in a weaving pattern to effective]y increase the width of the weld bead. Robotic welding systems maybe even more complicated.

a. Uchiyama, 1978; Arimoto, Kawamura, and Miyazaki, 1984 Moore, 1993 Welding also involves selection of proper values of the process independent variables, see Figure 3. Disturbances to the processor uncertainties in the welding conditions may result in a need for the welding process independent variables to be changed during welding. Consequently, we need to consider that the trajectory we must obtain involves multiple degrees of motion via the robot as well as multiple degrees of motion through welding parameter space. What we seek is a set of generic rules that will ensure that the weld is made in some manner that will result in a structurally reliable weldment. Further, we want the welding machine to tune those rules to obtain a more robust process than would result from a fixed set of rules.

Consider a specific welding control problem. We desire to fabricate a steel structure using arc spot welding. Thus, steel sheet will be welded to an underlying structure by means of weld nuggets deposited into circular holes in the sheet. This geometry is shown in Figure 4.

~~Figure 4. Cross section of gas metal arc spot weld showing a hole in the top sheet and a completed weld bti~d.~~

In this situation, the weld torch maybe moved to a suitable position over a weld site, using motion control M discussed ealier. The welding power supply contactor is actiwdted,the power supply voltage is set, the shielding gas is turned on, and the electrode wire is fed downward. This will result in ignition of an arc with corresponding heat and mass transfer to the weldment. After a suitable time, the power supply contactor is deactivated and the electrode wire feed is stopped. A short time later the shielding gas is turned off. Although this is perhaps the simplest arc welding example we can consider, there are still important control decisions that ensure that the weld will meet its acceptance requirements.

A good weld in this example is one that is strong enough, does not excessively over or under fill the hole, has minimal spatter, and does not contain gross defects such as cracks or porosity that could lead to failure. To be strong enough, the weld bead must adequately penetrate the lower structure (but not excessively melt through that structure) while fusing into the upper sheet. For most applications, the cross-sectional area of the weld bead in the plane of the interface between the upper sheet and the lower structure needs to be equal to or greater than some critical amount.

To obtain a good weld in this example, the current must be high enough but not too high and the weld time (the time the arc is on) must be equal to or greater than some critical minimum. This will ensure that adequate heat and mass have been transferred to the weldment. It is also necessary for the voltage to be above some minimum (to reduce spatter) and below some maximum (to avoid melt through and bum back).

~~172 GLOBAL OPTIMIZATION~~

One of the key challenges to achieving intelligent distributed learning with global optimization within our welding machine is the interaction between the global optimization cost function and local agent optimization cost functions. Each independent optimization agent must be able to make changes to its locally controlled parameters while keeping in mind its effects on the global cost/process. Traditionally, industrial process optimization is broken down into sub-components then optimized locally. If there is time and resources, once the sub-components have been optimized, an engineering team is formed to globally optimizing the interactions between sub-components through manual trial and error adjustments away from the sub-components optima. Today there is a growing interest in global process self-optimization, or near optimization, through the use of “swarm intelligence” [Bonabeau et al., 2000]. One method in particular is based on how ants function in nature while searching for food [Dorigo et al., 1996]. Each ant acts as an independent agent making random decisions on where to search with each move. As traffic increases along a particular path, ants crossing that path will be biased with a greder probability to follow the already more traveled path by its higher pheromone level. This tendency is reinforced as ants travel back and forth along the path between food and the anthill faster than other ants on competing paths. This leads to a faster increase in the pheromone trail on the shorter paths with respect to the longer competing paths, which attracts additional ants to the short paths. This is a never- -ending reinforcement of the global optimization cost function, i.e. increased food movement back to the anthill, However, as is pointed out by Bonabeau et al. [2000], there is also a kind of integral windup effect in ant behavior. When a shorterpath is introducedafter the “best path”has been found, the system has a hard time finding it unless the dynamicsare changed,e.g. the initial food source is used up. This limitationcan be overcomeby modelingthe pheromonetrial as evaporative[Bonabeauet al., 2000; Dorigoet al. 1996], It is importantto makeclear the key idvdsbeing presentedwithinthis optimimtion system each ant adds its ownpiece of cost to the global cost function(food delivered), and they are able to communicate to each other about their success (pheromone trail).

A slightly different intelligent distributed learning system can be expressed in human terms as an everyday project team, Here each team member is an individual agent that contains a wide range of experience, talents, and education. Norrndlly, such teams have a teandproject leader whose role is key to their achieving intelligent distributed learning on a global optimization problem. The team leader, and his allowed interactions, differentiates this method of distributed learning from the ant’s. Within this model of distributed learning, the global cost function is contained within the team leader and acts as an agent of its own. Tasks are distributed among team members as well as sub-groups of team members. These agents progress in solving their tasks, as well as developing localized communication paths between agents, i.e. real time reconfiguration of the sub-groups. More importantly, the key concept within this structure is that the tettm leader cannot dictate any particular action to a team member, In human terms, this is primarily due to the tedm leader’s lack of technical details and/or conceptual understanding required to solve any particular subtask. Remember, the team leader is globally oriented. However, team ltx~derscan attempt to influence a particular tedm member’s actions in order to achieve the global optimal solution. For example, the team leader can inform a member/agent that by increasing the tolerances within their portion of the process, all of the remaining process can speed up dramaticallyy, i.e. the other agents are waiting on that particular agent due to the extra time required to optimize his subtmk, even though it will not add much to the global cost function. We propose that this interaction between the team leader and individual team members is the key to the successful development of an intelligent global distributed learning algorithm, as opposed to “swarm intelligence.” Furthermore, we differentiate an intelligent global distributed learning algorithm from a centralized learning algorithm, such as traditional neural networks, by not allowing any agent to dictate to another agent its actions, i.e. the team leader is not allowed to force any agent into a particular action. In short, an intelligent global distributed learning algorithm must allow each agent its own localized cost function and the ability to solve its subtasks primarily by itself with non-dictated feedback from the other agents. Global optimization is actually achieved through the local optimization procedures employed by each agent while taking into account the global effects of its choices.

Using the human project team model just discussed, consider the intelligent spot welding machine outlined in Figure 1. This machine has a team leader, the Weld Quality Agent. Its job is to evaluate the overall success of welds produced by the machine and supply feedback to the local agents—i.e., x-axis agent, y-axis agent, z-axis agent, power suppiy agent, wire feeder agent-on their effectiveness in producing quality welds. The key to designing a particular algorithm is how the team leader, the Weld Quality Agent, is allowed to interact with each of the local agents. A further complication is by what methods will the team leader pass localized global cost information to each agent.

With this in mind, we consider the following initial architecture and algorithm for study, as outlined in F@me 1. This algorithm is based on a global cost function maintained and calculated within the Weld Quality Agent using generic weld parameter information developed from machine’s agents.

~~Weld _Quali~=V~(V~,V~ )+ S~(S,,V, )+ B~(S,,V, )+ M~(PI)+T~ where~~

~~V. represents the quality of the well nugget volume based on the desired volume, V~, and the measuredfcaIculated volume, V~.~~

~~S~ represents the quality cost of spatter produced during the welding process based on sensor inspection, S,, and operator visual inspection, V,.~~

~~B~ represents the quality cost associated with burn back.~~

~~ikl~ represents the quality of the mechanical joint produced by the machine based on the opemtor’s physical inspection, PI .~~

~~T~ represents the cost to quality due to the time involved in producing the weld~~

Now that the form of the global cost function has been chosen, the next step is to define the relationship and method for communicating global cost information to the local agents. We propose to accomplish this task by adding these effects of the localized global cost, C~’~’, to the traditional local cost function, C~~~. c(tgettt=LYc:;:;+(1- a)cf’

The ct term is used to adjust the balance between local cost and global cost variations on the local optimization process. It is planned that for new welding setups, the machine may f~xu to be 1 for an initial period of time, thereby allowing development of the initial relationships between the local agent costs and globaI costs before proceeding with the augmented local cost function above (i.e. ~ # 1). Note that the effect due to the global cost is based on multiple terms within the weld quality cost function, e.g. C~~} (V~, S~, ). These mappings form the uniqueness and key difficulty of the proposed algorithm;

174 namely, how will the algorithm obtain a mapping from global cost effects to local cost effects, i.e. Weld _Quality + C~~ ? To simplify the initial algorithm and its solution, it will be assumed that the effect of the global cost on a particular agent is a Iinew combination of each of the Weld _ Quality sub- terms: c:~;’(vQ,sQ,BQ,~Q,TQ)= alV~ -t-azS~ + a#3~ + adM~ + a5T~ where the aj’s are constants.

~~With this assumptionin hand, it is plannedto learn the forwarddirectionmap, from the local agent costs to the global cost fi.mctionterms,via a neural networkmapping:~~

where C~~!’~represents the wire feeder agent’s cost, C~ represents the i’”-axis agent’s cost, C:” representsthe power supplyagent’scost, and as above the ai’s are constants. This forwardneural network mapping will then be used to produce the reverse gradient mapping by way of the back- propagation training method. In addition to training the neural network based on the traditional error prediction feedback of the forward network, the change in each of the global cost terms ( AM~ ) due to

:;! , @.c(([ ;~l , @,)CU\~ , @W\ changes in the local agents (AC .A ,AC ~,y ) will be back propagated through the network all the way to its inputs (this process is not used to update weights). By doing this, one is attempting to use the back-propagation training method to relate a change in gIobal cost to the local agents by exploiting the gradient knowledge contained within the forward mapping of the neural network. We are not attempting to reverse map the input to outputs, instead we are only trying to obtain gradient information at the input of the neural network based on the change of the output of the network. In fact, the back-propagation algorithm is based on a gradient descent method, which back-propagates gradient information about the error in the outputs due to the inputs in a similar fashion,

It is planned to use radial basis neural networks within this part of the project because of their connection to Takagi-Sugeno fuzzy systems. This connection will be used to obtain a qualitative understanding of the mapping between the local agent costs and the global sub-cost. This is possible because radial basis neural networks and Takagi-Sugeno fuzzy systems have been shown to be rndthematica]ly the same, though developed from a different understanding [Spooner and Passino, 1996]. In essence, it is thought that one can develop a fuzzy model of the mapping process from local costs to global sub-costs by using a radial basis neural network [Passino, 1999]. This qualitative understanding of the relationships between local costs and global sub-costs can then be used in future model development for the welding process as well as in more traditional control systems for welding processes.

~~CONCLUSION~~

An approach to design of an intelligent machine has been presented based on distributed intelligence. Local agents are used to control individual machine functions and to process information needed by the machine functions. Examples of how this approach may be used to build a specific rntchine are presented for an arc spot welding application. A possible agent internal structure is presented that provides for local rules of behavior and safety considerations. An initial method for accomplishing distributed learning with global optimization has been presented. The learning method outline within this paper will form the basis for our continued research.

~~175 ACKNOWLEDGEMENT~~

~~This work is supported by the Basic Energy Sciences, Office of Science, U.S. Department of Energy, under DOE Idaho Operations Office Contract DE-AC07-991D 13727.~~

~~REFERENCES~~

~~Albus,James. S., “Outlinefor a Theoryof Intelligcncq”IEEETransactions on Systems, h4un,und Cybernetics, VOI 21, no. 3, MaylJunc 1991, pp. 473-509.~~

~~Arimoto, S., S. Kawamura, and F. Miyazaki, “Bettering Operation of Robots by Learning,” Journal of Robotic Systems, Vol. 1,pp. 123-140, March 1984.~~

~~Bonabcau, Eric; Th&aulaz, Guy. “Swarm Smarts:’ Scientific American, Mar. 2000, pp.72-79.~~

Dorigo, Marco; Maniezzo, Vittorio; Colorni, Alberlo. “Ant System: Optimimtion by a Colony of Cooperating Agents; IEEE Transactionson Systems, Man, and Cybernetics-PartB: Cybernetics, v 26, n 1, Fed. 1, 1996, pp. 29-41.

~~Holldobler, B. and Wilson, E. O., the ANTS, The Belknap Press of Harvard University Press, Cambridge, Mass.,1990.~~

~~Johnson, J. A., and H. B. Smartt, “Advantages of an Alternative Form of Fuzzy Logic,” IEEE Transactions on Fuzzy Logic, 3, pp. 149-157, 1995.~~

~~Lambrinos, D., Mollcr, R., Labhart, T., Pfcifcr, R., and Wchner, R., “A mobile robot employing insect strategies for navigation”, Robotics and Autonomous Systems, 30 (2000) 39-64.~~

~~Moore, K. L., Iterative Learning Control for Deterministic Systems, Series on Advances in Industrial Control, Springer-Verlag, 1993.~~

Overgaard, L., Petersen, H. G., and Pcrram, J. W., “A GcneraI Algorithm for Dynamic Control of Multilink Robots”, The International Journal of Robotics Research, Vol. 14, No. 3, June 1995, pp. 281-294.

~~Overgaard, L., Petersen, H. G., and Perram, J. W., “Reactive Motion Planning: a Multiagcnt Approach”, Applied Artificial Intelligence, 10:35-51, 1996.~~

~~Passino, Kevin. “Intelligent Control,” Workshop S-5, 38’1’IEEE Conference on Control, Phoenix, AZ, Dec. 7-10, 1999.~~

Rumelhart, D. E., G. E. Hiaton, and R. J. Williams, “Learning Internal Representations by Error Propagation,” Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1,cd. D. E. Rumelhart and J. L. McClelland, MIT Press, Cambridge, MA, pp. 318-362 (1986).

~~Schatz, B., Chameron, S., Beugnon, G., and Collett, T. S., ‘The use of path integration to guide route learning in ants”, Nature, Vol. 399, No., 24, June 1999, pp. 769-772.~~

~~Spooncr, Jeffrey; Passino, Kevin. “Stable Adaptive Control Using Fuzzy Systems and Neural Networks,” IEEE Transactions on Fuzzy Systems, v 4, n 3, Aug. 1996, pp. 339-359.~~

~~Uchiyama, M., “Forrndtion of High Speed Motion Pattern of Mechanical Arm by Trial,” Transactions of the Society of Instrumentation and Control Engineering, Vol. 19, pp. 706-12, May 1978.~~

~~176 LEARNING AND ADAPTATION IN MULTI-ROBOT TEAMS~~

~~Lynne E. Parker, Claude Touzet, and David Jung~~

~~Center for Engineering Science Advanced Research, Computer Science and Mathematics Division Oak Ridge National Laboratory, Oak Rldgc, TN 37831-6355~~

ABSTRACT While considerable progress haa been made in recent years toward the development of multi- robot teams, much work remains to be done before these teams are used widely in real-world applications. Of particular need are the development of mechanisms that enable robot teams to autonomously generate cooperative behaviors. This paper examines the issue of multi-robot learning and looks at various types of multi-robot learning. We briefly review various multi-robot learning approaches we have studied. The paper then presents the Cooperative Multi-robot Observation of Multiple Moving Targets (CMOMMT) application as a rich domain for studying the issues of multi-robot Icarning of new behaviors. We discuss the results of our hand-generated algorithm for CMOMMT and the potential for learning that was discovered from the hand-generated approach. We then describe our research in generating multi-robot learning techniques for the CMOMMT application and compare the results to the hand-generated solutions. Our results show that, whalethe learning approach performs better than random, naive approaches, much room still remains to match the results obtained from the hand-generated approach. The ultimate goal of this research is to develop techniques for multi-robot learning and adaptation that will generdlze to cooperative robot applications in many domains, thus facilitating the practical use of multi- robot teams in a wide variety of real-world applications.

~~INTRODUCTION~~

Research in multi-robot cooperation haa grown significantly in recent years. While the growth of this research is duc in part to a pure scientific interest in teams of autonomous robots, much of the growth is due to the increasing reahzation by the user community that teams of robots may provide solutions to difficult problems that previously were untenable. Certainly, it has been shown (e.g., in [1] and elsewhere) that multi-robot teams can increase the reliability, flcxibllity, robustness, and efficiency of automated solutions by taking advantage of the redundancy and parallelism of multiple team members. However, before multi-robot teams wilI ever become widely used in practice, wc believe that advances must be made in the development of mechanisms that enable the robot teams to autonomously generate cooperative behaviors and techniques. With the current state of the art, the implementation of cooperative behaviors on physical robot teams requires expert behavior programming and experimentation, followed by extensive tuning and revision of the cooperative control algorithms. It is unlikely that a significant real-world impact of cooperative robot teams will occur aa long as the current level of effort is required to implement these systems. Researchers have recognized that an approach with more potential for the development of cooperative control mechanisms is autonomous learning. Henccj much current work is ongoing in the field of multi-agent learning (e.g., [2]). Brooks and Mataric [3] identify four types of learning in robotic systems: . Learning numerical functions for calibration or parameter adjustment, . Learning about the world,

~~● Learning to coordinate behaviors, and~~

● Learning new behaviors. Our research h= examined several of these learning areas. In the first area - learning for parameter adjustment – wc have developed the L-ALLIANCE architecture [4],which enables robots to adapt their behavior over time in response to changing team capabilities, team composition, and mission environment. This archkecture, which is an extension of our earlier work on ALLIANCE [5], is a dktributed, behavior-based architecture aimed for usc in applications consisting of a collection of independent tasks. The kcy issue addressed in L-ALLIANCE is the determination of which tasks robots should select to perform during their mission, even when multiple robots with heterogeneous, continually changing capabilities are present on the team. In this approach, robots monitor the performance of their teammates performing common tasks, and evaluate their performance based upon the time of task completion. Robots then use this information throughout the lifetime of their mission to automatically update their control parameters according to the L-ALLIANCE update mechanism. We note, however, that the parameter update strategy used by LALLIANCE is dependent upon the assumption of independent subtasks whose performance can be evaluated based upon the time of task completion. This assumption does not hold for the CMOMMT application domain that we describe in this paper. We have also addressed approaches for learning in the second area - learning about the world. We have implemented a multi-robot system in which one robot learns to communicate symbolic information about the environment to another robot [6, 7]. In particular, we developed a two-robot team that was specifically designed to be heterogeneous, such that neither could successfully achieve the task alone. The robots were also endowed with a mechanism for learning to communicate task-specific symbolic information. To accomplish learning, a number of self-organized levels build upon each other. First, each of the robots learns a topological map of its environment. Once the topological map self-organizessufficiently,the robots can learn successivelyhigher-levelrelationships between locations, resulting in the emergenceof a navigation capability. When the robots have a consistent concept of “location” as defined in terms of their sensory and behavioral suite, they will begin to have succcss in communicating task-specific information. Specifically, each robot is endowed with behavior that results in the robots communicating in order to ground specific symbols to particular locations. Having learned a shared grounding that maps a set of symbols to locations, the robots can communicate important task-specificlocations to each other. The receivingrobot can interpret the communicated information, drive to the communicated location, and perform mission-specifictasks. The robot soon learns that this reliably assists in the completion of its tasks, and is more efficientthan performing the task without communication. The result is that the robots together learn to adapt their behavior toward more efficient mission completion by learning to represent and navigate around their environment and to communicate about it [8]. This approach has been successfully demonstrated in a laboratory cleaning task. In the remainder of this paper, wc discuss our research in the fourth topic area – that of learning new behaviors in multi-robot teams. The types of applications that are typically studied for this area of multi- robot learning vary considerably in their characteristics. Some of the applications include air fleet control [9], predator/prey [10, 11, 12],box pushing [13],foraging [14],and multi-robot soccer [15, 16]. Particularly challengingdomains for multi-robot learning are those tasks that are inherently cooperative. By this, wemean that the utility of the action of one robot is dependent upon the current actions of the other team members. Inherently cooperative tasks cannot be decomposed into independent subtasks to bc solved by a distributed robot team. Instead, the success of the team throughout its execution is measured by the combined actions of the robot team, rather than the individual robot actions. This type of task is a particular challenge in multi-robot learning, due to the cMllcultyof assigning credit for the individual actions of the robot team members. Of the.se previous application domains that have been studied in the context of multi-robot learning, only the multi-robot soccer domain addresses inherently cooperative tasks with more than two robots while also addressing the real-world complexities of embodied robotics, such as noisy and inaccurate sensors and effecters in a dynamic environment that is poorly modeled. To add to the field of challenging application domains for multi-robot learning, we have defined and have been studying a new application domain – the Cooperative Multi-robot Observation of Multiple Moving Targets (CMOMMT) – that is not only an inherently cooperative task, but, unlike the multi-robot soccer domain, is also a domain that must deal with issues of scalability to large numbers of robots. In the next section, we clcfincthe CMOMMT application. Wc then describe a hand-generated solution to this problem, along with the results we obtained with this approach. We then define a learning approach to enable robot teams to autonomously generate viable solutions to the CMOMMT application and compare the results to the hand-generated approach. The final section of the paper concludes with some summary remarks.

~~178 THE CMOMMT APPLICATION~~

The application domain that we are studying for use as a multi-robot learning testbed is the problem we entitle Cooperative Multi-robot Observation of Multiple, Moving Targets (CMOMMT). This problem is defined as follows. Given: s: a two-dimensional, bounded, enclosed spatial region v: a team of m robot vehicles, vi, i = 1,2, ...m. with 360° field of view observation sensors that arc noisy and of limited range o(t) : a set of n targets, q(t),j = 1,2,..., n, such that target oj (t) is located within region S at time t

~~We say that a robot, vt, is observinga target when the target is within vi’s sensing range. Define an m x n matrix B(t),as follows:~~

~~1 if robot vi is observing target oj (t) in S at time t 13(t) = [bij(t)]mXn such that btj(t) = { O otherwise~~

Then, the goal is to develop an algorithm, which we call A-Cit40MMT, that maximizes the following metric A A = )A: f: ~@$)~j) t=l j=l where: 1 if there exists an i such that b~j(t) = 1 g(qt), j) = { O otherwise In other words, the goal of the robots is to maximize the average number of targets in S that are being observed by at least one robot throughout the mission that is of length T time units. Additionally, we define sensor.coverage(q) as the region visible to robot vi’s observation sensors, for vi E V. Then we assume that, in general, the maximum region covered by the observation sensors of the robot team is much less than the total region to be observed. That is, u sensor-coverage (Vj) <

This implies that fixed robot sensing locations or sensing paths will not be adequate in general, and instead, the robots must move dynamically as targets appear in order to maintain their target observations and to maximize the coverage. The CMOMMT application is an excellent domain for embodied multi-robot learning and adaptation. CMOMMT offers a rich testbed for research in multi-robot cooperation, learning, and adaptation because it is an inherently cooperative task. In addition, many variations on the dynamic, distributed sensory coverage problem arc possible, making the CMOMMT problcm arbitrarily more difficult. For example, the relative numbers and speeds of the robots and the targets to bc tracked can vary, the availability of inter-robot communication can vary, the robots can differ in their sensing and movement capabilities, the terrain may be either enclosed or have entrances that allow objects to enter and exit the area of interest, and so forth. Many other subproblems can also be addressed, including the physical tracking of targets (e.g. using vision, sonar, IR, or laser range), prediction of target movements, multi-sensor fusion, and so forth.

~~A HAND-GENERATED SOLUTION TO CMOMMT~~

We have developed a hand-generated solution [17, 18] to the CMOMMT problem that performs well when compared to various control approaches. This solution has been implemented on both physical and simulated robots to demonstrate its effectiveness. The hand-generated solution, which we call A- Cit40h4MT, is described briefly as follows. Robots use weighted local force vectors that attract them to nearby targets and repel them from nearby robots. The weights are computed in real time by a higher-level reasoning system in each robot, and are based on the relative locations of the nearby robots and targets. The weights are aimed at generating an improved collective behavior across robots when utili~cd by all robot team members.

~~179~~

~~T., >,.,..$..:..-:,., ...... ,,,a-7 ..*....4-. —7 — —.. — w~~

Figure 1: Simulation results of three robots and six targets (first image), and five robots and twenty targets (second image), with the robots using the hand-generated solution to CMOMMT, and the targets moving randomly.

The local force vectors are calculated as follows. The magnitude of the force vector attraction of robot V1relative to target ok, denoted I f~ 1,for parameters O< dol < do2 < dos, is: –1 Z71 for d(vl, ok) < dol 1 for dol < d(vl, ok) s do~ ]fl~1= do:ziol dos–doz for do2 < d(w, ok) S oh {2 o otherwise where d(a, b) returns the distance between two entities (i.e., robots and/or targets). The magnitude of the force vector repulsion of robot V1relative to robot vi, denoted I gli 1,for parameters O < drl < drz, is:

~~for d(vl, vi) < drl I gli 1= -- for drl < d(vl, vi) s dr2 { o otherwise~~

Determining the proper setting of the parameters dol, dq, do3, drl, and dT2 is one approach to solving the CMOMMT multi-robot learning task using a a priori rnodel-bmed technique. Using only local force vectors for this problem neglects higher-level information that may be used to improve the team performance. Thus, the hand-generated approach enhances the control approach by includlng higher-level control to weight the contributions of each target’s force field on the total computed field. This higher-level knowledge can express any information or heuristics that are known to result in more effective globaI control when used by each robot team member locally. The hand-generated approach expresses this higher-level knowledge in the form of a weight, Wlk, that reduces robot T1’s attraction to a nearby target ok if that target is within the field of view of another nearby robot. Using these weights helps reduce the overlap of robot sensory arc.as toward the goal of minimizing the likelihood of a target escaping detection. The higher-level weight information is combined with the local force vectors to generate the commanded direction of robot movement. This direction of movement for robot V1is given by:

n m ~ Wl~fi~ + ~ gli !4=1 i=l,ijd where flk is the force vector attributed to target ok by robot vi and gli is the force vector attributed to robot vi by robot VI. To generate an (z, y) coordinate indicating the desired location of the robot corresponding to the resultant force vector, we scale the resultant force vector based upon the size of the robot. The robot’s speed and steering commands are thcm computccl to move the robot in the direction of that dcsirecl location.

180 Figure 2: Robot team executing hand-generated solution to CMOMMT. The first photo shows robots operating in area with no obstacles. The second photo shows the robots amidst random distributed obstacles.

Results from Hand-Generated Solution Figure 1 shows two of the simulation runs of the hand-generated algorithm (out of over 1,000,000 simulation test runs), in which (first image) three robots attempt to observe six targets, and (second image) five robots attempt to observe twenty targets. Figure 2 shows snapshots of two of the physical robot experiments (out of over 800) in which the the robots perform the task either with no obstacles in the work area (first photo) or with randomly distributed obstacles (second photo]. The results of the hand-generated approach to CMOMMT vary depending upon a number of factors, including the relative numbers of robots and targets, the size of the work area, the motions of the targets (i.e., whether random or evasive), and the setting of the weights. In general, the A-CMOMMT algorithm performed best for a ratio of targets to robots greater than 1/2. We compared the hand-generated A- CMOMMT approach with a non-weighted local force vector approach, os well as two control cases in which robots either maintained fixed positions or arc moved randomly. Figure 3 gives a typical set of these comparative results. Refer to [17] for more details on these results.

~~LEARNING lN THE CMOMMT APPLICATION~~

Wc have studied the CMOMMT problem from a learning perspective without the assumption of an a prz”on”model [19]. This approach uses a combination of reinforcement learning, lazy learning, and a Pessimistic algorithm able to compute for each team member a lower bound on the utility of executing an action in a given situation. The challenges in this multi-robot Iearning problem include a very large search space, the need for communication or awareness of robot team members, and the difficulty of assigning credit in an inherently cooperative problem. In this learning approach, lazy learning [20] is used to enable robot team members to build a memory of situation-action pairs through random exploration of the CMOMMT problcm. A reinforcement function gives the utility of a given situation. The pessimistic algorithm for each robot then uses the utility values to select the action that maximhs the lower bound on utility. The resulting algorithm is able to perform considerably better than a random action policy, although it is still significantly inferior to the hand-generated algorithm described in the previous section. However, even with a performance less than that of the hand-generated solution, this approach makes an important contribution because it does not assume the existence of a model (as is the case in the Partially Observable Markov Decision Process (POMDP) clomain), the existence of local indicators that help individual robots perform their task.., nor the use of symbolic representations. The following subsections describe this approach and its results in more detail. Lazy learning and Q-learning Lazy learning [20] – also called instance-based learning – promotes the principle of delaying the use of the gathered information until the necessity arises (see Fig. 4). The same pool of information (i.e., memory) is used for different behavior syntheses. The lz~y memory provides a good way of ~cducing the duration of any robotic learning application. In the context of reinforcement learning, lazy Iearning provides an instantaneous set of situation-action pairs (after the initial and unique sampling phase). Lazy learning samples the situation-action space according to a random action selection policy, storing the succession

~~181 . ..- .. . .,” . . .. --— .“ . . ..~~

, , \ ______\ $ ~pJluMr I --.r-.l- a’ \ ...... rid t ~,\ n t :\ ( A.M,JIII, t ‘______t —.14 t :im t ~-... \ ,1.JJ”IIU, i “ t _.1..4 { \ n ( ~-~-—: y..&- I \ \ n: \ \ i “ - ‘u‘ ‘<$, .> “?.:, 1 ... ‘. ~ al >,, ., ., \ .,. ------03 -- ...X ------. ------. ..- “------...... ------‘------~ ...... a . 0 0 0 mm 31.um ?.mm Wml Wnn 0 Iunl mLw W-J -$- YJJ- D Im -mu. .Wnl JoLvJ mm It.#+,tJ. ”L””’lu ld.,d. ”k. c.m, U&., d.dw. (w [s) h- U5.T=x=UUIQWm&ti (b) Mm- U2.T.IVII .w*. mcd.nd, [d ah - l, TmP1r u-** CMdc+ , < ;;ywr a. ~- --. R4..L. ---.. #l,.+ 1) n“ :i~ \\ .6 N \\ --—— ———— — ‘\\ $ 1 . \,\ > -.—— .—— —— ‘t *.,\ “? ... .2 .} . ..:.- _ . . .. . ------...... - ..-...... 0 ...... ------:Ium m.cm .Um 81ml S9X 0 Iolwmmmmmn.lu.n !.In. Xa.,d. wk”c. tm, m MU. l% T.mrM mm.rsaderdy

Fiare 3: Simulation results of four distributed amroaches to cooperative observation, for random/linear tm”get movements, for various ratios of number of ~&gets (n) to number of robots (m). of events in memory and, when needed, probes the memory for the best action. The exploration phase is performed only once. By storing situation-action pairs, a lazy memory builds a model of the situation transition function. In order to express a behavior, the memory must be probed. To do thk probing, we use a modified version of the technique proposccl in [21]. In [21] the objective is to provide a method for predicting the rewards for state-action pairs without explicitly generating thcm. For the current real world situation, a situation matcher locates all the states in the memory that are within a given distance. If the situation matcher has failed to find any nearby situations, the action comparator selects an action at random. Otherwise, the action comparator examines the expected rewards associated with each of these situations and selects the action with the highest expected reward. This action is then executed, resulting in a new situation. There is a tlxed probability (0.3) of generating a random action regardless of the outcome of the situation matcher. New situation-action pairs arc added to the memory, along with a Q-value computed in the classical way [22]. Among similar situation-action pairs in the memory, an update of the stored Q-values is made. However, there is a limit to the generality of this lazy memory because the Q-values associated with the situation- action p,airs only apply for a particular behavior. With the desire of reducing the learning time as much as possible, as well as preserving the generality of the lazy memory, wc modified the algorithm as follows: (1) the situation matcher always proposes the set of nearest situations - no maximum distance is involved, (2) there is no random selection of actions by the action comparator, and (3) the Q-values are not stored with the situation-action pairs, but computed clynamically as the need arises. The Pessimistic Algorithm We define a Pessimistic Algorithm for the selection of the best action to execute for a given robot in its current local situation as follows: find the lower bounds of the utility value associated with the various potential actions that may be conduct,cd in the current situation, then choose tkm action with the greatest utility. A lower bound is defined as the lowest utility value associated with a set of similar situations. The idea behind the Pessimistic Algorithm is that a local robot situation is an incomplete observation of the true state of the system. Thus, instead of trying to solve the observation problem by completing the observation (usual POMDP approach), we arc only interested in ranking the utility of the actions. If we use a unique instance of the memory to obtain the utility of the situation, then chances arc that the

~~182 Rinrtlomlybuilt lookupmblc: Reinforcemcm situiiion, uction funcliou~~

~~i T~~

~~Evislw~tion Situationrnutchcr function~~

~~t I Siluution Action I I~~

Figure 4: Lazy learning: randomly sampled situation-action pairs in the lookup table are used by the situation matcher to select the action to execute in the current situation. The reinforcement function qualifies the actions proposed, helping to select the best one.

utility attributed to this local situation is due in fact to other robot’s actions. This probability decreases proportionally with the number of similar situations that are taken into account. If a large number of situations are considered, then there must be at least one for whkh the reward directly depends on the local situation. By taking the minimum utility value of the set of similar situations, we are guaranteed that, if the value is null, then the situation achieved does not imply loosing target(s). The Pessimistic Algorithm is then given as follows:

~~● Let H be the memory, a lookup table of situation-action pairs gathered during an exploration phase -- M = [(sea), .... (sea), (s(t + l), a(t + l)), ...].~~

~~● Let s~t be the current situation.~~

~~● Find S(sit), the set of n situations of M similar to A!.~~

~~● Let Sf .Ilow(sit) be the set of the situations that directly follows each situation of S(sit).~~

~~● Compute the lower bound (LB) of the utility value (U) associated with each situation s(k) C SjO~lOW(sit): – LB(s(k)) = min(~(s(m))), for s(m) c S(s(k)), the set of situations similar to s(k).~~

● Execute the action that should take the robot to the new situation s*: s* = max(~~(s)) and s~s~ollo~(sit), The utility U associated with a given situation can be computed in many ways. It can be the exact value of the reinforcement function for this particular situation-action pair, or it can be a more elaborate variable. For example, in our experience we store the situation-action pairs, plus the number of targets under observation in the lookup table (M). However, the value that is used as utility is +1 if one or more targets have been acquired compared to the previous situation, -1 if one or more targets have been lost, or O otherwise. An exact Q value requires running the Q-learning algorithm with the samples stored in the memory. Results of Learning Approach Wc studied the efficiency of the Pessimistic Algorithm by comparing the performance of a team of robots with a purely random action selection policy, a user-defined non-cooperative policy and A- CMOMMT. In these experiments, each robot situation is a vector of two times 16 components. The first 16 components code the position and orientation of the targets. It simulates a ring of 16 sensors uniformly distributed around the robot body. Each sensor measures the distance to the nearest target. The sensor position around the body gives the orientation. The second ring of 16 components code in the same manner the position and orientation of neighboring robots. The maximum range for a target or a robot to be seen is 1, for an arena radius of 5. The actions of each robot arc rotation and forward movement. The measure of performance is the mean observation time of all targets.

~~183 70 targets under observation~~

~~m aD. A-CMOMMT 20~~

~~8D Pcs.silni.slit I!JIZV Leaning : so -’ I .i~ m ) Locul 30 2Q~~

F@re 5: Performances of the Pessimistic lazy Q-learning approach compared to a random action selection policy, a user-defined non-cooperative policy and the hand-generated solution A- CMOMMT. The size of the lazy memory varies between 100 to 900 situation-action pairs. There are 10 robots and 10randomly moving targets. The results arc the mean of 10 different experiments per point for lazy learning policy, and 100 experiments for the other 3 policies. Each experiment duration is 1000 iterations.

Figure 5 shows the performance of a Pessimistic lazy Q-learning policy versus the size of the lazy memory, from 100 to 900 situation-action pairs. Each point is the average of 10 experiments. The standard deviation is also plotted on the graph. The lazy memories are obtained through an initial exploration involving from 15 to 25 targets and a single robot. During the sampling, the targets are fixed and the robot’s policy is random action selection (with 5% chance of direction and orientation changes). The reinforcement function returns +1 if the total number of targets under observation increases, -1 if this number decreases, or Ootherwise. As we see there is an important performance gain associated with the Pessimistic lazy Q-learning over a purely random selection policy. This clearly demonstrates the importance of lw~yQ-learning as a learning technique. Even more interestingly, lazy Q-learning performs much better than the user-defined non- cooperative policy (Local). It is important to note that neither policy is aware of the existence of the other robots. Both policies usc the same sensory information – i.e., the distance and orientation of nearby targets. It is our opinion that the variation of performance is due to the fact that the lazy Q-learned behavior is somewhat less rigid than the user-defined policy. A lazy Q-learning guided robot will follow a target further than it could be, and, in doing so, will exhibit an erratic path, moving from one side of the target to another, back and forth without losing the target. In doing so, the surface under observation per unit of time is larger than the covered surface by the more rigid center-of-gravity-oriented robot. On the other hand, because it does not take into account the neighboring robots, it is easy to understand why the lazy Q-learned behavior performance cannot reach the level of the A- C’MOMMT performance.

~~CONCLUSIONS~~

In thki paper, we have proposed that the Cooperative Multi-robot Observation of Multiple Moving Targets (CMOMMT) application domain provides a rich testbed for learning and adaptation in multi-robot cooperative teams. We have described the need for learning and adaptation in multi-robot teams, and have defined the CMOMMT application, along with the characteristics that make it an interesting testbed for learning and adaptation. Wc reported on a hand-generated solution to the CMOMMT problem and discussed how the results from the implementation of this solution reveal the need for learning and adaptation in this domain. We discussed our work that uses the CMOMMT problem as a learning domain. The ultimate objective is to develop learning techniques using the CMOMMT domain that will generalize to other real- world domains, and will thus help realize the ultimate goal of enabling the widespread, practical use of multi-robot teams.

~~184 ACKNOWLEDGEMENTS~~

This research is sponsored by the Engineering Research Program of the Officeof Basic Energy Sciences, U.S. Department of Energy. Accordingly,the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U. S. Government purposes, Oak Ridge National Laboratory is managed by UT-Battelle, LLC for the U.S. Dept. of Energy under contract DEAC05-OOOR22725.

REFERENCES [1] L. E. Parker. On the design of behavior-based multi-robot teams. Journal of Advanced Robotics, 1996. [2] Gerhard Weiss and Sandip Sen, editors. Adaption and Learning in Multi-Agent Systems. Springer, 1996. [3] Rodney A. Brooks and Maja J. Mataric. Real robots, real lemming problems. In Jonathan H. Connell and Sridhar Mahadcvan, edi$ors, Robot Learning. Kluwer Academic Publishers, 1993. [4] L. E. Parker. Lifelong adaptation in heterogeneous tcamsx Response to continual variation in individual robot performance. Autonomous Robots, 8(3), July 2000. [5] L. E. Parker. ALLIANCE: An architecture for fault-tolerant multi-robot cooperation. IEEE Transactions on Robotics and Automation, 14(2):220-240, 1998. [61 David Jung, Gordon Cheng, and Alexander Zelinsky. Robot cleaning An application of distributed planning and real-time vision. In Alexander Zelinsky, edkor, Field and Semite Robotics, pages 187-194. Springer, 1998. [7] David Jung and Alexander Zelinsky. An architecture for distributed cooperative planning in a behaviour-based multi-robot system. Robotics and Autonomous Systems% 26:149-174, 1999. [8] David Jung and Alexander Zeliaaky. Grounded symbolic communication between heterogeneous cooperating robots. Autonomous Robot+ 8(3), July 2000. [9] Randall Stceb, Stephanie Cammarata, Frederick Hayes-Roth, Perry Thorndykc, and Robert Wesson. Distributed intelligence for air fleet control. Technical Report R-2728-AFPA, Rand Corp., 1981. [10] M, Bcnda, V. Jagannathan, and R. Dodhiawalla. On optimal cooperation of knowledge sources. Technical Report BCS-G201O-28, Boeing AI Center, August 1985. [11] R. Korf. A simple solution to pursuit games. In Working Papers of the Ilih International Workshop on Distributed Artificial Intelligence, pages 183-194, 1992. [12] Thomas Haynes and Sandip Sen. Evolving behavioral strategies in predators awl prey. In Gerard Weiss and Sandip Sen, editors, Adaptation and Learning in Multi-Agent Systems, pages 113-126. Springer, 1986. [13] S. Mahadevau and J. Connell. Automatic programming of behavior-based robots using reinforcement learning. In Proceedings of AAAI-91, pages 8-14, 1991. [14] Maja Mataric. Interaction and Intelligent Behavior. PhD thesis, Massachusetts Institute of Technology, 1994. [15] P, Stone and M. Veloso. A layered approach to learning client behaviors in the robocup soccer server. Applied Artificial InteUigence, 12:165-188, 1998. [16] S. Marsella, J. Adibi, Y. A1-Onaizan, G. Kaminka, L Mualea, and M. Tambe. On being a teammage: Experiences acquired in the design of robocup teams. In O. Etzioni, J. Muller, and J. Bradshaw, editors, Proceedings of the Third Annual Conference on Autonomous Agents, pages 221-227, 1999. [17] L. E. Parker. Distributed algorithms for multi-robot observation of multiple moving targets. To appear in Autonomous Robots, 2000. [18] L. E. Parker. Cooperative robotics for multi-target observation. Intelligent Automation and Soft Computing, special issue on Robotics Research at Oak Ridge National Laboratory, 5(1):5-19, 1999. [19] C. Towet. Distributed lazy q-learning for cooperative mobile robots. Submitted for publication, 2000. [20] D. Aha, editor. Laz~ Learnin~. Kluwer Academic Publishers, 1997. [21] J.W. Sheppard and S.L. Salzberg. A teaching strategy for memory-based control. In D. Aha, editor, Lazy Learning, pages 343-370. Kluwer Academic Publishers, 1997. [22] C. Watkins. Learning from Delayed Rewards. PhD thesis, King’s College, Cambridge, 1989.

~~185 INFORMATION FUSION IN PHYSICAL SYSTEMS USING PHYSICAL LAWS~~

~~Nageswara S. V. Rae, David B. Fteister, Jacob Barhen~~

~~Center for Engineering Science Advanced Research Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6355~~

ABSTRACT A physical system can be described by a set of parameters which are related to each other by certain physical laws. We consider that each parameter is either measured by sensors anchor estimated computationally. As a result, the estimated or measured values for a single parameter could be widely varying. We address the problem of fusing various meamrements and/or estimates to improve the accuracy in estimating the parameter, when the error distributions of sensors and estimators arc unknown. We propose a fusion method based on the least violation of physical laws that relate the parameters. Under the bounded variation condition of the physical law, we derive distribution-free performance bounds for a fusion rule computed using a finite sample. This result also implies the asymptotic convergence of the estimated fusion rule to the best possible rule which can bc obtained under a complete knowledge of the error distributions.

~~INTRODUCTION~~

We consider a multiplc sensor system that measures physical parameters of a system. Each parameter is either measured using an instrument or estimated using a computational method based on the measurements. There could be both systematic and random errors in the measurements as well as in the estimators. Furthermore, it may not be possible to know the actual parameter values, since all measurements and estimators (based on measurements) can introduce errors of different types. Consequently, there are a number of estimated and/or

~~186 I~~

measured values for each parameter. In general, very accurate sensor noise models could be clerivcd from device properties. But such models are difficult to derive for estimators based on complicated computer codes. On the other hand, it is relatively easy to collect measurements using the sensors, and then compute the estimators based on measurements. Fusion rules based on measurements have been developed [6], and are shown to bc very effective in practical engineering and robot systems. We consider the fusion of various measurements and estimators such that for each parameter the fused estimate is superior to the individual estimator or measurement. Since the actual parameter values are not known, the traditional pattern recognition or fusion solutions are not applicable here, The actual values, if available, could be used as the training data to design powerful fusers [6, 7, 5]. The lack of traditional” training data motivated a new paradigm [8] that utilizes physical laws. In this paper, we extend the results of [8], which are valid for only Lipschitx physical laws, to include non- smooth physical laws. The parameters of physical systems are related by physical laws, which are typically derived from first principles, and arc vcrifiecl by independent mechanisms. For example, for a simple mass sliding on a friction-less surface, we have j = ma, where ~ is force, m is mass and a is acceleration. If we choose a measurement or an estimator for each parameter, the accuracy of this set depends on how well the physical law is satisfied, and the “violation” of physical law is an indication of error. Thus, the set of estimators that achieves the least violation of the physical law is the most preferred. By fusing the measurements and estimators, on can achieve, in principle, performances superior to any set of estimators. The performance of the fuser, however, depends on the knowledge about the error distributions. If the sensor error distributions are known, the isolation fusers [5] can be designed to ensure fuser performance at least as good as best set of estimators. In the practical case, where we only have sensor measurements, we showed in [8] that (smooth) Lipschitz physical laws can be used to design the fuser. In particular, this result holds asymptotically (i. e. as sample size approaches infinity) and for finite samples, under Lipschitz properties of the physical law and fusion functions. These results arc not valid if the physical law is discontinuous or the individual fusion functions are not smooth. In this paper, we show that the bounded variation of the physical law is sufficient to obtain the finite sample as well as the asymptotic guarantees of the fusion procedure. This is achieved by employing fusers classes with the isolation property [5] and the bounded pseudo-dimension [1]; these conditions are satisfied by a number of fusers such as certain feedforward networks and linear combinations. The results of this paper enable us to utilize discontinuous physical laws and fusion rules to achieve performance superior to the best set of measurements. For finite sample sizes, wc show distribution-free result that given large enough sample the fuser performs better than the best set of estimators within a specified precision and with a specified probability. This result also implies that the computed fuser asymptotically approaches the best fusion rule (computable under complete knowledge of the distributions) as the sample size increases. In section 2, we describe the fusion problem originally formulated in [8], We show how physical laws can be used to design a fuser in Section 3 under the above conditions. We briefly discuss fusion of data collected in the exploration of methane hydrates in Section 4. PHYSICAL SYSTEMS AND LAWS

A physical system is specified by the parameters P(z) = (pl (z), p2(z),..., pn(z)) with pi(z) G $?, where z is one-climcnsional variable such as time or position. Each parameter pi is measured by ai instruments and estimated by 1Aestimators (ai ~ O,bi >0, and ai + bi > 1). The measurements corresponding to pi (z) are denoted by

~~?7Zi(Z) = {77ti,l(Z), ?7ti,2(Z)j .... 7L?i,ai(Z)} and the corresponding estimators arc denoted by~~

f3i(Z) = {ei,l(Z), ei,2(Z), . . . . (?i,~i(Z)}. Thus, there are ai + bi competing values for each parameter, and in general we do not know which one is more accurate. The measurements are assumed to be noisy in that repeated measurements by a sensor of pi(z) = z for a fixed value are distributed independently according to the distribution Pm{,jlx, which is denoted by Pmi,j lPi(Z).Thus, mi,j is a random variable. The estimator eiti is a (deterministic) function of the measurements, and hence is also a random variable. The joint distribution of the measurements is denoted by P~l,~z,...,lPIPl ,PZ,...,P.. There is a physical law J%(Z))P2(Z)) . . .%(~)] = o which relates the actual parameters corresponding to z. For the example of mass in the previous section, we have L[~, m, a] = (~ – ma)2 = O. We assume that L[.] satisfies the reasonable monoikmicitg condition: for any VI,y2, lyl I s ly21,we have

lL~l(z) ,... ,pi(z)+yl,. . ., Fu(z)]l S lL~l(Z),...,~i(Z) +Y2)...>Pn(z)]1. Monotonicity means that accurate parameter estimators yield no lesser “magnitude” of violation of the law compared to less accurate estimators. Consider a single estimator or measurement @i for the parameter. The closeness of L@1(z)>j2(z)>. . . ,@n(z)] to O determines how closely the law is satisfied. Let a basic set, denoted by S, be a set of measurements and estimators such that for each parameter wc choose precisely one measurement or estimator (but not both). The total error due to S is given by J!?(S) = ~L@l(z), fi2(z), . . . ,@n(Z)]. z

~~In all there are fi (ai + hi) possible basic sets, and ~ be the one with least error such that icl 2(S) = m~n2(S). The expected error of S is denoted by~~

and let S* be the one with the least expected error such that -?3(S”)= rn~ E(Y). Note that S* minimizes the expected error but S in general does not. More detailed discussion of the physical laws can be found in [8].

~~188 DATA FUSION BASED ON PHYSICA1 LAWS~~

A jusion junction ~~ G Xi for parameter p; combines the measurements and estimators such that fi(rni(z), e~(z)) is an estimate of pi(z). Let f = (fl,..., ~~) denote the fuser for all parameters. The expected error due to the fused estimate is

w = x@fl(Mz))el(z)) ,””” , L(m(z)j en(z))]~~ml,...,mnIpl,pnl,pnl .2 andlet~’~~l x... x ~n be the one with the least expected error. In general E(f) cannot be computed if the ~rror distributions are not known, and hence ~“ is not computable. In stead, wc compute f that minimizes the empirical cost given by

~~~(f) = ~ L [fl(nzl(z), cl(z) ),..., fn(rnn(z), en(z))], z based on a set of iid measurements (also called the sample)~~

~~{<(ml(z), el(z)),..., (inn(z), en(z))>: z = 1,...,s}.~~

Now we disc~ss methods that ensure 13(~*) S 13(S*), and more importantly based on a computable f that E(f) < E(S*), with a specified probability based entirely on the measurements and without any knowledge of the underlying distributions. A fuser class %i = {fi(y) : $la’+~’ H R}, for y = (YI,..., y[a,+~il), has the isolation property [5] if it contains the function ~-(y) = gj for all j = 1,2,..., (ai + ~i). If each 3; satisfies the isolation property, then the following conditions are directly satisfied.

~~E(f*) < J!?(S*) and a(f) < E(3).~~

The first condition is useful only if f* can be computed, which in tur~ requires the knowledge of the distributions. If the distributions are not known, then j can be used as an approximation. In [8] we showed that with probability 1 – 6, we have

~~E(f) – E(f*) <6~~

given a sufficiently large sample, when the physical law and the fusers classes arc Lipschitz. In general, however, physical laws may not be Lipschitz, especially if they involve discrete components or discontinuitics. For example, consider the simple case of H20 heated in a container, where pl denotes the temperature and P2 ~ {O,1} is the state, i. e. p2 = Odenotes liquid and 192= 1 denotes steam. Let To denote the boiling temperature under this condition. Then, one of the physical laws is: p2 = Oif pl < To and p2 = 1 otherwise. This law can be represented as

~~q.pl, w] = P21{p,~~

189 with bounded variation [2], which allow for discontinuities and discrete values, and include Lipschitz functions as a subclass. Consider a function one-dimensional function h : [–A, A] H R. For A <00, a set of points ~ = {zo, zI, . . . , Zn} such that –A = Z. < xl <... < x. = A is called a partition of [–A, A]. The collection of all possible partitions of [–A, A] is denoted by P[–A, A]. A function g : [–A, A] * 3?is of bounded variation, if there exists M such that for any partition P={zo, zl,. ... Xn}, we have ~(~) = 5 I.f(z~) – j (x~–1)I s M. A multivariate function k=l g : [–A, A]~ - Y?is of bounded variation if it is so in each of its input variable for every value of the other input variables. The following are useful facts about the functions of bounded variation: (i) not all continuous functions are of bounded variation, e.g. g(z) = x cos(7r/(2z)) for x # O and g(0) = O; (ii) differentiable functions on compact domains are of bounded variation; and (iii) absolutely continuous functions, which include Lipschitz functions, are of bounded variation. We utilize the fuser classes with finite pseudo-dimension [1], which is described as follows. Let G be a set of functions mapping from a domain X to R and suppose that S= {X1,X3..., x~} Q X. Then S is pseudo-shuttered by F if there are real numbers rl, TS, . . . r~ such that for each b ~ {O,I}m there is a function go in ~ with sgn(~b(~~) – ~i) = bi for’ 1 s z s m. Then g has the pseudo-dimension d if d is the maximum cardinality of a subset S of X that is pseudo-shattered by g. If no such maximum exists, we say that g has infinite pseudo-dimension. The pseudo-dimension of g is denoted Pdim(@. Pseudo- dimensions arc known for several classes such as sigmoid neural networks, vector spaces, and linear combinations (see [1]). Let ~ be the ckws of functions from Z to into [0,M], where M > 0, and let F’ be a probability measure on Z. Then d~,l(r) is the pseudo metric on g defined by

dL~(pl(gl, g2) = E(lgl – /721)=~ Igl(z) – g2(.z)ld.P(z) for all .91,g2 ~ g. The covering num~er N(c, g, d~l(P)) of a function class g is the smallest cardinality for a subclass g“ = {g”} of g such that dI,l(P)(g, g*) s ~, for each g ~ ~.

Theorem 1 Consider that the physical law is of bounded variation such that IL(P) I s MT, for all p. Let parameters, estimators and measurements are bounded. Let each fuser class Fi have finite pseudo-dimension di7 and each juser junction g be bounded such that ~g[.]] < M ?1 jor all parameters. Let d = ~ di. Then given a sample oj size in 1 ‘=25:~Fd1n(12:M)+(n+1)1n(4’’)l, we have P [E(f) – E(j”) > e] s d, irrespective oj the sensor distributions. Furthermore, E(f) + E(.f*), as s + cm.

190 Proofi Consider the function class L = {L(.fl, j2,..., ~~) : ~1 c 31,.. ”j~ ~ ~n}, where qL.f2,..., f ?1) is defined on a bounded domain. By combining Vapnik’s argument (see [8] for details) with Theorem 3 of Hausslcr [4], wc obtain

~~P [E(f) – l?(.f”) > c] ~ 2E (rein (2~(e/32, L, d~l))] e-a. (1)~~

We subsequently show that Af(c, -C,d~l(p)) < 22n (~ in ~)2~, for any ~. The sample size follows byusing this cover bound inright hand side of Eq (l), andequating to6 and then solving for s. Intherest of theproofwe establish the bound on~(.). Since L(.) isofbounded variance, it can be represented as a sum of two monotone functions L = L1 + L2. For i = 1,2, let

~~~i = {~i(.fl,.f2,.,. j.fn) : fl ~ flj . . ..fn E ~n}.~~

Then let Cilj = {Li(pll . . . ,Pj-1, fj, Pj+l,. . . ,p.) : .fj ~ Xjl which is a class of function obtained by composing a monotone function with functions from Fi with bounded pseudo dimension. By Theorem 11.3 of [1], we have pdirn(~ilj) < pdirn(~i). Then by US@ Theorem 6 of [4] we have

~~for any measure F’. By applying this cover bound for every component of Li, we obtain~~

~~by the product rule. Since L = Ll + L2 we obtain~~

~~4eM ~n 4eM 2d N (q L, dLl(p)) < N(e/2, ,CI,d~l(p))N(e/2, & dLl(p)) s 22n — — . ( e 6 ) By noting that this bound is independent of P, we obtain~~

~~which yields the sample size as shown above. The asymptotic convergence follows from the Borel-Cantelli Lemma by showing~~

~~for every e >0 in a manner identical to that in [8]. ❑ The following corollary is a weaker version of Theorem 1 since li?(f*) s l?(S*) s 13($.~~

Corollary 1 Let Fi satisfy the isolation property jor all i = 1,2,...,n. Under the same conditions as Theorem 1, we have jollowing conditions satisjied. P [E(i) – E(S*)> 6]< J and P [.E(~) – J??($ > e] < &

191 Informally speaking, this corollary shows that the error of the computed fuser ~ is not likely to be much higher than that of the best basic set, and could be much smaller. Theorem 1 states that ~ will be closer to ~* which can have much smaller error than S*.

~~METHANE HYDRATES WELL LOGS~~

Gas hydrates are crystalline substances composed of water and gas, in which gas molecules are contained in cage-like lattices formed by solid water. One of the challenging problems is to predict the prescence of hydrates using measurements collected at wells located in certain locations such as off the US coast in mid-Atlantic and Mackenzie Delta in Northwest Canada. At each well, a number of measurements are collected using a suite of sensors. These measurements include density, neutron porosity, acoustic transit-time, and electric resistivity, collected at various depths in the well [3]. Our focus is on the estimation of the porosity at various depths. Our data consists of 3045 sets of measurements each collected at different depths in a single well. There area variety of methods to estimate porosity based on different principles and utilizing different measurements. We employed six known methods for estimating the porosity based on neutron measurements (~1), d~nsity measurements (~2), fluid velocity equat~on (@3),acoustic travel tim~ based on S-wave (#4), time-average equation based on P-wave (~s), and Wood’s equation (f#G). One of the well-established physical laws relates the parameters of porosity (~), density (p), and hydrate concentration (~), as follows

~~~[d>4, PI = (d[Pm – (1 - ‘V)P7JJ+ IfWll– P + Pm)’ = Q~~

Where pm, PW, and ph are known constants. In this equation, we usc the only one measurement for density ~ and and a single estimator ~ for the hydrate concentration using the Archie’s equation. We consider a fuser based on the linear combination of the estimators

~~~F = W7 + ~Wi6i, i=l~~

where (wl, ..., W7) G 0?7 is the ,.weight vector that minimizes the error based on measurements. The error achieved by ~~ is about 20 times better than that of the best estimator ~4 (details Can be found in [8]). Note that L[.] and the fusers employed here satisfy the con~itions of Corollary 1. Incidentally, they also-satisfy the smoothness conditions of [8].

~~COIVCLUS1OIW3~~

We presented an information fusion method that applies to physical systems wherein accurate measurements of physical parameters are not possible. We presented a method that combines various measurements and estimators to achieve performance at least as good

~~192~~

. .“ . . as the best set of measurements. We showed that a close approximation to the this optimal fuser can be computed such that with a high probability the solution performs at least as good as the best set of measurements, given large enough sample size. This work is an advance our earlier work [8]which is applicable to only Lipschitz laws and fusers, The study of projective fusers and metafusers [7] for the proposed formulation will bc of future interest. It is also of interest to see if the boundedness of pseudo-dimension in Theorem 1 can be replaced by that of fat-shattering index [1], which would result in a weaker condition.

~~ACKNOWLEDGEMENTS~~

This research is sponsored by the Engineering Research Program of the Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DEAC05-OOOR22725 with UT-Battelle, LLC, the Office of Naval Research under order No. NOO014-96-F-0415, and by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory.

~~REFERENCES~~

~~[1] M. Anthony and P. L. Bartlett. Neural Network Learning: Theoretical Foundations. Canbridge University Press, 1999.~~

~~[2] T. M. Apostol. Mathematical Analysis. Addison-Wesley Pub. Co., 1974.~~

[3] S. R. Dallimore, T. Uchida, and T. S. Collett, editors. Scientific Results from tJAPEX/JNOCIGSC Iklallik 2L-38 Gas Hydrate Research Well, Mackenzie Delta: Geo- logical Survey of Canada Bulletin 544. Geological Survey of Canada, Bulletin 544, 1999.

~~[4] D. Hausslcr. Decision theoretic generalizations of the PAC model for neural net and other learning applications. lnjormation and Computation, 100:78–150, 1992.~~

~~[5] N. S. V. Rae. A fusion method that performs better than best sensor. In First Interna- tional Conference on Multisource-Multisensor Data Fusion. 1998. 19-26.~~

~~[6] N. S. V. Rae. Multiple sensor fusion under unknown distributions. Journal of Franklin Institute, 336(2):285-299, 1999.~~

~~[7] N. S. V, Rae. On optimal projective fusers for function estimators. In IEEE/SICE\RSJ International Conference on Multisensory Fusion and Inte.qration for Intelligent Systems, pages 1-6.1999.~~

~~[8]N. S. V. Rae, D. B. Rcistcrj and J. Barhen. Fusion method for physical systems based on physical laws. In Proceedings of 3rd .lnternational Conference on Information Fusion$ 2000. —~~

~~INTEGRATION OF NANOSENSORS IN MICROSTRUCTURES~~

~~Li Shi, Guanghua Wu, Arun Majumdar Department of Mechanical Engineering University of California, Berkeley, CA 94720~~

~~ABSTRACT~~

This paper reports two examples where nanosensors have been integrated with microfabricated structures to provide new functional devices. The first is the integration of nanoscale temperature sensors on probe tips that have been used to study thermophysics of low-dimensional nanostructures such as carbon nanotubes. Thermal images at 50 nm spatial resolution are revealing the dissipation mechanisms in multiwall and single-wall carbon nanotubes, We report the direct observation of defect scattering on phonon transport in such nanotubes. The second example involves the generation of nanomechanical motion of a cantilever beam using specific biological reactions such as DNA hybridization and protein-ligand binding. We report here some new observations as well as the thermodynamic principles of how motion is created at nanoscales.

~~INTRODUCTION~~

A major engineering challenge that is common to several areas of nanotechnology is the integration of nanostructures into well-defined micro-patterns. For example, microelectronics and MEMS currently use optical lithography for generating such patterns. Optical lithography, however, is limited to a spatial resolution of about 100 nm whereas many of the exciting new nanoscale phenomena occur in the range of 1-10 nm. It is critical to bridge this 1-100 nm length scale gap such that nanostructures could be interfaced with MEMS and microelectronics systems and thereby interface with the macroscopic or “human” length scales. Although electron beam lithography can be used to fabricate structures in the 10-20 nm range, it is not truly scalable because it is performed sequentially. Lithography is often called the “top-down” approach to

194 making nanostructures since they are used to etch out a pattern. Self assembly of nanostructures, on the other hand, is a “bottom-up” approach where the process of integration or aggregation is thermodynamically driven. The combination of the top-down and bottom-up process will provide a means to integrate nanostructures in microstructure, thereby enabling engineering systems containing nanoscale components to be built.

In this paper, we report two examples where we have integrated nanoscale sensors onto microfabricated structures. By doing so, we have developed new functional devices that are now resulting in new scientific discoveries. The examples that we report here span both the physical and biological sciences, exempli~ing the wide application of integrating systems across length scales.

~~SCANNING THERMAL MICROSCOPY OF NANOSTRUCTURES~~

In recent years, a number of low dimensional materials with length scale smaller than 100 nm have been developed. Carbon nanotubes, silicon nanowires, and semiconductor/metal nanocrystals are examples of such synthesized nanostructures. There is a great interest to experimentally investigate electron and phonon transport and heat dissipation phenomena in these materials. Such transport and dissipation phenomena are also important in ultra large-scale integration (ULSI) devices, whose minimum feature sizes are scaling down to sub-100 nm. Traditional measurement techniques, however, cannot resolve thermal features below 100 nm. For example, the spatial resolution of fiw-field optical thermometry techniques based on infrared and laser reflectance is diffraction limited to be on the order of wavelength, which is much larger than the length scale of sub-100 nm nanostructures currently of interest.

Scanning thermal microscopy (SThM) is capable of thermally investigating nanostructures and ULSI devices with spatial resolution in the sub-100 nm regime. The SThM maps surface temperature distribution by raster scanning a sharp temperature-sensing tip across the surilace [1], The tip is mounted on a micro cantilever beam such that a constant tip-sample contact force is maintained by the force feedback of an atomic force microscope (AFM). Tip-sample heat transfer changes the tip temperature, which is measured and used to determine the sample temperature.

The key element of SThM is the thermal probe. Figure 1 shows the schematic diagram of a SThM probe, which contains a thermocouple junction at the tip end. The tip-sample heat transfer mechanisms include solid-solid conduction through the contact, liquid conduction through a liquid film bridging the tip and sample, and air conduction. The thermal design of the cantilever probes is extremely important for SThM performance, The thermal resistance network in Fig. 1 suggests that for given ambient, Ta, and sample, TS, temperatures, the tip temperature Tf, can be written as ~ = T, + (T. – T, )/(1 +$), where # = Rc/R1f is the ratio of the cantilever, RC, and tip- sample, Rf~, thermal resistances. Hence, changes in sample temperature can be related to changes in the tip temperature as AT /ATt =$/(1 +$). This relation suggests that the accuracy and sensitivity of sample temperature measurement by the tip depends on #, which must be large for T, better SThM performance. Hence, the thermal design of the cantilever resistance, Rc RC, is extremely important. The spatial resolution, Ax of SThM measurements can T, be expressed as Ax= AT. /(d~ /&) where Rt~ AT. is the noise in the temperature -+ Air Conduction measurement and d~ /dx is the measured ~ i T~ temperature gradient. Because the tip and Fig. 1 Schematic diagram of a cantilever probe used for scanning thermal microscopy. The heat transfer mechanisms between the tip, cantilever,and sample temperatures are related through $, the sample are also indicated,as is the thermal resistance network. the spatial resolution can be expressed as 1++ (1) b= (dfi&) ()~ Equation (1) clearly suggests that small values of@ lead to poor spatial resolution of SThM.

Previous experiments have reported that R1. x 105 IUW [2].Therefore, the thermal design of the cantilever must require R, > 105 IUW. In the past, SThM probes were made of a high thermal conductivity material such as metal or silicon, with no attention to paid to thermal design. This often led to probes with R. << Rts which led to inaccuracies, loss of resolution, and artifacts. In addition, they were usually fabricated individually, making the process very time consuming and irreproducible. Recently, several groups have attempted to batch fabricate probes for scanning thermal microscopy. Two groups fabricated thermal probes using only optical lithography and wafer-stage processing steps. However, the probes were made of silicon, leading to the aforementioned inaccuracies and artifacts [3,4]. Silicon nitride thermal probes were also fabricated with a thermocouple junction defined at the tip by electron beam lithography [5]. The low throughput of electron beam lithography prohibits the process for being used for large- volume fabrication.

To address these issues, we have thermally designed and fully batch fabricated cantilever probes for SThM [6]. Based on heat transfer modeling, we chose SiOz and SiNXas the tip and cantilever materials, respectively, in order to increase RC as much as possible. It was shown by the modeling results that compared to silicon probes with similar geometry parameters, our current design could largely improve the thermal isolation of the sensor from ambient. In addition, Pt and Cr were chosen for the thermocouple materials for their high thermopower difference and low thermal conductivity. Finally, we optimized the geometrical parameters of the Probe for increasing thermal resistance of the cantilever.

The thermal probes were fully batch-fabricated using wafer-stage process steps, with more than 300 probes fabricated on one single wafer. Figure 2 shows two micrographs of a finished cantilever probe with the tip containing a Fig. 2 Electron micrograph of the scanning thermal microscope Pt-Cr thermocouple junction, with the Pt probe. The picture on the right shows the cantilever beams and and Cr lines patterned along each the tip whereas the one on the left shows the tip structure with a cantilever arm. The tip region containing Pt-Cr thermocouple junction on the tip.

~~196 ?.~~

the overlap of Pt and Cr thin films (a) Topography was 0.5 pm tall and had a tip radius of about 50 nm. The height of this region controlled in the fabrication process to be in the range of 0.1-0.5 (b) Thermal ym. Because the thermal resistance of these probes was very high (= 106 ~), a low-power laser beam (x 1 mW) directed at the tip would m increase its tip temperature-by 80-90 Fig.3(a) Topographic and (b) thermal images of a multiwall carbon “C, Hence, to optically measure the nanotubecircuit under dc current of 27 mA for applied dc voltage cantilever deflections for atomic of1.5Vbetween contacts 1 and 3. Contacts 2 and 4 are floating. force microscopy, a thermally isolated laser reflector was fabricated.

The batch-fabricated thermal probes have been used for quantitative temperature measurement of VLSI via structures and for studying dissipation in multi-wall (MW) and single- wall (SW) carbon nanotube (CN) circuits. Figure 3a shows the AFM topography of one MWCN circuit that was imaged using the SThM probe. The sample contained a 14 nm diameter MWCN and four 30 nm thick gold contacts on an oxidized silicon wafer. Resistance measurement found that the tube was broken between contacts 3 and 4. The defect could be located in a high resolution AFM image. Figure 3b shows the thermal image of the sample obtained for a DC current of 27 pA flowing in the segment between contacts 1 and 3. The fill width half maximum (FWHM) of the temperature profile across the CN was on the order of 50 nm, indicating the spatial resolution of the thermal imaging technique. This was approximately equal to the tip diameter. The temperature rise in the nanotube between contacts 1 and 3 can be clearly observed, To verify that the image was not due to topography-induced artifact, the thermal image was taken at different applied voltages and the thermal signals were found to increase with the voltage. Another possible artifact in the thermal image could be caused by current flow from the sample into the probe because of the difference in electrostatic potentials of the tip and sample. To rule out this possibility, we measured the tip-sample contact electric resistance when the tip was on top of the CN and the contacts, and found the resistance to be larger than the 1 GC2 measurement range of an Ohmmeter for the low contact force used in thermal imaging. The lack of electric contact was due to a chrome oxide layer formed at the tip during probe fabrication. This fact suggested that the thermal images were not due to electron flow at the tip-sample junction. In addition, the thermal probe was connected to a voltage amplifier with floating ground, such that no current would have flowed into the probe even if electric contact had been established at the tip-sample junction. We further confirmed the absence of electrostatic potential-induced artifacts in the thermal images by raising the electrostatic potential of the entire CN circuit without passing current through it. As we did so, no noticeable thermoelectric signal could be measured using the thermal probe scanned on the circuit. Therefore, the electrostatic potential did not introduce artifacts in the thermal images, and the thermal images were indeed due to phonon coupling instead of electron coupling at the junction. Furthermore, what the probe measured was the phonon temperature of the sample, which might or might not be at equilibrium with the electron temperature. It is interesting to note that although no current flowed in the segment between contacts 3 and 4, the temperature of the left part of this segment was higher than that of the segment between contacts 2 and 3. This leads us to speculate that heat might be dissipated at the contacts and not in the bulk of the CN. Spatially uniform bulk dissipation would have led to parabolic temperature profiles instead. Note that switching the polarity of the applied voltage did not change the temperature distribution of the tube, indicating no thermoelectric effects at the contacts. The fact that the CN section between contacts 3 and 4 did not involve any electron transport and yet appeared hot suggests that phonon transport is very efilcient in carbon nanotubes. In addition, it also demonstrates that SThM measured the phonon temperature and the not electron temperature. The temperature between contacts 3 and 4 dropped rapidly at a point indicated by the arrow. We suspect that this was due to scattering by a defect in the CN, presumably the same defect that also blocked electron transport.

This study raises several questions, namely: Does the dissipation indeed take place at the contacts or along the nanotube? How efficient is phonon transport in the nanotube? What are the mean free paths for elastic and inelastic electron and phonon scattering? What are the roles of defects in nanotube transport phenomena? Some of these questions are currently being addressed experimentally using the SThM and will be presented later.

In conclusion, we have carefully designed and batch-fabricated probes for scanning thermal microscopy. The probes have been used to obtain thermal images of electrically heated carbon nanotube circuits. Our experimental results demonstrate that SThM measured the phonon temperature of the sample, and the tip-sample thermal coupling was dominated by heat conduction through a liquid bridge. Consequently, the spatial resolution of SThM was limited by the tip radius and was found to be 50 nm in this study. With tlis resolution, SThM offers the promising prospects of studying electron-phonon interaction and phonon transport in some low dimensional materials such as carbon nanotubes.

~~FROM BIOLOGY TO MOTION~~

Understanding the mechanisms of how biological reactions produce motion is fundamental to several physiological processes [7]. While most of the past effort has focused on studying single molecular motors [8], recent experiments [9,10] using microcantilever beams have reported the collective effect of multiple DNA hybridization and antigen-antibody reactions to produce nanomechanical motion. While this offers the promising prospects of interfacing molecular biology with micro and nanomechanical systems, an understanding of how this motion is produced has, however, remained elusive. Here we show that cantilever motion is created due to the interplay between changes in confirmational entropy and intermolecular energetic induced by specific bimolecular reactions. The entropy contribution can be critical since it determines the direction of motion. Using these thermodynamic principles in conjunction with DNA hybridization experiments, we demonstrate that both the direction and the magnitude of cantilever motion can be controlled and optimized. This thermodynamic framework is also used to explain the nanomechanical motion created by protein-ligand binding.

198 Figure 5 illustrates the experiment that we Probe Molecule used for studying nanomechanical motion created by multiple specific bimolecular Beam reactions. The cantilevers used in our study were ,Target Blndhrg made of silicon nitride (SiNX), with ~ gold coating on one surface. The experiment started by first placing a Au/SiNx cantilever in a fluid Fig. 5 Specific biomo!ecularinteractions between target and cell and then injecting a Sohtion of sodium probe molecules alters the intermolecular energy interactions withina self-assembled monolayer on one side of a cantilever phosphate buffer (PB) at pH -7.0 into the cell. beam. l%is produces sufficientlylarge force to bend the cantilever The next step was to immobilize the probe beamand generate motion. The originof this nanomechanicel motion lies in the interplay between changes in confirmational molecule on the cantilever surface, which was entropy and the intermolecular energetic. followed by injection of a solution containing target molecules. The cantilever motion was optically monitored at both the immobilization and probe-target binding steps. To form a self-assembled monolayer of probe SSDNA 0.0 0.2 0.4 as o.a 1,0 on the Au-coated cantilever paCencen&etlOn ~] surface, the SSDNA was Figure 6 (A) Change in Au/SiNX cantilever deflection as a function of time modified with thiol gxoups for three different experiments: (i) exposure to 0.1 M phosphate buffer (PB); attached to either the 5’ end. (ii) exposure to unthiolated probe SSDNA (iii) exposure to probe SSDNA Figure 6A shows the thiolated at the 5’ end. Concentrations of unthiolated and single-end thiolated cantilever deflection as a SSDNASwere all 50 ng/~1 or approximately 3.2 PM. Unthiolated SSDNA and pure PB solutions did not produce any significant deflection. The inset shows fiction of time for a 50nt the steady-state cantilever deflection as a function of length of the probe SSDNA long probe SSDNA. Here, thiolated. The results indicate that immobilization of probe SSDNA produces negative deflection compressive stress bending the cantilever down. (B) Steady-state cantilever represents the downward deflections caused by immobilization of SSDNA at different PB concentrations. bending of the cantilever with the probe molecules on the top surface. Also shown are the deflection plots after the injection of unthiolated SSDNA and only PB. The inset in Fig. 6A shows the steady-state cantilever deflection as a fi.mction of the length of the probe SSDNA. Figure 6 B shows the cantilever deflection for immobilizing 30nt-long probe SSDNA as a function of PB concentration. It is clear from these experiments that regardless of the length of SSDNAor the ionic strength, the repulsive interactions between immobilized SSDNA created a compressive stress to bend the cantilever downwards.

After immobilizing the probe SSDNA,the complementary target SSDNAwas injected into the fluid cell at the same PB concentration that was used to immobilize the probe SSDNA. Figure 7A shows the deflection plots for the hybridization reactions where the probe SSDNAwas 20nt long and the target SSDNAwere of four different lengths (20nt, 15nt, 10nt and 9nt) and distally complementary. The nanomechanical signal was sufficiently sensitive to detect single nucleotide length differences. The observation that the cantilever bent upwards in all cases suggests that hybridization relieved the compressive stress created during immobilization of thiolated probe SSDNA. To confirm that the signals were due to hybridization, a solution of a non- complementary target SSDNAwas used and was found to produce no deflection signal. Figure 7B plots the steady-state deflection signal for the hybridization reaction under different PB

~~199 20 20 I I r , 1 concentrations. An optimum Tq,!(nl) Pmb@)- Hybridizationof3ChtDNA~~

PB concentration of 0.2-0.4 M 15 15 - was seen to produce the ● * b 10 maximum deflection. 10 - .0 ● 5 * ● The fact that the 5 - 0 cantilever deflections for both the immobilization and 4 0 0 500 1000 1500 2000 2500 0.0 0.2 0.4 0,6 0.8 1.0 hybridization steps were lime [s] PB Concentration [M] influenced by ‘the PB Fiaure7 (A) Chanaes in Au-Si cantilever deflection due to hybridization concentration suggests that of-aprobe&DNA150 ng/pl or 8 j.LMconcentration) in the di~tal end with electrostatic repulsive forces complementary target SSDNAof different lengths — 20nt, 15nt, 10nt, and 9nt(40ngl~lor3-6UMconcentration). Also shown is the absence of between neighboring DNA cantilever deflection for a non-complementary target SSDNA. The data clearly molecules must have suggeststhatdifferences in nanomechanical motion due to one nucleotide produced the compressive difference in length can be observed. (B) Steady-state changes in cantilever deflection for hybridization of 30-nt long SSDNA at different PB concentrations. stress that bent the cantilever Notethatimmobilization of probe SSDNAwere at the same PB concentration down. Because each as thehybridizationreaction. nucleotide carries a negative charge due to the presence of a phosphate group, one would expect ybridization that hybridization would cause even more repulsion due to the presence of additional negative charge. However, the data in Fig. 7 clearly indicates that regardless of the PB concentration in the range of 0.05-1 M, hybridization Figure 8 Schematic diagram illustrating the mechanism of always relieved the stress and motion generation due to DNA immobilization and hybridization. produced upward cantilever motion. Immobilization of SSDNAon the top surface bends the cantilever down. The persistence length of SSDNAis 7.5 A which leads to Therefore, electrostatic or steric higher confirmational entropy resulting in compressive stress. repulsion alone cannot explain the Hybridization increases the persistence length to about 50 nm, which significantly reduces the confirmational entropic driving behavior. force, thereby relieving the compressive stress and producing an upward cantilever motion. It is worth noting that the persistence length of SSDNA is about 0.75 nm [11] whereas that of double-stranded DNA (dsDNA) is about 50-80 nm [12]. We propose that the confirmational entropy of the SSDNA provides- the driving force to bend the cantilever down. Upon hybridization, th~ confirmational entropy contribution is significantly reduced which then relieves the compressive stress resulting in upwards cantilever motion (see Fig. 8).

~~ACKNOWLEDGEMENT~~

This work was performed under the support of the Engineering Program of DOE Basic Energy Sciences. Our many thanks to Paul McEuen, Sergei Plyasunov and Adrian Bachtold of UCB- Physics for the carbon nanotube experiments, and to Thomas Thundat, Karolyn Hansen, and

~~200 Haifeng Ji of Oak Ridge National Lab, Ram Datar and Richard Cote of USC-Pathology, and Arup Chakraborty of UCB-Chemical Engineering, for their immense help and support for the DNA experiments.~~

~~REFERENCES~~

1. A. MAJUMDAR, “Scanning Thermal Microscopy, ” Annu. Rev. Mater. Sci. 29,505 (1999), 2. K. LUO, Z. SHI, J. VARESI, A. MAJUMDAR, “Sensor Nanofabrication, Performance, and Conduction Mechanisms in Scanning Thermal Microscopy, ” J Vac.Sci. Tech. B 15, 349 (1997). 3. T. LEINHOS, M. STOPKA, E. OESTERSCHULZE, “Micromachined fabrication of Si cantilevers with Schottky diodes integrated in the tip,” Appl. I%ys. A 66,65 (1998). 4. Y. ZHANG, Y. ZHANG, J. BLASER, T. S. SRIRAM, A. ENVER, R. B. MARCUS, “A thermal microprobe fabricated with wafer-stage processing~’ Rev. Sci. Inst. 69,2081 (1998). 5. G, MILLS, H. ZHOU, A. MIDHA, L. DONALDSON, J, M, R, WEAVER, “Scanning thermal microscopy using batch fabricated thermocouple probes~’ Appl. Phys, Let/. 72,2900 (1998). 6. L. SHI, O. KWON, G. WU, A. MAJUMDAR, ASME Int. Mech. Eng. Congress & Exposition, MEMS 1, 93 (1999); The details of the modeling, design, and fabrication process of the thermal probes will be published in a separate paper. 7, R, D. VALE & R. A. MILLIGAN, “The way things move: Looking under the hood of molecular motor proteins;’ Science 288,88 (2000). 8. D. KELLER&C. BUSTAMANTE, “The mechanochemistry of molecular motors~’ Biophys. J 78,541 (2000). 9. R, RAITERI, G. NELLES, H.-J. BUTT, W. KNOLL, P. SKLADAL, “Sensing of biological substances based on the bending of microfabricated cantilevers,” Sensors and Actuators B 61,213 (1999). 10. J, FRITZ, et al,,’’Translating bimolecular recognition into nanomechanics,” Science 288, 316 (2000). 11, S. B. SMITH, Y. CUI, C, BUSTAMANTE, “Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules~’ Science 271,795 (1996). 12. C. G. BAUMANN, S. B. SMITH, V. A. BLOOMFIELD, C. BUSTAMANTE, “Ionic effects on the elasticity of single DNA molecules,” Proc. Natl. A cad. Sci. 94,6185 (1997). GENERATION OF HIGH CONCENTRATION NANOPARTICLES FOR FILTRATION STUDIES

~~Da-Ren Chen and David Y. H. Pui~~

~~Particle Technology Laboratory Mechanical Engineering Department University of Minnesota Minneapolis, MN 55455, U.S.A.~~

~~ABSTRACT~~

Nanoparticle filtration is important in the recovery of nanoparticle products from materials synthesis processes, and for preventing nanoparticle emissions in the environment and protecting workers against exposure to nanoparticles. Theories have shown that the penetration of nanoparticles through the filter would increase due to thermal rebound between the nanoparticles and filter collection surfaces. In this study, we report on preliminary results of an experimental study of nanoparticle penetration through a model filter. In addition, a high concentration nanoparticle generator has been developed with high mass-throughput. It will be used to challenge high efficiency filters so as to obtain the penetration values. Additional beneficial effects will include the production of industrial quantity of nanoparticles for pharmaceutical and materials applications.

~~INTRODUCTION~~

Nanostructured particles and materials, and the physical or chemical combination of substances at the nanometer scale, can result in the discovery of new innovative materials for rechargeable batteries, ceramic fuel cells and solar cells, which can lead to the advancement of clean energy conversion and storage systems. Traditionally, the synthesis route for producing nanoparticles is based on the solution processing technique derived from established solution chemistry. The technique is restricted to limited combinations of constituents for the synthesis process. Gas-phase processing is increasingly used because of its versatility and its

202 applicability to most materials. One of the challenges in gas-phase processing is to collect nanoparticle products ilom reactors efficiently. Filtration is one of the principal methods for collecting the nanostructured materials. Further, it is important for preventing nanoparticle emissions in the environment and for protecting workers against exposure to nanoparticles.

It is well known that the illtration efficiency vs. particle size curve has a characteristic v-shape with its minimum between 0.1 and 0.3 pm. Figure 1 shows that the efficiency increases with increasing particle size due to inertial impaction and interception mechanisms, and also increases with decreasing particle size due to diffusion mechanism. The minimum occurs during the transition horn the impaction/interception to diffusion mechanisms. While theories for particles larger than 50 nm is well developed, there is insufficient understanding of the filtration mechanism in the nanometer particle size range, i.e., 1 nm c Dp < 50 nm. From classical filtration theories, the collection efficiency should approach 100% for nanoparticles due to the diffusion mechanism. However, it is also commonly known that gas molecules can penetrate through fibrous and membrane filters due to thermal rebound between the molecules and filter surfaces. Consequently, the filtration efficiency should begin to fall off when particles approach molecular dimensions, i.e., nanometer sizes. There are recently some limited theoretical (Wang and Kasper, 1991) and experimental evidences (Ichitsubo et al., 1996) to suggest that nanoparticles would penetrate through the filter media due to thermal rebound effects.

~~120.0’+’0 I I I Thermal -1 Rebound DMMon Interception + Ixnpaotion - ~~~ - 100.0%-~~

80.0% - 1 a ~ 60.0% - 3 A 3 40,0% - U = 5.0 em/see L= O.5cm a=o.1 Dc= 5.0 pm 20.0’% CJP,~= 1 erg/cm 2 t I I 0.0% I I I I 0.001 0.010 0.100 1.000 10.000 Pactio10Dismeter @n) Figure 1. Atheoretical filter efficiency curve showing alocalmitimum at 0.3 pm and the rapid decrease in efficiency (increased penetration) below 10 nm.

Nanoparticles are producing in increasing quantity in materiaIs industry because materials in the nanostructure form possess many desirable properties, including hardness improvement, internal friction reduction (i.e., improved ductility), melting point reduction, and special optical and magnetic properties (e.g., Kofinan et al, 1994; Endo et al, 1996; Lin et al, 1995). These properties are the basis of many so-called ‘high-tech’ applications, including quantum dots, drill bit coatings, fuel cells, solar cells, and tunable laser, and so they promise to revolutionize the materials industry. Production of such materials via the aerosol route provides enhanced levels of materials purity and production control. Penetration of nanoparticles through the filter media would reduce the quantity of recovered nanoparticle products, and would allow nanoparticle emissions in the environment. Nanoparticles are also by-products of many high-tech coating processes (Chan et al., 1995) for thermal or corrosion resistance or for increasing the surface hardness, and in emissions horn semiconductor processing equipment and combustion engines, As a result, workers in many modern manufacturing facilities have increasing potential for exposing to nanoparticles emissions.

There is an increased awareness in the occupational health community on the possible adverse health effects of exposure to nanometer particles (e.g., Cheng et al., 1993, 1996; Ferin, 1994; Donaldson et al, 1996; Oberdorster et al., 1992, 1995; Ferin et al., 1990). It has been speculated that nanometer particles depositing in the human respiratory tract may enter the interstitial spaces and may penetrate through the cell membrane, so that even relatively insoluble material may pass beyond the respiratory tract. Those which are retained in the lung may become sequestered and remain there for very long periods. Recent intratracheal injection studies using rats, reported by Donaldson et al. (1996), have shown that material which is relatively inert for micrometer-sized particles (e.g., titanium dioxide) can be highly inflammogenic for particIes in the nanometer size range. It is clearly suggested, therefore, that nanometer particles may, depending on their chemical composition, be associated with the possibility of serious ill-health. Therefore, the present study will allow a detailed undel*standing of nanoparticle filtration and provide a firm basis for developing a new generation of particle removing devices/systems for protecting workers from nanoparticles exposures, and for collecting nanoparticle products from reactors for high-tech applications.

In this paper, we will report on preliminary results of an experimental study of nanoparticle penetration through a model filter. In addition, a high concentration nanoparticle generator has been developed with high mass throughput. It will be used to challenge high efficiency filters so as to obtain

~~204 penetration values. Additional beneficial effects will include the production of industrial quantity of nanoparticles for pharmaceutical and materials applications.~~

~~NANOPARTICLE FILTRATION EFFICIENCY~~

The filtration efficiency of nanoparticles was studied both experimentally and theoretically. A model screen filter was used for the particle penetration study. Nanoparticles in the size range of 3 to 20 nm were generated as test aerosols and the penetration of these particles through the model filter was measured.

Silver nanoparticles were produced using the evaporation-condensation technique. The nanoparticles were then passed through a radioactive neutralizer to obtain a bipolar charge distribution. This was followed by a Nanometer Differential Mobility Analyzer (Chen et al., 1998) that was used to class~ the silver aerosol into a monodisperse size fraction. The upstream and downstream concentrations of the screen filter were measured by an ultrafine condensation particle counter (UCPC, Mode13025A, TSI. Inc., St. Paul, MN). A tape heater controlled the air temperature inside the chamber. A thermal couple that was installed close by the screen measured the aerosol temperature.

The screen-type filter media were 635-mesh, 270-mesh, and 200-mesh type 304 stainless steel wires screens with openings of 0.0008”, 0.0021” and 0.0034”, respectively. The aerosol flow rate through the screen holder chamber was kept at 1.5 lpm. To study the electrostatic effect, penetration of neutralized and singly charged particles were measured and compared with Cheng and Yeh’s theory. Figure 2(a) shows the penetration of singly charged particles through the 635-mesh screen. The experiments were performed for particle diameter smaller than 15 nm and with different number of screens (n). As shown in the results, the experimental penetration deviates from Cheng and Yeh’s theory for particles smaller than 10 nm. The experimental penetration is lower than that predicted from theory. This is in the opposite direction of thermal rebound effect. The lower penetration has been attributed to the enhanced collection of the charged particles by the metal screen due to electrostatic effect. Figure 2(b) shows the penetration of neutralized particles through three different mesh screens. The experimental penetration values are shown to agree well with Cheng and Yeh’s theory.

Measurements were performed at elevated temperature of 50-800C. Figure 2(c) shows that the results follow closely with the theory of Cheng and Yeh down to 10 nm. Increased penetration is observed for particles smaller than 5 nm and at elevated temperature of 800C, suggesting the possibility of thermal rebound between the nanoparticles and the screen filter. Additional experiments will be performed with different pairs of particle and screen types.

~~205~~

-r <., ,..,...,,~,~ ,,, / ‘. ;:“:;::.,.’:.;.,, ,,,. ..(..;Y ~“.LW2-3i ,“ ‘:?rJf.....;-,;->77,,L...~. >“——. ;..-,,..>-.-’,.,..:, .:??.$.&.+.,.<-,:,>;.,.?: ,<;...,-.-m, ...-,. . ,, .. -—....,,..,- .. ,,. —+=...... — —

Figure 2. Experimental penetration of nanoparticles through a model screen filter: (a) singly charged particles through 635 mesh screen, (b) neutralized particles through different mesh screens, (c) neutralized particles through different mesh screens at elevated temperature of 50- 800(3

~~HIGH CONCENTRATION NANOPARTICLE GENERATOR~~

A multiple-nozzle arrangement of electrospray has been developed to produce high mass-throughput of nanoparticles. Electrospray has been used to produce nanoparticles fkom solutions or colloidal suspensions. It is capable of producing particles 10-100 times smaller than the conventional pneumatic atomization technique. This will allow the product materials to have 100-10,000 times larger surface area than those produced from the conventional technique, for a given quantity of spray solution. The increased surface forms the basis of enabling technology for several important applications, e.g., fast response and high bioavailability for drug products.

The electrospraying system setup and the details of the capillary tube are shown in Figure 3 (Chen and Pui, 1997). The spraying chamber is in the point-to- plate configuration with the capillary tube facing the plate. An orifice is located on the center of the plate allowing the produced particles to enter the neutralization chamber. A coaxial tube allows C02 to flow as a sheath surrounding the capillary tube for suppressing possible corona discharge. Compressed air is supplied from the top of the chamber in order to transport the particles through orifice. Liquid with the desirable solute materials is fed from a programmable syringe pump.

A negative high voltage is applied to the plate and the neutralization chamber. The capillary tube is connected to an electrometer that is used to measure the spraying current. The current reading gives a measure of the particle concentration. At a sufficiently high voltage, the liquid meniscus from the capillary forms a cone jet shape. Liquid column issuing born the tip of cone jet is of the nanometer dimension. The instability of the liquid column causes it to break up into nanometer size particles. The size of the produced liquid droplets can be further reduced by the evaporating the solvent of a known concentration solution.

One limiting factor in deploying the electrospraying technique is that a single spray-nozzle dispenses only a small quantity of solution in pl/min. A major challenge will be to increase the mass-throughput from the sprayer. We have successful implemented a multiple-nozzle electrospray that will allow 1,000 to 10,000 times higher mass throughput rate than the single-nozzle electrospray

~~206 1~~

~~0.1~~

~~0.01~~

~~O.CQ1~~

~~O.ml~~

~~10 “s~~

~~,0 .6~~

~~lo -7~~

~~10 “s 3 4 s 6 78910 20 J3p[nm)~~

~~0.1~~

~~0.01~~

* Rq[270u,n- 1] 0.001 8xp(27WJ,n=2) : Rp(200n,Wl] A 8q@JCul,11-2) m L?xpll,xin.n-1) 0.0001 v EY],[63S!J,II-2 . —------kit.. !<-; 0,, r,- I, —... - Themy(270#,n-2) ------Theory(200#.n- 1) 10 “s ...... lh.(,~wll!,n+ v ----- Tl,,:K)y(ljJfj H,,P 1) — - TJIcoIY(63SM,,I-2) r 10 “6 v 3 i s 6 ii 9 lb DP[-)

~~0.1~~

0,01 .+ + Explwl)i,tilw] Ex14270H,50C) /&”’ : Exp[fi35f/,50c) —TIwwYI’’OCM,LXX’) ●#“ — - “J’hwny@7(Jll ,5(JCI ----- Tlwwy(635#,50C) I I 1i 0,001 1 3 4 5 678 9 10 20 Dp (mm) Syringe Pump

~~~.. Flowrneter ...... C02 rl.fi ......~~

~~lf~ll J{l Filter Flowmeter - H.V. $ *1-k + COfl ‘7 Dryer Compressed Air~~

~~Hadi Source (lo~~

~~\ 81 pm I.D. 750 ~ 224 pm O.D. I TheCapillaryTested~~

~~Figure 3. Schematic diagram of a single nozzle electrospray nanoparticle generator. .~~

A single electrospray nozzle can deliver only a limited range of feedrate within the operating envelope of the sprayer. The feedrate can be increased by using multiple nozzles bundled together. The challenge in spraying highly charged nanoparticles fi-om tightly packed bundle of nozzles is to overcome the space charge effect of these nanoparticles. The voltage required to form the cone-jet mode increases with decreasing inter-capillary distance.

Figure 4 shows the voltage required as a function of inter-capillary distance for three nozzle patterns. The voltage required for a single capillary is 7,500 V. As the inter-capillary distance decreases, a higher voltage is required to “expel” the high charged nanoparticles away from the nozzles in order to form the cone-jet mode. Ultimately, the required voltage reaches the breakdown electric field which defines the closest distance for the inter-capillary spacing.

Three different arrangement of the nozzle placement pattern is shown in Figure 5, i.e., the rectangular pattern, the diamond pattern, and the circular pattern. Figure 4 shows that the circular pattern requires the least voltage to form the cone jet mode. It infers that the circular pattern allows the most compact bundle arrangement for the capillaries without breakdown in electric field. With the circular pattern, it is possible to put 1,000 nozzles within a 3“ diameter disk that is a typical area to operate a single spray nozzle. It thereby increases the mass

~~208 throughput by a factor of 1,000 times. The increase mass throughput will make it attractive for possible industrial applications.~~

~~14,00~~

~~8.00~~

~~e.oo ao 5.0 10.0 15.0 20.0 Inlcr-mplll.ny Distance(mm)~~

~~Figure— 4. Voltage required to form the cone-jet mode as a function of inter-capillary distance for three nozzle patterns.~~

~~000~~

~~000 Rectangular Pattern 000~~

~~0 00 000 Diamond Pattern 00 0~~

~~Circular Pattern~~

~~Figure 5. Three arrangements of nozzle placement pattern under investigation.~~

~~-.___ -._, --4”==’7 --”--7 --- ., ; . , . -., ,,. .--. -.— — . ——~~

~~ACKNOWLEDGEMENT~~

~~This work was supported by the U.S. Department of Energy through a grant from the Office of Basic Energy Sciences.~~

~~REFERENCES~~

Chan, T. L., Rouhana, S. W., Mulawa, P. A., and Reuter, R. J., (1995) “Occupational Health Assessment of the High Velocity Oxy-Fuel Thermal Metal Spray Process;’ Appl. Occup. Environ. Hyg., 10(5) 482-487.

~~Chen, D. and D. Y. H, Pui (1997) “Experimental investigation of scaling laws for electrospraying: Dielectric constant effect,” Aerosol Sci. Technol. 27, 367-380.~~

Chen, D., D. Y. H. Pui, D. Hummes, H. Fissan, F. R. Quant and G. J. Sem (1998) “Design and Evaluation of a Nanometer Aerosol Differential Mobility Analyzer (Nano-DMA)~’ J Aerosol Sci., (in press, 1998).

~~, Chen, D., D. Y. H. Pui and S. L, Kaufinan (1995) “Electrospraying of conducting liquids for monodisperse aerosol generation in the 4 nm to 1.8 mm diameter range,” 1 Aerosol Sci., 26(6), 963-977.~~

~~Cheng, Yung-Sung, Su, Yin-Fong, Yeh, Hsu-Chi, Swift, David L. (1993) “Deposition of Thoron Progeny in Human Head Airways,” Aerosol Sci. Technol., 18,359-375.~~

Cheng, Y. S., Yeh, H. C., Guilmette, R. A., Simpson, S. Q., Cheng, K. H,, and Swift, D. L, (1996) “Nasal Deposition of Ultrafine Particles in Human Volunteers and Its Relationship to Airway Geometry,” Aerosol Science Technol., 25,274-291.

Donaldson, K., Gilmour, P., Brown, D. M., Beswick, P. H., Benton, E., and MacNee, W. (1996) Surface free radical activity of PM1Oand ultrafine titanium dioxide: a unifying factor in their toxicity. Paper presented at the Eighth International Symposium on Inhaled Particles (Cambridge, UK in August 1996), to be published in Inhaled Particles ?V1l(Ed. T. L. Ogden), Pergamon Press.

~~Endo, Y., One, M., Yamada, T., Kawamura, H,, Kobara, K., Kawamura, T., (1996) “Study of htireflective and antistatic coating with ultrafine particles, “Advanced Powder Technolo~, 7, 131-140.~~

~~Ferin, J. (1994) “Pulmonary Retention and Clearance of Particles,” Toxicology Letters, 72, 121- 125.~~

Ferin, J. Oberdorster, G., Penney, D. P,, Soderholm, S. C., Gelein, R., Piper, H. C., (1990) “Increased pulmonary toxicity of ultrafine particles 1, Particle Clearance, translocation, morphology,” 1 Aerosol Sci., 21,381-384.

~~210 Ichitsubo, H., T. Hashirnoto,M. Alonso, and Y. Kousaka (1996) “Penetration of ultrafine particles and ion clustersthroughwire screens:’ Aerosol Sci. TechnoL, 24, 119-127.~~

~~Kofinan, R., Cheyssac, P., Aouaj, A., Lereah, Y., Deutscher, G., Ben-David, T., Penisson, J. M., Bourret, A., (1994) “Surface Melting Enhanced by Curvature Effects,” Surface Science, 303, 231-246.~~

~~Lin, H., Hsu, C. M., Yao, Y. D., Chen, Y. Y., Kuan, T. T., Yang, F. A., Tung, C. Y., (1995) “Magnetic study of both nitrided and oxidized Co particles~’NanostructurediMaterials., 6,977- 980.~~

Oberdorster,G., Ferin, J., Finkelstein,J., Baggs, R., Stavert,D. M., Lehnert,B. E., [1992) “Potential HealthHazards from Thermal Degradation Events: Particulatevs. Gas Phase Effects,” SAE Technical Paper Series, Publ. By SAE, Warrendale, PA, USA, 921388,1-15.

~~Oberdorster,G., Ferin, J., Lehnert,B. E,, (1995) “Correlation between Particle Size, in Vivo ParticlePersistence and Lung Injury,” Environmental Health Perspectives, 102, (Suppi. 5), 173- 1790~~

~~Wang, H. and Kasper, G. (1991) “Filtration of efficiency of nanometer-size aerosol particles:’ 1 Aerosol Sci., 22(l), 31-41. .—~~

~~BIOPHYSICALDIRECTEDASSEMBLYOF NANOTRUCTURESFOR NEUROCOMPUTING~~

~~J.C. Wells*, L. Mayaz, K. Stevenson, T.G. Thundat3, J. Barhenl, Y. Braiman’, and V. Protopopescul~~

Center for Engineering Science Advanced Research ‘Computer Science and Mathematics Division 2Chemical and Analytical Sciences Division 3Llfe Sciences Division Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6355

~~ABSTRACT~~

This paper reports progress in the development of a quantum-dot array that can be operated at room temperature for carrying out nontrivial and innovative computations. We discuss the actual fabrication of 2-rim metal clusters to serve as the quantum dots, device architecture, device simulation, and the development of a computational model. Innovative and unconventional paradigms underlie the different sttages of this work. For example, regular array geometry is achieved by directing appropriately derivatized metal clusters to preselected locations along a stretched strand of an engineered DNA sequence. The proposed applications include the implementation of neuromorphic algorithms for pattern recognition.

~~INTRODUCTION~~

Emerging revolutionary advances in nanoscale computing, communication, detection, and sensing, subsume a profound understmding of the complex dynamics and properties of small arrays of quantum structures, including quantum dots (QD), ultrasmdl Josephson junctions, quantum-dot lasers, and others. Such arrays produce robust hi-stable and multi-stable behavior, which can be exploited for unconventional, yet powerful computational concepts, e.g., neuromorphic computing. Obtaining lattice architectures of sufficient size and regularity to perform actual computations at room temperature has been a formidable challenge, unsurmounted to date. Our objective here is to apply innovative biophysical assembly techniques to overcome this challenge. In particular, appropriately derivatized and passivated gold clusters (i.e., “quantum dots”) can be directed to preselected locations along stretched strands of engineered DNA sequences to produce an operational device. Controlling the placement of the clusters with subnanometer precision will enable the electron-transport properties of the array to be engineered precisely at the scale where they are determined. Our effort includes the actual synthesis of quantum dots approximately 2 nm in size, directed self-assembly of a 1D quantum-dot array via DNA templates, device simulation, and development of a computational model.

~~212 SYNTHESISOF GOLDCLUSTERS~~

We have carried out the synthesis of colloidal gold clusters of core size less than 3-rim by a variety of strategieswith appropriateorganic coatings. A passhwtingcoating provides a dual function. It provides a barrier for cluster growth as well as functional chemical groups for attachment to DNA nucleotides.This designedpropensityfor the functionalizedgold cluster to bind with a nucleotide is used to assemble the nanoparticle at prescribed locations along an engineered DNA strand. Nanometer-sized metal clusters are a leading candidate for the implementation of single-electron devices at room temperature. The strategy described here for attaching the cluster to a DNA molecule involves synthesizing gold clusters coated in hydrocarbons terminated with carboxylic-acid functionality. The carboxylic acid is made to react with thymine bases modified with amino groups (see below). Specifically, we have prepared gold colloids, which are thiol-bound to 12-carbon aliphatic hydrocarbons. This was accomplished by a procedure that involves the use of polyamido dendrimers [1], (see Fig. 1). These centro-symmetric polymers act as a “nanoreactof’ to confine metal ions in the cavity of the polymer. The comple~ed metal ‘io& are then reduced to the charge- neutral state by means of a chemical reductant such as borohydride. In this particular case, an intermediate step is required because the dendrimer has insufficient afilnity for gold ions. This step involves complexation of copper ions, which are then reduced to the metal and subjected to electroless displacement with gold ions. This dk.placement is feasible because gold is more noble than copper. At this point, the gold cluster must be functionalized with the carboxylic acid and the dendrimer eliminated. This is accomplished by treating an aqueous/tetrahydrofuran solution of the gold-dendrimer complex with 12-mercaptododecanoic acid and subjecting the resulting suspension to solvent extraction with toluene. The desired product, free of dendrimer, is isolated at the interface as an insoluble film, which can be solubilized in dimethylformatnide. By this procedure, we have implemented the synthesis and electrophoretic separation of passivated gold clusters. Measurements of Figure 1. Polyammido dendrimers are the cluster-size distribution from preliminary results centro-symmetric polymers that act as a “nanoreactor” in confining metal ions in show a mean diameter of approximately 2 nm with a cluster synthesis. standard deviation of 30%.

~~DNA TEMPLATES~~

The need to produce regular arrangements of nanoparticles led to the idea of using DNA as a scaffold or template for assembly of nanoscale arrays. Beginning in the 1980’s, Seeman and coworkers experimented with combining DNA fragments to produce regular geometrical shapes. To date they have succeeded in producing a variety of DNA structures, including cubes [2], triangles [3], and truncated octahedrons [4]. They have also produced two-dimensional arrays [5,6] and various forms of DNA knots [7,8]. Using DNA as a structural or template molecule has the following advantages. DNA can be synthesized using any sequence and in any length from one to several hundred nucleotides. (The length along the DNA molecule of a single nucleotide is 0.34 rim.) DNA can be joined end to end to produce longer linear molecules or more complex shapes. It can be modified at predetermined sites to allow for the attachment of other molecules in a specific manner with subnanometer resolution. It can be cut at specific sequences and can be easily degraded when its role in assembly is complete.

213 Taking advan~age of these properties of DNA, we have created linear arrays of DNA with binding sites located at periodic intervals for functionalized gold clusters. As a first step, we designed a single stranded DNA template with modified thymines located every 11 bases. These thymines, modified with amino groups, allow at~achment of the nanoparticles at specific sites along the DNA strand through peptide bonds with carboxylic-acid functionalities (see previous section). The complementary DNA strand was synthesized and annealed to the modified strand to produce a double- stranded DNA molecule. The double-stranded DNA was then ligated to produce DNA of various lengths. Strands of the desired length can be isolated using gel electrophoresis to use for specific purposes. After ligation, the carboxyl-acid functionalized gold was bound to the amino groups on the thymine bases using l-ethyl-3 -(3-dimethylaminopropy l)carbodiimide and N-hydroxysuccinimide [9]. The DNA-gold complex was precipitated with ethanol and washed, releasing the free gold. We analyzed the products using gel electrophoresis for purposes of size selection, and Figure 2. AFM image of gold clusters. The using transmission electron microscopy (TEM), Fig. 3. measurement of the cluster height provides For purposes of the TEM analysis, the DNA-gold accurate information. The width complex was coated with cytochrome C and stained measurement is distorted by the size of the with uranyl acetate to facilitate the visualization of AFM tip. DNA. In summary, we have engineered and produced DNA templates up to 200 nm l&g containing about 60 binding sites for gold clusters. We are refining our procedures to ensure that every binding site along the strand is occupied with a gold cluster and that each cluster is bound to only one DNA strand. Future work will involve the extraction of a single strand of DNA with the gold and attachment to electrodes for measurements of the current-voltage (i.e., 1(V)) characteristics of the array.

~~ELECTRODE CONSTRUCTION~~

Operating the quantum-dot array as an electronic device requires placing the QDs between two electrodes, with the electrodes coupling to the array via electron tunneling. This alone is a challenging task, as the electrodes are the objects that span the gap between the nanoscopic and macroscopic domains. Using our currently available facilities, electrodes can be fabricated with separation of approximately 20 nm using a focused-ion beam (FIB). In the near future, we anticipate having avaiIable an electron-beam facility, which may also be applied to the fabrication of electrodes. The DNA-gold complex can be stretched between the electrodes to provide electrical connectivity to the quantumdot array [101. A thiol group will modify one end of the DNA, A drop of DNA in solution can be placed between the electrodes using a micro-positioner. The drop size will be much larger than the gap width of the electrodes. Since the electrodes are made of gold, the thiol-modified end of DNA will attach to both gold electrodes. These anchored DNA molecules can be stretched under DNA buffer solution using hydrodynamic forces. It is also possible to use an electric field to achieve orientation of the DNA molecules between electrodes. Drying the DNA molecules can cause alterations in structure and orientation due to a variety of effects. Using the technique of critical point drying [11,12] can

214 preserve the geometry of the stretched DNA. The resulting QD structures can be visualized using an AFM. If more than one DNA strand is stretchedbetween the electrodes,the AFM can be used to selectively dissect unwanted DNA strands. The DNA strand may act as conduit for leakage currents, and should be removed, but without removing or modifying the gold clusters. One might consider heat treatment for this task, but heat treatment is likely to result in rearrangement of the quantum- dot-array geometry, and can also affect the electrodes due to diffusion. We will utilize a novel UV-Ozone technique that will chip away the DNA molecules without affecting the position of the electrodes or the clusters. The UV-Ozone technique involves exposing organic molecules (such as DNA) to 180-nm W light. Figure 3. TEM image of DNA- The UV light creates ozone from oxygen, which oxidizes the gold complex. carbon containing molecules to carbon monoxide, which readily leaves the surface.

~~SINGLE-ELECTRON TUNNELING IN QUANTUM-DOT ARRAYS~~

Consider a onedimensional array of N tunnel junctions constructed from metallic source and drain electrodes weakly coupled to a linear array of N-1 metal clusters. We review the results of the “orthodox theory” of single-electron tunneling [13] to describe the charge transport through the array under small, but finite, bias voltage. (We are interested in nanometer-sized metal clusters in which the Coulomb blockade of conductance may be observed at room temperature, but for simplicity here we neglect any discreteness in the density of electronic states in the cluster resulting from their small size.) The vector ii defines the state of our system, ii= (n,,.-”,n,,””-,/1~.,), where n, is the number of excess electrons accommodated by the i’”quantum dot. The Gibbs free energy E(ii,V) describing the electrostatic energy of the array of quantum dots and its interaction with the external voltage is +;$,L$+,CU(0/-@)~-YQ, -Y/Q.~ (1.1) ~(fi,v)=~~ciio~2 j=, where co= c,, is the mutual capacitance betw~en conductors i and ~, O, is the electrical potential of cluster i measured with respect to the substrate. The source and drain electrodes are enumerated i = Oand i =N, respectively. The source potential is $0= V, =Vi 2, and the drain potential is @M= ~, =-V /2. V is the transport voltage across the array. The charge on the source electrode is Q,= cO,(00–o,)+ en,,and the charge on the drain electrode is Q~= C~-,,~(o. -o~.,)+ e~,, where n. (~~~) is the number of electrons that has tunneled from the source (drain) electrode through the first (last) junction. To determine the free energy, the potentials J =(0,.-., o.-,) must be determined from the static charge configuration. Using the charge conservation law, the total charge on island i can be written in terms of the potentials, h’

~~~i “i@l+ ~ clJ(@f–@j)2 ‘eni+~O,i* ‘=l>...>l–l. (1.2) i=O,l*j~~

The background charges -e/2 c q,,< +e/Z are due to incompletely screened charges in the environment of the islands. Equation (1.2) can be written in matrix form Q=@, where the generalized capacitance matrix elements are defined (1.3)

and the augmented charge vector is defined QI= q, + Cio@o+ [email protected] generalized capacitance matrix can be inverted to obtain the potential distribution given any charge distribution. For convenience, we rewrite the free energy of the array using matrix notation

-.. _.— ,,.,, .,: ,,. :,,.?:,.:<..’.’,,-.!;.?./7 , : .,,.,.. ,-,.,,,, ,.l,,;:,,.:,..:..),~r....,.’:,.,,“,.....)...,“~..:;,. .,v.-.. .1> ::, ., (1.4) In describing the electron transport through the array, we neglect here the effects of co-tunneling, and consider only single-electron tunneling between nearest neighbors in the array. That is, the final state FIof the tunneling differs from the initial state ii by the transfer of a single electron though the k’” junction, e.g., h = ii t Au“~, where Ati~= ti~– ill., and i~ is a unit vector for the k’”quantum dot. The ~ sign gives the direction of tunneling through the junction. If the transition rates are sufficiently small, one can perform a calculation using Fermi’s Golden Rule to obv~in[13] r;(ii,v)= r;(fw;ti,v])=— XI’-’’’(H’ (1.5) where A~f(Z,V)s E(ii ~ hk ,V) - /;(,V,V) is the change in the free energy of the system due to the tunneling, R~ is the effective resistance of the tunnel junction, e >0 is the fundamental unit of charge, and the thermal energy is k,,T. One can use probability conservation to write the corresponding master equation describing the time evolution of the probability P(ii,t) of finding the circuit in the state Z dP(ii,t) d, ‘x[ri-l (fi-%I)P(i-Afi ~-l,t)+r; (fi+Ati~)P(fi+Ati~,t)]-~[r: (Z)+r; (fi)lp(ii,t). (1.6) k k=l Practical approaches to solving the master equation are described in Refs. [14-15]. Given the solution, the average tunneling current is given by computing the net flow through any junction k in the array: f(V)= l,(V) =e~P(Z)[r; (fi,v)-r; (ii,v)]. (1.7) Ii Since the summation is performed over the charge states, the current is a function of the transport voltage.

~~NEUROMORPHIC ALGORITHMS FOR COMPLEX INFORMATION PROCESSING~~

Quantum dot nanoelectronic devices represent a promising hardware technology that offers both conceptual opportunities and engineering challenges for complex information processing applications. One such application, pattern recognition, is of considerable interest to the development of modern intelligent systems and will be considered here. In recent years, the quest for innovative approaches to machine intelligence has received considerable attention. The proven ability of neuromorphic algorithms to deal with uncertain information and to interact with dynamic environments is therefore providing a strong incentive to explore the feasibility of their implementation on arrays of quantum dots. However, in contrast to conventional hardware approaches, we must develop here computational paradigms that exploit from the onset not only the concept of massive parallelism but also, and most importantly, the physics of the underlying device. Artificial neural networks are adaptive systems that process information by means of their response to discrete or continuous input [16]. Neural networks can provide practical solutions to a variety of artificial intelligence problems, including pattern recognition [17], autonomous knowledge acquisition from observations of correlated activities [18], real-time control of complex systems [19], and fast adaptive optimization [20]. At the heart of such advances lies the development of efficient computational methodologies for “learning” [21]. The development of neural learning algorithms has generally been based upon the minimization of an energy-like neuromorphic error function or functional [22], Gradient- based techniques have typically provided the main computational mechanism for carrying out the minimization process, often resulting in excessive training times for the large-scale networks needed to address real-life applications. Consequently, to date, considerable efforts have been devoted to: (1) speeding up the rate of convergence [23-251 and (2) designing more efficient methodologies for deriving the gradients of these functions or functional with respect to the parameters of the network [26,27], The primary focus of such efforts has been on recurrent architectures. However, the use of gradient methods presents challenges even for the less demanding muki-iayer feed-forward architectures, which naturally

216 occur in quantumdot arrays. For instance, entrapment in local minima has remained one of the fundamental limitations of most currently available learning paradigms. The recent development of the innovative global optimization algorithm TRUST [28] has been suggested [29] as a promising new avenue for addressing such difilculties. Roychowdhury and his collaborators were the first to propose the implementation of neural networks in terms of quantumdot arrays [30]. In their Gedankenexperiment a generic array of nanometer-sized metallic islands would be deposited on a resonant tunneling diode. Furthermore, all islands would have a direct conductive/capacitive link to their nearest neighbors established, for example via organic moleculm wires. They considered both continuous and discrete charge networks. The latter are of interest here. The Roychowdhury team showed that the evolution of an initial charge distribution toward a svable find equilibrium distribution can be given a neuromorphic interpretation and that this property emerges purely as a result of the discreteness of the electronic charge [31]. There are several shortcomings in their proposal. First, they assumed that all inter-island capacitance could be modified arbitrarily, but offered no mechanism to achieve this essential property. Moreover, their architecture involved capacitive coupling between all islands, a “jkxzting” plate, and a grounded plate. Tunneling is assumed to occur only between the islands and the floating plate, but not between islands. Thus, even though their paradigm would allow some elementary form of combinatorial optimization, it could not be used for neural learning needed in pattern recognition. In the previous section we have illustrated the underlying physical concepts of single-electron transport in arrays of quantum dots. As pointed out by Roychowdhury and coworkers [30-31], there is a profound similarity between the dynamics of neural networks and that of quantum-dot arrays. In the latter, the free energy of an army characterized by a charge distribution can be lowered in terms of tunneling events. For neural networks, on the other hand, Hopfield has shown that the stable states of the network are the local minima of a bounded Lyapunov function of the net’s output parametrized by the synaptic interconnection weights. A careful analysis, however, reveals that this formal similarity is not adequate for implementing learning algorithms for pattern recognition. By comparing the leading terms of the free energy in Eq. (1.4), i.e., @c-’Q, and the Lyapunov function in a Hopfield network, i.e., q~,tv)=-+x’ M-X, we see that the inverse ~f the augmented capacitance matrix would have to play the role of the synaphc matrix. However, the elements of G, are jixed, and cannot be modified. An alternative approach for controlling the dynamics of the system has to be found. In principle, one could manipulate thefree energy of the array via capacitive gating of each of the quantum dots. However, for an array of quantum dots 1 to 2 nm in size, which is necessary for room temperature operation, we are not aware of technology capable of implementing such gating on a nanometer scale. Studies of the dynamics of arrays of quantum dots in the presence of the time-dependent excitation (e.g., RF signal [33,34]) reveal a rich structure of dynamical behaviors that offers a tremendous potential for performing the computation we need. In particular, a team led by Oosterkamp has recently made available an extensive survey of experiments and methods for photon-assisted tunneling in qwantum dots [35]. In the absence of a time-dependent field, current flows through a quantum dot via tunneling when an unoccupied internal energy state is aligned to the Fermi energy of the leads. However, as pointed out by Oosterkamp et al following seminal work by Likharev et al., if a time-varying AC voltage ~cos(hwr) k applied, inelastic tunnel events are induced when electrons exchange photons of energy W with the oscillating field. Tien and Gordon first described theoretically this phenomenon of multiphoton-assisted tunneling [36]. A direct inclusion of this phenomena in a master equation that takes into account Coulomb blockade can be made by writing the tunneling rate ~ through each barrier in the presence of an electromagnetic excitation in terms of the rates without the external AC fieId, (1.8) where J= denotes the Bessel function of the first kind and c%denoting the number of photons exchanged. This generalized master equation is obtained by substituting the rates in Eq. (1.8) into Eq. (1.6). The current through this device is a function of the transport voltage V, and the amplitude AOand frequency v of the AC field,

~~217 (1.9)~~

We will consider the transport voltage V as the input variable and the current I as the output function in implementing neuromorphic computation. For a two-dimensional quantum-dot array with K input and K output nodes, we can readily generalize the description given here to consider K input voltages vk and K output currents /k(Vk,Ao, v) (see Fig. 4). This vector-valued function IK is controllable through the parameters of the external, alternating field, AUand v, by minimizing the error function &, defined over the number*of L training patterns as the squared difference between the observed currents, 1~ and the target currents, I K,(see below), (1.10) .

For convenience, matrix and vector dimensions are explicitly indicated as subscripts. If a larger number of controls are necessary, then a polychromatic AC field may be implemented as the global control, rather than a monochromatic field. The pattern recognition scheme can now readily be implemented using the following method. We assume that two sets of L vectors are used for training. They are stored as rows of two matrices L?Uand Rm respectively, which represent the input signal patterns and the target outputs. We denote the number of columns of each matrix as 1 for input and O for output, without confusion. Since typically L >>1, two preprocessing steps are used [25]. Fir-t, clustering is used to transform ~lJ and Rm into ~*K/ and R K~.Then, two successive “~@@@@ .“ nonlinear transformations map f2*Klinto H~K,a nonsingular K x K I’(zJ presynaptic matrix, which constitutes the actual input into the o---l@@@@ A“ quantumdot array. We also decouple the nonlinearity of the ‘~—l@@@ @ A“ transfer function, (p, at the output layer of the neural net from the linear interlayer pattern propagation mediated by the synaptic ~ weights WKO . This transformation is used to compute the postsynaptic input to the output layer of the neural net as a K x O S’ rectangular matrix. Since the latter is connected via a bijective sigmoid mapping to the output training examples, the synaptic Figure 4. Two-dimensional QD interconnection matrices WKOcan be determined by solving the array showing voltages as input linear system HKKWKO =(p-l(R ~o) using gradient iteration. In channels and currents as outputs. simulation on a conventional computer, this can be accomplished by exactly solving a system of line& equations using singula;-value decomposition techniques. On nanoelectronic hardware, this will be achieved by directly optimizing the error function in Eq. (1. 10) in terms of the parameters of the external field, AOand v. If the dimensions O of the output pattern is smaller than the number K of output nodes of the quantum-dot array, the output error is calculated using the O dimension in the Euclidean distance.

In this minimization process, we can directly account for uncertainties to obtain best estimates for the device parameters and responses of interest. For example, nominal values for the elements of the capacitance matrix will be computed from “first-principles” simulations of the metal clusters and substrate via density-functional-theory-based molecular dynamics [37] and the current through the device will be computed via numerical solutions to the master equation [14,15]. To obtain best estimates for critical parameters (e.g., A. and v), we must consistently combine computational results and experimental measurements. We achieve this by optimizing a generalized Bayesian loss function that simultaneously minimizes the differences between the best estimate responses and the measured responses on one hand, and the best estimate and calculated parameters on the other hand. Our optimization process uses the inverse of a generalized total covariance matrix as the natural metric of the calculational manifold in conjunction with response sensitivities to all parameters [38].

~~218 ACKNOWLEDGMENTS~~

Resewchpartially sponsoredby the EngineeringResearchProgramof the Office of Basic Energy Sciences, U.S. DOE, and partially by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the U. S. DOE under Contract No. DE-AC05-OOOR22725. The authors wish to express gratitude for the assistance of Dr. Muralidharan Govindarajan for assistance with the TEM analysis.

~~REFERENCES~~

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~~219 .——..—~~

~~EXPERIMENTAL AND THEORETICAL ASPECTS OF QUANTUM TELEPORTATION~~

~~Lei Zhang, Jacob Barhen, and Hua-Kuang Liu~~

Center for Engineering Science Advanced Research Computer Science and Mathematics Division Oak Rklge N~tiond Laboratory Oak Ridge, TN 37831-6355,USA zhand@,ornLgov, barheni (Z20rnl.gov,and 9hl@,ornl.gov

~~ABSTRACT~~

We present a short summary of progress achieved at the Center for Engineering Science Advanced Research (CESAR) of the Oak Ridge National Laboratory(ORNL) in the recently initiated Quantum Teleportationproject. The primary objectiveof this effort is to study the signaling potential of quantum informationprocessingsystems based on quantum entanglement.Our initial effort has focused on the development and demonstration of a novel, ultra-bright EPR source, basedupon the innovativeconceptof cascadedtype-11optical parametricdownconversion, The main features of this source are analyzed, and results of a multi-photon entanglement experiment are presented. Theoretical challenges for superluminat communications are also highlighted.

~~I. INTRODUCTION~~

in recent years, there has been increased interest in exploiting the unique capabilities that quantum mechanics offers for the processing of information. In that context, quantum teleportation (QT) is a pallicularly attractive paradigm. It involves the transfer of an unknown quantum state over an arbitrary spatial distance by exploiting the prearranged entanglement (correlation) of “carrier” quantum systems in conjunction with the transmission of a minimal amount of classical information. This concept was first discussed by Aharonov and Albert (AA) using the method of nonlocal measurements [1].

Over a decade later, Bennett. Brassard, Crepeau. Jozsa, Peres, and Wooters (BBCJPW) developed a detailed alternate protocol for teleportation [2]. It consists of three stages. First, an Einstein-Podolsky- Rosen (EPR) [3] source of entangled particles is prepared. Sender and receiver share each a particle from a pair emitted by that source. Second, a Bell-operator measurement is performed at the sender on his EPR particle and the teleportation-target particle, whose quantum state is unknown. Third, the outcome of the Bell measurement is transmitted to the receiver via a classical channel. This is followed by an appropriate unitary operation on the receiver’s EPR panicle. To justify the name “teleporta/ion”, BBCJPW note that the unknown state of the transfer-target particle is destroyed at the sender site and instantaneously appears at the receiver site. Actually, the state of the EPR particle at the receiver site becomes its exact replica. The teleported state is never located between the two sites during the transfer. A number of exciting theoretical developments has appeared since the publication of the AA and BBCJPW protocols. For instance, Vaidman has shown [4] how nonlocal measurements can be used for

220 the teleportation of the unknown quantum states of systems with continuous variables. In AA, nonlocal refers to measurements that cannot be reduced to a set of local measurements; for example, the measurementof a sum of two variables related to two separated spatial locations. He was also the first to suggest a method for two-way teleportation. Braunstein and Kimble extended Vaidman’s analysis to incorporate finite degrees of correlation among the relevant particles and to include inefficiencies in the measurement process [5]. In their proposed implementation of QT of continuous quantum variables, the entangled state shared by sender and receiver is a highly squeezed two-mode state of the electromagnetic field, with the quadrature modes of the field playing the roles of position and momentum. Stenholm and Bardroff have generalized the BBCJPW protocol to systems of arbitrary dimensionality [6]. Zubairy has considered the teleportation of a field state (a coherent superposition of 2“ Fock states) from one high-Q cavity to another [7]. In the previously cited studies, QT dealt with “intruspecies” teleportation e.g., photon-to-photon. Maierle, Lidar, and Harris were recently the first to introduce an “interspecies” teleportation scheme [8]. Specifically, in their proposal, the informationcontained in a superpositionof molecular chiral amplitudes is to be teleported to a photon. Finally, let us mention that Brassard, Braunstein, and Cleve have argued [9] that QT is an essential ingredient for quantum computing, and have presented a simple circuit that implements QT in terms of primitive operations in quantum computing, Let us turn to experimental realizations of QT. The first laboratory implementation of QT was carried out in 1997 at the University of Innsbruck by a team led by Anton Zeilinger [10]. It involved the successful transfer of a polarization state from one photon to another. A type-II degenerate, pulsed parametric downconversion process was used to generate the polarization-entangled EPR source. The experimental design is relatively easy to implement. The drawback is that only one of the four EPR-Bell states can be distinguished. in 1998, the Zeilinger team demonstrated that freely propagating particles that never physically interacted with one another could also readily be entangled [11]. In this experiment, one photon each from two pairs of polarization-entangled photons were subjected to Bell-state measurement. As a result, the other two photons were projected into an entangled state. This result is remarkable, since it shows that quantum entanglement does not require entangled particles to originate from a common source or to have interacted in the past. The second QT experiment reported in the open literature in February 1998 was carried out at the University of Rome by a team lead by Boschi and Popescu [12]. It involved a quantum optical implementation. The polarization degree of freedom of one of the photons in the EPR pair was employed for preparing the unknown state. The idea is to exploit the fact that the two degrees of freedom of a single photon can be k-vector entangled. This method cannot, however, be used to teleport an external, unknown quantum state. The conservation of energy and time photon entanglement over distances exceeding 10 km has been demonstrated experimentally [13] using a telecommunications fiber network. In a similar vein, the distribution of cryptographic quantum keys over open space optical paths of approximately 1km was also reported [14].

The potentially enormous economic and national security implications of a successful realization of a loopholes-free QT system has led to an intense competition among the few laboratories that have the experimental capabilities to adequately address this challenge. A particularly “hot” topic is to demonstrate which scheme is more “cumplele” [15] or more “unconditional” [16]. However, Vaidman has proved that reliable QT can not be achieved using the methods implemented in the experiments reported to date [17]. Specifically, it is impossible to perform complete Bell operator measurements without using interaction between the quantum states of the particles.

Our purpose in this paper is to present a short summary of progress achieved at the Center for Engineering Science Advanced Research (CESAR) of the Oak Ridge National Laboratory (ORNL) in a recently initiated QT project. The primary objective of this effort is to study the signaling potential of quantum information processing systems based on quantum entanglement. Our initial effort has focused on the development of an ultra-bright EPR source. Thk has been accomplished successfhliy, and is discussed in Section 11.The theoretical challenges are highlighted in Section 111.Near-term objectives (e.g., multi-channel quantum teleportation employing multi-particle, or GHZ photons) and conclusions reached so far are included in Section IV. IL EXPERIMENTS

The simplest quantum states for QT involve two-level systems, including spin states of a spin % particle, the polarization states of a photon, the ground and excited state of an atom or ion, or the Fock states of a microwave cavity. In the following discussion, without loss of generality, we will use polarization states. Before a polarization-entangled photon can be used for QT (including applications such as quantum cryptography or quantum remote sensing), it is essential to characterize the EPR source in detail.

Preparation of entangled photon pairs The preparation of polarization-entangled photons uses the process of optical parametric downconversion (OPDC) [18] to produce correlated photon pairs. This process employs a nonlinear medium, which allows pump photons to decay into pairs of photons under the restrictions of energy and momentum conservation. Since the two “decay” photons are created at the same time, the detection of one photon indicates with almost certainty the existence of the other. The conservation of energy and momentum also allows the determination of one photon’s wavelength and direction provided the other one’s are known. Three phase-matching methods are available for generation of correlated photons. They are referred to as type-I, type-II and cascaded type-I. In a type-I process, the generated photon pair shares the same polarization. With this method, a broad range of momentum and energy entangled photon pairs can be produced, either in a non-degenerate geometry, such that they have different wavelengths, or in a degenerate geometry, where the two photons share the same wavelength. The limitation of type-I OPDC is that the photons are actual]y created in polarization product-states, and may not violate a true test of Bell’s inequalities. In a type-II process [19], the photon pair is created with orthogonal polarizations. Therefore, as opposed to the type-1 source, the photons emitted into two distinct modes are usually not entangled, because they can be distinguished on the basis of their polarization. It was found that, when the cut angle of the crystal is larger than that of the degenerate OPDC (or when the crystal is tilted toward that direction), the two emission cones corresponding to different modes would overlap. In the two directions determined by the cones’ intersection the polarization distinguishability disappears. Therefore, such a source can produce polarization-entangled photon pairs. Typical emission patterns of type-I and type-Ii OPDC are shown in Fibwre 1. The type-I BBO crystal has a cut angle of 29.6° and was tilted 0.2° (internal) while the type-II BBO crystal has a cut angle of 42.9° and was tilted 2.5” (internal). Detailed explanations are provided in the caption.

Figure 1 Simulated emission patterns of idler beams (left), signal beams (center) and separations between idler beams (a) (“x”) and signal beams (“+”) with (a) type-I and (b) type-n phase matched OPDC in a BBO crystal. The pump wavelength is 395 nm. The solid circles correspond to a degenerate case. All patterns are calculated over a 10OX10°solid angle except the top right one, which is calculated over a 4°X40solid angle. (b)

Figure 2 shows the geometry when the crystal cut angle is larger than that of the degenerate OPDC, Polarization-entangled photon pairs, labeled as A and B, propagate along the two directions where the cones intersect. The horizontal polarization (+, ordinary) and the vertical polarization (1’,extraordinary) are orthogonal, and the corresponding polarization-entangled two-photon state is given by

~~Iv.,.,,)=+(l+,,,t.)+e’”p,,+.)) (1)~~

222 The relativephasea arkes fromthecrystalbirefringence,andan overallphaseshiftis omitted.Withthe help of additionalhalf wave or quarterwave plates,one can easiiy produce any of the four EPR-Bell states,

~~Figure 2 Geometry of a type-Ii OPDC. Polarization entangled photonsare foundalongthe two intersectiondirections(Aand B) of the two emissioncones.~~

We havealreadydemonstratedtype-11OPDCwitha femtosecondpumpsource.The pump laser system is a mode-locked Ti: Sapphire laser (Mira 900-F from Coherent) pumped by an Argon laser (INNOVA Sabre from Coherent). The output gives a 76 MHz puke train at a wavelength of 790 nm, with 120 femtosecond pulse width and 1.2 watt CW power. The UV beam is generated with a 7-mm thick LBO crystal (from CASIX) cut for second harmonic generation (SHG) at 790 nm. The conversion efficiency from lR to UV k about 40%. After passhg througha prkm pair for dispersioncompensationand fundamentalremoval,thefinalUV beamhasa pulseWidthof lessthan200 fs and300 mW power. Figure 3 shows the overlapped photon cones, generated by type-II OPDC. An interference filter with a bandwidth of 2 nm (from Avdover) is placed before the single photon countin module (SPCM-AQR-I 4 -F from EG&G Canada). The maximum photon counting rate is 7000 (see ) (counted by fiber with background subtracted).

Figure 3 Emitted photon cones scanned with a 100-pm diameter fiber over a I cm x 1 cm area, 6.5 cm behind the crystal’s output surface. A 3-mm thick BBO with cut angle of 43° is used for type-II OPDC. An intetierence filter with bandwidth of 2 mn is placed before the SPCM. a) corresponds to a collinear and b) corresponds to a non- collinear case. 0 corresponds to effective internal angle between the optical axis and the pump UV beam direction. a) 6 = 43.o deg b) 0 = 44.2S deg

The polarization correlations were measured using the setup shown in Figure 2. With (31set at -45° and @ rotated from -45° to 315°, the coincidence rate from the two detectors was recorded. It corresponds to the I~+> state. Then a half-wave plate was inserted into one of the arms to rotate the polarization by 90° in that arm. The corresponding polarization entanglement was measured and gave the 1#> state. These measurement results can be seen in Figure 4.

Figure 4 Measurement of the polarization entanglement of an EPR source generated with a type-11phase matched BBO crystal. The solid square corresponds to the Iy+> state and the circle corresponds to the ]~> state. The solid line is the fitting with sin2(01+ 82) and the dashed line is the fitting with cos2(0I+ 02). Cascaded Type-1 Downconversion Source of Correlated Photons A new method, that uses the process of OPDC in an innovative geometry involving two type-I crystals, has recently been repelled [20]. Two adjacent, relatively thin, nonlinear crystals are operated with type-I phase matching. The identically cut clystals are oriented so that their optic axes are aligned in perpendicular planes. Under such conditions, a 45° polarized pump photon will be equally likely to down convert in either clystal. Generally photons generated by different crystals can be distinguished by their polarizations. This problem was solved by inserting quarter-wave plates behind the crystal pairs. Furthermore, these two possible down-conversion processes are coherent with one another.

Cascaded Type-l/ Optical Parametric Down-conversion We now present some new experimental results that we have achieved in the short period since the inception of this project. First, we discuss our novel EPR source, which is based on optical parametric down-conversion, but with a cascaded type-II OPDC configuration. It combines the main advantages of, and outperforms previously reported entangled photon generators. Next, we analyze its main features and limitations. Our new source consists of two adjacent thin nonlinear crystals with identically cut angles, which correspond to degenerated type-11phase matching. The two crystals are oriented with their optic axes aligned in opposite direction. A pump photon may be equal Iy down-converted in either crystal, and these two possible downconversion processes generate two pairs of correlated photons (see Figure 5). The advantage of our proposed configuration is obvious. First, the limitation in overlap of idler and signal photons has been greatly relaxed (see Figure 1) compared with the case in cascaded type-I OPDC. Our architecture can thus provide much brighter polarization-entangled photons in either degenerate or non- degenerate cases. Second. the outputs are naturally polarization-entangled, Third, in the directions corresponding to the intersections of the two cones, the two pairs of polarization-entangled photons coincide exactly. By selected alignrnent, sLlcha source may work as a.four-photon entanglement source.

Figure 5 Emitted photon cones generated by type-n OPDC. scanned with a 100-pm diameter fiber over a 1.6 cm x 1.6 cm area. 7.5 cm behind the crystal’s output surface. The background has been subtracted. The residual of the UV pump photons at the center has been cropped. The thickness of both BBO crystals is 1-mm and cut at an angle of 43.9°.

The single photon counting modules (SPCM-AQR- 14 from EG&G, Canada) that we used have internal amplifiers. For each photon detected, there is a 5 V output signal with 30 mspulse width. Since the pump source is a mode locked Ti: Sapphire laser with 76 MHz modu Iation frequency, the separation between pulse trains is 13 ns. Hence, we have used a Quad Constant-Fraction Discriminator (935-CFD from EG&G ORTEC) to compress the output pulse width to 5 ns. The outputs from two CFD output connectors are then routed to a Quad 4-h~put Logic Unit (C04020 from EG&G ORTEC) for coincidence count. The output from C04020 is sent to a Universal Time Interval Counter (SR620 from Stanford Research Systems). The outputs from the 935-CFD are also sent to a Quad Tinier/Counter (974 from EG&G, ORTEC) to record the single counting rate.

~~Two-photon intetferometry for analyzing the entanglement~~

If one overlaps two photons at a beamsplitter, interference effects determine the probabilities to find the two photons incident one each from A and B either both in one of the two outputs or to find one in each output. Only if two photons are in the state

~~224 (4)~~

will they leave the beam splitter in different output arms. If one puts detectors there, a click in each of them, i.e. a coincidence, means the projection of the two photons onto the state 1~-s. For the other three Bell states both photons will exit together through one of the two output arms. To register two photons in one output arm additional detectors or a certain detuning of the setup is necessary since these detectors do not distinguish between one or more photons.

~~A Figure 6 Experimental setup for measurementof entanglement and interference Uv~~

~~The experimental results for multi-photon entanglement, obtained using our cascaded type-II OPDC source in the setup shown in Figure 6 above, are illustrated in Figures 7 and 8.~~

Figure 7 Coincidence rate as a function of the delay between the arrival of photon A and photon B. The lower curve shows the measured destructive intefierence when the polarization in one path was rotated 90°. The upper curve shows the measured constructive interference with no polarization rotation, It includes a strong biphoton efecf in our cascaded type-II OPDC. Ikldiwd+y.\ 131pmtlwl

~~8 1100~~

u Figure 8 Measurement of the polarization G 800 % entanglement. The polarization analyzer of photon D “~ 650 was varied, while that of photon A was fixed at -45°. The solid line is the fitting with sinz(el + 82).

~~0, (0,= -45°) in degree~~

~~111.THEORETICAL CHALLENGES~~

The nonlocality of the correlationsof two particlesh quantumentanglementhasno classicalanalog.It allows coherent effects to occur instantaneously in spatially separate- locations, The question natur~liy arises as to whether a more general formulation of QT could provide a basis for superlumina] communications. This issue has recently been the subject of considerable debate in the open literature.

225 There are basically two schools of thought: one, which precludes this possibility (based, for example, on conflicts with the theoly of special relativity), and one which allows it under special provisions. We will discuss these issues in some detail in the sequel. First, however, we briefly high(ight a few of the more significant new findings in the growing experimental and theoretical evidence of superluminal effects. A conference on .superluminal velocities took place in June 1998 in Cologne [21]. Theoretical and experimental contributions to this topic focused primarily on evanescent mode propagation and on superluminal quantum phenomena. The issues of causality, superlurninality, and relativity were also examined. In the area of electromagnetic propagation, two exciting developments were addressed. Nimtz reported on experimental measurements of superluminal velocities achieved with frequency band-limited signals carried by evanescent modes [22]. Specifically, he timed a microwave pulse crossing an evanescent barrier (e.g., undersized waveguides, or periodic dielectric heterostructures) at 4.7c. He demonstrated that, as consequence of the frequency band limitation of information signals, and if all mode components are evanescent, an actual signal might travel faster than the speed of light. Capelas de Oliveira and Rodrigues introduced the intriguing theory of superlumina! electromagnetic X-waves (SEXW) defined as undistorted progressive waves solutions of the relativistic Maxwell equations [23]. They present simulations of finite aperture approximations to SEXW, illustrate the signaling mechanism, and discuss supporting experimental evidence. What are the key arguments put forward against the possibility of superluminal signaling? Chiao and Steinberg analyze quantum tunneling experiments and tachyon-[ike excitations in laser media [24]. Even though they find the evidence conclusive that the tunneling process is superluminal, and that tachyon-]ike excitations in a population-inverted medium at frequencies close to resonance give rise to superluminal wave packets, they argue that such phenomena can not be used for superhuninal information transfer, In their view, the group velocity can not be identified as the signal velocity of special relativity, a role they attribute solely to Sommerfeld’s front velocity. In that context, Aharonov, Reznik, and Stern have shown that the unstable modes, which play an essential role in the superluminal group velocity of analytical wave packets, are strongly suppressed in the quantum limit as they become incompatible with unitary time evolution [25]. Let us now examine EPR-based superluminal schemes. Furuya et d analyze a paradigm proposed by Garuccio, in which one of the photons of a polarization-entangled EPR pair is incident upon a Michelson interferometer in which a phase-conjugation mirror (PCM) replaces one of the mirrors [26]. The sender (located at the source site) can superluminally communicate with a receiver (located at the detector site), based on the presence or absence of interferences at the detector. The scheme uses the PCM property that a reflected photon has the same polarization as the incident photon (contrary to reflection by an ordinaly mirror), allowing to distinguish between circular and linear polarization. in a related context, Blaauboer et al also proposed [27] a connection between optical phase conjugation and superluminal behavior. Furuya ef al prove that Garuccio’s scheme would fail if non coherent light is used, because then the interferometer could not distinguish between unpolarized photons prepared by mixing linear polarization states or by mixing circular polarization states. They admit, however, that their counterproof would not apply to a generalized Garuccio approach, which would use coherent light states. Final Iy, in terms of criticism, let us mention the recent atlicle by Peres [28], where criteria that prevent superluminal signaling are established. These criteria must be obeyed by various operators involved in classical interventions on quantum systems localized in mutually spacelike regions. What are the arguments in favor of superluminal information transfer? Gisin shows [29] that Weinberg’s general framework [30] for introducing nonlinear corrections into quantum mechanics allows for arbitrary fast communications. It is interesting to note that, in a recent book [31], Weinberg himself states: “I could not find a way to extend the nonlinear version of quantum mechanics to theories based on Einstein’s special theory of relativity (...) both N. Gisin in Geneva and my COIleague Joseph Polchinsky at the University of Texas independently pointed out that (...) the nonlinearities of the generalized theory COUM be used to send signals instantaneously over large distances”,

~~226 ..-~~

At the Cologne symposhm [2I] Mhtelstaedtreviewed the arguments that hadbeen putforwardin recent years in order to show that non-local effects in quantum systems with EPR-like correlations can not be used for superhrminal communications. He demonstrated that most of these arguments are based on circular proofs, For instance, a “locality principle” can not be used to exclude superhnninal quantum signals and to justi~ quantum causality, since the locality principle itself is justified by either quantum causality or an equivalent “covariance postulate” [32]. In a similar vein, van Enk shows that the proof given by Westmoreland and Schumacher in [33] that superluminal signaling violates the quantum no- cloning theorem is in fact incorrect [34]. Hegerfeld uses the formalism of relativistic quantum mechanics to show that the wave function of a free particle hhially in a finite volume instantaneously spreads to infinity and, more importantly, that transition probabilities in widely separated systems may also become nonzero instantaneously [35], His results hold under amazingly few assumptions (Hilbert space framework and positivity of the energy). Hegerfeld observes that, in order to retain Einstein causality, a mechanism such as “clouds of virtual patlicles or vacuum fluctuations” would be needed. To conclude this review, we note a recent suggestion of Mittelstaedt [36]. If the existence of superlurninal signals is assumed ub initio (viz. [22] and [35]), and consequently a new space-time metric (different from the Minkowskian metric) is adopted, all the paradoxes and difficulties discussed above would immediately disappear.

Iv* FUTURE ACTIVITIES In this paper, we have presented recent progress achieved at CESAWORNL in the area of QT. We have also highlighted some of the formidable theoretical challenges that must be overcome if an application of this technology to communications is to become possible. The feasibility question is, in our minds, still open. To summarize, we ]1OWsuccinctly indicate our near-term proposed road map. From a theory perspective, we will focus our attention on two recent proposals for superluminal communications. Greenberger has demonstrated [37] that if one can construct a macroscopic Schrodinger cat state (i.e., a state that maintains quantum coherence), then stlch a state can be used for sending superluminal signals. His scheme assumes that the following two requirements can be realized. First, it should be possible to entangle the signal-transmitting device with the signal itself, thereby constructing a GHZ state. Second, that non-unitary evolution can be established and controlled in a subset of the complete Hilbert space. This latter property has already been demonstrated successfully in several downconversion experiments. Greenberger uses an optical phase shifter as model for his signaling device. We believe that as of this date better alternatives are available. The second Gedankenexperiment we intend to examine was introduced by Srikanth [37]. His proposed method uses a momentum-entangled EPR source. Assuming a pure ensemble of entangled pairs, either position or momentum is measured at the sender. This leaves the counterpart in the EPR pair as either a localized particle or a plane wave. In Srikanth’s scheme, the receiver distinguishes between these outcomes by means of interferornetry. Since the collapse of the wavefunction is assumed to be instantaneous, superlurninal signal transmission would be established. We intend to explore possible experimental realizations of the above paradigms. We will also continue to focus on cascaded type-H OPDC, with emphasis on walk-off, optical collimation, optimal generation efficiency, and maximal entanglement. Special attention will also be given to multi-photon entanglement.

ACKNOWLEDGMENT This research was performed at the Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the United Stated Departmentof Energy (U. S. DOE) under Contract No. DE-AC05-000R2272S. Funding for the effort was provided the Basic EnergySciencesEngineering ResearchProgramof the Oftice of Science. U.S. DOE. REFERENCES

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18. L. Mandeland E. Wolf. OpIica/ Coherence rJrrdQmm/aJII O@s. Cambridge University Press (1995). 19. P. G. Kwiat. K. Mattle. H. Wcinfhrter. A. Zeilinger. A. V. Sergieako and Y. Shib, “New high-intensity source of polarization-entangled photon pairs.’”P/JJW.Rev. Le//.. 75(24), 4337-434 I (1995). 20. P. G. Kwiat. E. Waks. A. G. White. 1.Appelbaum and P. H. Eberhnrd. “Ultraright source of polatiz~tiol)+lltallgled photons”. P/ryY.Rev. A., 60(2). R773 -R776 ( 1999).

21. P. Mittelstaedt rmdG. Nimtz eds.. “’Workshop on Supcrluminal Velocities’”,Annalcn der Physik, 7(7-8), 591-592 (1998). 22. G. Nimtz, “Superlrm]inalsignal velocities”. Anmdenrier Physik. 7(7-8). 618-624 (1998). 23. EC. de Olivcira and W. Rodriguez. %perluminal electromagnetic waves in free space””.Awralen der Physik, 7(7-8). 654-659 ( 1998). 24. R. Chiao and A. Steinberg “Quantum optical studies of tunneling and other superhuninal phenomena”. Physics Scrip/a. “~76, 61-66 ( 1998). 25. Y. Aharonov. B. Reznik. and A. Stem. “Quantum limitations of superhuninal propagation”. PhJ:t Rev. /e/r.. 81(I I). 2190-2193 ( 1998). 26. K. lhmryn. P. Milonni. A. Steinberg. and M. Woliasky. “Failure of a proposed superhuninal scheme””.Ply. Left., A 2S1, 294-296 (1999). 27. M. Blaauboer, A. Kozekhin. A. Kofiuan, G. Kurizki. D. Lenstra. and A. Loder, “Superhmlinrd pulse transmission through a phase conjugatingmirroi’, Opfics Co/it/itf{/?ico[iolIs, 148.295-299(1998). 28. A. Peres, “Classical intervention io qurmtum systems. II. Relativistic invariance”. PhJw.Rew.A61.02211 7(8) (2000). 29. N. Gisiu. “Weinberg-s non-linear quantum mechanics and superhnninai communications””,Phy.r. Le//.. A 143. I-2(1990). 30. S. Weinher& “Testing Quantum Mechrrnics”.Anm Php.. 194.336-386 (1989). 31. S. Weinberg. Dreram qfa Fired Theory. pp. 88-89. Vintage Books (1992). 32. P. MiUelstaedt.“Can EPR-correlations be used fix the transmission of superhnninal signals?’. Arrmrlender Phjsik, 7(7-8), 710-715 ( 1998). 33. M. Westmoreland and B. Schumacher. “Quantum entanglement rmdthe non existence of superhnninrd signals’-,arXiv: qunnt-phys19801014. Los Alamos National Lrrboratory(March 1998). 34. S. van Euk. “No-cloning rmdsuperhrminal signaling””.ar.Yiv: qI/c{nf-p/v.s/9803030. Los AlamosNationalLaboratory(March 1998). 35. G. Hegerfeldt,“hrstantaneousspreadingand Einstein causality in quantum theory”, .hmalen tier Physik, 7(7-8). 716-725 (1998). 36. P. Mittclstaedt. “What if there are superhnninal signals7”. Eur. Phys. Jonr., B 13,353-355 (2000).

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~~228 ENZYME ADSORPTION AND FUNCTION AT INTERFACES~~

~~L.G. Casciio-Pereira, C.J. Radke and H.W. Blanch Department of Chemical Engineering University of California Berkeley, CA USA~~

Thin-film forces between fluid interfaces with adsorbed protein are of pivotal importance for the stabilization of many foams and emulsions encountered in the dairy and pharmaceutical industry. We have developed a novel type of microfabricated film holder, which extends the thin-film balance (TFB) technique to the study of protein foam films. With this technique we can directly measure the forces responsible for stable film formation and investigate film drainage and coalescence, Force curves are presented for the first time for two proteins: @nsein and bovine serum albumin. Stable protein films are obtained at pH close to the protein isoelectric point or away from it where all the charge is screened by addition of electrolyte. These films are stabilized nminly by steric repulsive forces leading to black films of the dimensions of a protein bilayer. Gray films stabilized by mainly electrostatic forces are only observed at extremely low forces. As a necessary condition for film stability, protein must readily adsorb at the interface, which correlates with a significant reduction in surface tension. Film history is shown to strongly influence thin-film stability and drainage.

~~THIN-FILM FORCES~~

We have extended the thin-film balance technique (TFB) to the study of protein films under varying conditions of concentration, ionic strength, pH, and degree of aging at the interface. A novel film holder hm been designed to investigate small protein and enzyme samples under equilibrium and dyrudmic conditions. With this technique we can study the rates of drainage of thin films and examine the forces that dictate their stability. The behavior of single thin films is ~presentative of the observed macroscopic behavior of foams and emulsions. When the distance of separation between two fluid-fluid interfaces in a foam or emulsion is below 100 nm, the effects of van der Waals attraction and electrostatic repulsion become important. At distances of separation below a few nanometers repulsive steric and structural forces become importmt. The combined effects of these forces are expressed through the disjoining pressure II(h), which is the net sum of forces per unit area acting normal to the interfaces as a function of their sepamtion h. Moreover, the disjoining pressure is the negative derivative of the potential of mean force or interaction potential W, per unit area with respect to film thickness h [1-3]. m-g (1) Thin-film stability is achieved when the. disjoining pressure is repulsive, the tilm then resists thinning and rupture due to small perturbations. Because proteins adsorb at interfaces, they affect thin-film stability through their contribution to the disjoining pressure II(h). At equilibrium and in the flat portion of the film, the disjoining pressure l_Iis equal to the imposed capillary pressure PC The latter, is simply the difference between the gas pressure, PG, and the bulk liquid pressure, Pf,, in the Platem border region surrounding the film:

~~It is customary to separate the various contributions to the disjoining pressure into different components as in Figure I:~~

~~H st~l-i~ )%._rl electrostatic~~

~~Vc h~~

~~~ = ~ dispersion+ n electrostatic + ~ steric~~

~~Figure 1. Idealized Disjoining Pressure Isotherm.~~

~~The well-known DLVO theory accounts for the dispersion and electrostatic components of II as respectively expressed below:~~

~~II(h) = -* + 64n ‘)kTy2exp(–ti) 6nh3 (3) exp(Z/ 2) – 1 ‘y= , Z–elhl exp(z/ 2) + 1 kT~~

where A12 is known as the Hamaker constant. nois the number density of ions in the bulk solution, k is the Bohzrndnn constant, T is the temperature, fcis the inverse Debye length, e is the electron charge and W)is the potential. The weak-overlap approximation is used here for the electrostatic contribution. The simplest way to account for steric repuIsion at small separations is to assume a hard-sphere potential. Details can be found elsewhere (6]. Scheludko and Vrij use thermodynamic and fluid-mechanical analyses to establish that thin-films can not exist at thicknesses for which WM.lh>0 [4,5]. Accordingly, only thickness branches along which dIT/dh<0 are accessible through experiment.

~~230 THIN-FILM BALANCE~~

Disjoining pressure isotherms can be measured using a device now called a thin-film balance [7- 1l]. Thk device operates by maintaining a balance between capillary and thin-film forces. Thin films are formed in a film holder fused to a capillary tube, which is enclosed in a hermetically sealed cell with the capillary tube exposed to a constant external reference pressure.

~~porous glass disc (- pm) \ I hC E thin ii] J Computer- driven pump -7id Figure 2. Schematic of Conventional Film Holder Figure 3. Schematics of a Porous-Plate Cell. and Cell.~~

The cell is mounted on a pneumatic vibration isolation table and can be thermostated if desired. The gm pressure in the cell is regulated with both a manual and a computer-driven syringe pump. Manipulation of the cell pressure alters the imposed pressure on the film (i.e. the capilhuy pressure) and thus, sets the disjoining pressure. Film thicknesses are mtxdsuredinterferometricully,within * 0.5 nm, using the method of Scheludko and Platikanov [10]. The experimental setup is summarized in Figure 4. Video Camera

P Figure 4. Schematic of a Thin-Film Balance. We developed a unique microfabricated film holder suitable for the study of protein solutions b~ed on a previous design by Velev et al [12]. This new design combines the advantages of both types of film holders currently used for the investigation of surfactant solutions. It is referred throughout the rest of this paper as the bike-wheel microcell, for reasons that will become apparent shortly. The principle of operation of the bike-wheel microcell is similar to that of the capillary type. However, due to the modified design the dimensions of the capillary into which the film is formed are reduced 10-fold, whereas the dimensions of the pores through which solution drains are reduced 100-fold, The capillary pressures attained am comparable to those obtained with the porous-plate technique and film dimensions are closer to those encountered in real foams and emulsions [13,14]. Due to the miniaturization of the whole structure, the drainage time necessary to observe thin plane-parallel films is drastically reduced allowing the investigation of force laws as a function of time. Moreover, the surface area in contact with protein solution is also decreased, rendering the loss of protein due to adsorption on the glass walls negligible and allowing the investigation of systems for which only small amounts are available. A micrograph of the bike-wheel microcell is shown in Figure 5,

~~Figure 5. Portion of Microcell Upper Plate Magnified Under a Microscope.~~

RESULTS AND DISCUSSION ~-casein The next series of experiments deals with ~-casein a naturally occurring dairy protein used industrially as a stabilizing agent in many foams and emulsions. ~-casein from bovine milk is a flexible, loosely structured protein without disulfide bonds, of molecular weight 24 kDa, pI 5.2 and a mdius of gymtionof46A[15- 17]. The effect of protein concentration is presented for ~-casein aqueous solutions with no added electrolyte. The results are summarized in F@re 6. A black thin film is observed at 0.05 wt.% ~-casein solutions. These films are stable over several orders of magnitude of the disjoining pressure. At (),1 wt.% only gray thicker films are observed for the disjoining pressure range investigated. At the intermediate concentration of 0.075 wt.% a thickness transition from gray (outer branch) to black (inner branch) films occurs. Thelefore, as the protein concentration is increased, the formation of thicker films and appearance of an outer branch becomes possible. The observed 18-rim thick black films are consistent with the picture of a fl-casein bilayer stabilized by purely steric repulsive forces. Gray films are stabilized by long range repulsive forces, albeit low in magnitude. The nature of these forces is less clear. As the protein concentration is increased the

~~232 outer branch becomes sharper, thus suggesting an electrostatic effect associated with the protein charge, even if low at this pHsincewearecloseto theisoelectricpoint.~~

~~-— ... ..”. —.-. .--— ...... —— ------. .—.— .,—--. ——.-— . . ..—.— 1 ● (a) (b) ☎~~

●

~~: ✍❉ ( 1 , I , , o 10 20 30 40 50 80 70 80 90 0 10 20 30 40 50 60 70 80 90 FilmThickness h [rim] Film Thickness h[nm]~~

~~w 500 % 450 (c) E 4oo $ 350 g 300 !? 250- a. * 200 \ ‘g 150-r @oo” .g 50- o“ , 0 10 20 30 40 50 60 70 60 90 Film Thickness h [rim]~~

~~Figure 6- The Effect of $Casein Concentration on the Disjoining Pressure Isotherm,~~

Disjoining pressure isotherms are presented in Figure 7 for 0.1wt.% fkisein aqueous solutions with NaCl as the added electrolyte. Data obtained dynamically is in close agreement with equilibrium values. Solutions with 100 mM NaCl exhibit only one branch, 25-rim thick. Differences in the observed isotherms at this electrolyte concentration may arise from differences in solution preparations. Solutions with 10 mM NaC1 exhibit a thickness transition from a 28-rim gray film to an 18-rimblack film. The thickness of the inner branch is the same as previously observed for ~-cmein solutions at low concentrations and no added electrolyte (Figure 6@ and (b) inner branch). Whh no added electrolyte, only thick gray films are observed M in Figure 6(c). These findings are consistent with the picture of an inner branch stabilized by steric forces due to the excluded volume of the proteins and an outer branch stabilized by electrostatic double-layer forces. Indeed, m the electrolyte concentration increases the outer branch becomes sharper due to the ionic screening of the protein charges by the electrolyte. Eventually, a thickness tmnsition arises as with 10mM NaCl solutions. This tlickness transition is consistent with the squeezing out of one protein diameter. When the electrolyte concentration is further increased, no transition is observed and films are 25-rim thick. Comparison of F@re 7(b) and Figure 8 provides further evidence that electrostatic forces stabilize thicker, gray films. As the solution pH is increased from 5.8 to 9.0, keeping all other parameters the same, the outer branch becomes less sharp probably due to the increased repulsion between charged protein molecules. ‘i7500 - -.-——— ...... -...... -...... - ..-—. ,...... -- ~450 (a) ~ (b) ~400 ● ~ ~ 350 9 i %300 - & ; 250 - O*.A ! 9 ~zoo A ! “~150 - ! :gl 00- co : 50 01 I o-1 o 10 20 30 40 50 60 70 0 10 50 60 70 Film Thickness h [rim] F%mthi%ness4t! [rim]

Figure 7- Effect of electrolyte concentration on the disjoining pressure isotherms of ~-casein. -. .. .. -.-...———...... -.-.--.—.-—.-.——. . - ...... ~ 500 ! & 450- ~ E 400”- ! $ 350 0 :300 0 %+ ~ g 250- n ~ 200- .g 150- =loo - g5fJ - —.-— 0“ I , I —i 0 10 20 30 40 50 60 70 Film Thickness h [rim]

~~Figure 8- Disjoining pressure isotherm for a solution of 0.1 wt.% ~-cawin with 10 mM NaCl, pH 9.0.~~

Bovine Serum Albumin We decide to contrast the observed film behavior of ~-casein with that of bovine serum albumin, a model globular protein. In opposition to the flexible, loosely structured J3-casein,BSA is a large, rigid, globular protein, of approximate dimensions 60 ~ in aqueous solution, molecular weight 66.5 kDa, pI 4.7 and 17 disulfide bonds. The primaty function of this protein is regulation of the colloidal osmotic pressure of blood [17]. The disjoining pressure isotherms for O.I wt% BSA at pH 5.2 under different electrolyte concentrations are shown in FiguR 9. The overall force measured is low, similar to fl-casein films. At about 500 Pa there is film rupture. Only one branch is observed. The isotherm at 0.1 mM or 1.0mM NaC1fall on top of v~ch other. At this pH, close to the isoelectricpoint there is very little charge on the protein. This net charge is most like]y all screened by the available electrolyte in both cases. The final tilm thickness is close to i2 nm (k 1 nm given the scatter in the ddta for these runs) which is about twice the size of a BSA molecule in solution, thus suggesting a bilayer with no bulk solution in between stabilized by steric repulsive forces alone due to the excluded volume of the proteins.

~~234 G’ 00 0 L&m ●o 00 0 1= I 0 ‘1 0 100. a%Omfj I ● I o~ ol~ 051015203S30 35404550 0510 I53O25LW 35404550 Thickness [rim] Thickness [rim]~~

~~Figure 9- Effect of electrolyte addition on the Figure 10- Effect of electrolyte addition on the disjoining pressure isotherm of BSA at pH 5.2. disjoining pressure isotherm of BSA at pH 8.3.~~

At pH awayfromthe koeleetricpoint,suchas 8.3 wherethere is a net negativechargeon the protein,the pictureisverydifferent asshownin Figure 10. Asamatter of factnostable filmsare formedwithO.1mM NaC1. Withl mMNaCla 40-nmthick protein filmisformed atextremely lowprmsums suchm50 Pa. Upon an increase in pressure up to 60 Pa already a transition is observed until a 18-nm thin film is obtained. Upon further increases in pressure the film will rupture. Stable filnvs are obtained at this pH upon addhion of 25 mM NaC1. All the charge on the protein is screened and a black, thin film is immediately obtained. The film obtained is about 8-rim thick, just slightly bigger than the dimension of BSA in solution thus suggesting that a monolayer of protein bridging in between both film interfaces may be enough to stabilize this film. 80- 75- . •.**~ ~.. 70- -.0 %, 65- “..., ‘ ““k 60-..a..:\ “ ●*..., \ 55- . 50- 45-

~~40-~~

~~35- m 30~ 10 100 looil Iowo Time [s]~~

~~Figure 11- Dynamic surface tensions for 0.1 wt% BSA under different pH and ionic strengths.~~

Dynamic tension measurements for the solutions discussed above are extremely useful for complementing our understanding of the overall stability meehanism. In Figure I I we notice that at pH 5.2, 1mM NaCl and pH 8.3, 25 mM NaCl the measured tension quickly decreases from the value of the puR air/water interface 72 mM/m to values close to 55 mN/m. On the other hand, at pH 8.3 and only 1 mM NaCl when the protein is charged and there is not enough electrolytes present to semen these charges, the measured tension value remains close to 72 mM/m for considerably longer times. There is a significant electrostatic barrier for adsorption at high charges indicating little adsorption of protein molecules for extended times. Stable films of proteins are obtained at pH close to the isoelectric point or at pH away from the isoelectric point with enough electrolyte to screen the net charges present on the molecule. Under these conditions protein is able to adsorb at the air/vmterinterface as indicated by a significant lowering in surface tension. Steric repulsive forces stabilize the films obtained.

~~THICKNESS TRANSITION MECHANISM AND RATES OF DRAINAGE AND COALESCENCE~~

Our studies indicate that thin-film stability and ratm of drainage and coalescence are highly dependent on film history. Figure 12below shows the case of a fresh BSA protein film, i.e. the protein was allowed to adsorb at the interface for 30 minutes prior to measurement, undergoing a first-orderthickness transition at a constant applied pressure.

~~Fresh film 2 sec 5:17 min 6:3 I min~~

~~8:12 min 9:30 min 9:34 min 10:07 min~~

~~10:50 min 11:50 min 17:50 min~~

~~Figure 12 – Initial formation and thickness transition of a 0.01 wt% BSA fresh film at pH 5.2, 1mM NaC1.~~

The features discussed hereafter are typical of protein films, ~-casein having a similar behavior. Upon bringing the two menisci from a thick biconcave lens into contact, the film is formed as indicated by the characteristic circular Newton interferencerings. This tllm is initially very thick (hundreds of nanometers), with a dimple in the center, and it will drain after about 8 min to a homogeneous equilibrium flat film of constant thickness throughout, At about 9:30 min a thickness transition from a yellow, gray about 40-rim thick film to a more stable thin, black film takes place. Black spots appear close to the center and grow by fingering until eventually (after another hour) the entire film interface is that of a black film 15-rimthick.

236 The drainage and transition mechanism of a protein film is completely different than that of low molecular weight surfactants. Contrary to surfactant films, the dimple thins in place. Mo&over, small particles present at the film interface remain in relative position while thinning. The thickness transition happens through a fingering mechanism with non-equilibrium lines of tension. The overall rate of drainage is much greater, on the order of minutes to hours mther than seconds. These are features chandcteristicof immobile interfaces most likely due to gelation at the level of the interface through protein entanglement already at very early times. This black film is stable over hundreds of Pascal and will resist upon further increases in pressure, One must consider films formed from protein soIutions that had been at the interface for seveml hours. The film in Figure 13 is highly heterogeneous and does not drain to a flat film. It presents large protein agglomerates surrounded by regions of black films. This pattern remains under contraction and/or relaxation of the interface. When subject to large disturbances such as”a capillary pressure increase, aged films will not thin further without breakage. Upon film reformation chunks of protein agglomerates are observed. Aged films seem to be brittle and have solid-like behavior. Other than aging at the interface, this type of film is also favored at high protein concentrations, solution pH value close to the isoelectric point, and at high electrolyte concentrations that decrease the electrostatic screening.

~~Figure 13- Film formation from BSA 0.01 wt% pH 5.2 aged at the interface for several hours.~~

REFERENCES 1.) Derjaguin, B. V., and L. Landau, “Theory of the Stability of Strongly Charged Lyophobic Salts and of the Adhesion of Strongly Charged Particles in Solutions of Electrolytes,” Acts Physicochimica URSS, 14 pp,633-663 (1941) 2.) Verwey, E. J. W., and J. T. G. Overbeek, Theo~ Elsevier, Amsterdam (1948) 3,) Derjaguin, B. V., and E. Obuchov, “Anomalien diinner Fkissigkeitsschichten III,” Acts Physics URSS, 5(1) PP.1-22(1936) 4.) Scheludko, A., “Sur certaines particularity%des lames mousseuses: II. Stabilit6 cin6tique, 6paisseur critique et 6paisseur d’6quilibre,”Nederlandre Akademie van Wetenschappen - Proceedings B - Physical Sciences, B65 pp.87-96 (1962) 5,) Vrij, A., “Possible Mechanism for the Spontaneous Rupture of Thin, Free Liquid Films,” Discussions of the Faraday Society, 42pp.23-33(1966) 6,) Israelachvili, J., Intermolecular&Surface Forces, (2nd Ed.) Academic Press, (1992) 7,) Scheludko, A,, “~er dm Ausfliessen der Losung aus Schaumfilmen,” KoUoid-~itschrifi, 155( 1) pp.39-44 (1957) 8.) Scheludko, A., “Thin Liquid Films,” Advances in Colloid and lnterJacialScience, 1pp.391 (1967) 9.) Bergeron, V., and C. J. Radke, “Equilibrium Measurements of Oscillatory Disjoining Pressurw in Aqueous Foam Films,” Langmuir, 8 pp.3020-3026 (1992)

237 10.) Scheludko, A., and D. Platikanov, “Untersuchung dunner fliissiger Schichten auf Quecksilber,” b/bid-~itSCh@, 175 (1960) 1I.) Scheludko, A., and D. Exerowa, “Uber den elektrostatischen und van der Waalsschen zusiitzlichen Druck in wiisserigenSchaumfilmen,” Kolloklfiitschrfi, 168(1)pp.24-28 (1959) 12.) Velev, O. D., G. N. Constantinides, D, G. Avraam, A. C. Payatakes, et al., “Investigation of Thin Liquid Films of Small Diameters and High Capillary Pressures by a Miniaturized Cell,” Journal Of Coffoid and Inter-j-ace Science, 175(1) pp.68-76 (1995) 13.) Dalgleish, D. G., D. S. Home, and A. J. R. Law, “Size-Related Differences In Bovine Casein Micelles,” Acts Biochimica Et Biophysics, 991(3) pp.383-387 (1989)

14.) Singh, G., C, A. MNer, and G. J. Hirasaki, “On dimple forrndtion in foam films,” Journal Of C’olloid and Inteq$ace Science, 187(2) pp.334-337( 1997) 15.) Leaver, J., and D. G. Dalgleish, “The Topography of Bovine Beta-Ca..einat an Oil Water Interface as Determined from the Kinetics of Trypsin-Catalysed Hydrolysis,” Acts Biochimica Et Biophysics, 1041(3) pp.217-222 (1990) 16.) Dickinson, E., D. S. Home, J. S. Phipps, and R. M. Richardson, “A Neutron Reflectivity Study of the Adsorption of b-Ca.seinat Fluid Interfaces,”Langmuir, 9 pp.242-248 (1993) 17.) Atkinson, P. J., E. Dickinson, D. S. Home, and R. M, Richardson, “Neuqon Reflectivity of Adsorbed beta-casein and beta-lactoglobulin at the Air/Water Interface,”Journul of the Chemistry Society Faraday Transactions, 91 pp.2847-2854 ( 1995)

~~238 METABOLIC ENGINEERING OF BIODEGRADABLE PLASTIC PRODUCTION BY CYANOBACTERIA: MODEL STUDIES IN Syneclzocysiis sp. PCC6803~~

~~Gaspar Taroncher-Oldenburg and Gregory Stepha.nopoulos~~

~~Chemical Engineering Dept., Massachusetts Institute of Technology Cambridge, Massachusetts 02139, U.S.A.~~

~~ABSTIUCT~~

The accumulation of poly-3-hydroxyalkanoates (PHAs) by cyanobactcria has been proposed as a plausible process for the sequestration of atmospheric COZ and concomitant production of biodegradable plastic-like polymers. The application of metabolic cnginccring approaches to tic analysis of PHA biosynthesis in cyanobactcria is illustrated here for the model organism Syneclumyslis sp. PCC6803.

~~INTRODUCTION~~

Over the past decade the need for a reduction of green house gases in the atmosphere has become an area of high priority in global warming research II]. In particular, the development and implementation of technologies for the reduction and stabilization of COZemissions through biotic carbon sequestration has been proposed p]. One such application involves the accumulation of carbon-rich compounds by bacteria [s]. Several prokaryotes produce lipid storage materials called poly-3-hydroxyalkanoates (PHAs) that exhibit properties ranging from thermoplastic to elastomeric and arc completely biodegradable [4]. The coupling of biosynthetic pathways leading to the production of PHAs with the ability of photoautotrophic organisms to provide the necessary precursors from COZ assimilated through photosynthesis, has been recognized as a promising approach to the cfflcient sequestration of atmospheric carbon dioxide (Fig. 1) [Y. In addition, the potential of commercializing these materials as plastic substitutes makes this application attractive from a commercial point of view [3]. This contribution explores some of the biological aspects of the application of metabolic engineering to the production of PHAs in a group of photoautotrophic prokaryotcs, the cyanobaeteria. Recent advances in the genetics and physiology of PHA production in the model organism S’ynechocysfis sp. PCC6803 arc presented, as well as some of the more practical issues related to the implementation of this technology are also discussed.

~~239 POTENTIAL FOR COZUPTAKE BY CYANOBACTERIA~~

Cyanobacteria, a group of autotrophic photosynthetic organisms, have been proposed for implementing biological carbon sequestration systems [6]. Cyanobacteria exhibit significant y higher growth rates and C02 fixation efficiencies than higher plants [7]. The resuiting high output per unit of biomass is further possible because of their high surfiace to volume ratio, the existence of specialized intracellular C02 concentrating mechanisms and the lack of any major supporting structures [8]. Cyanobacteria are currently being studied for production of the biofuels hydrogen and ethanol [~] and protein for the food industry and other technological applications [IO]. Some of the factors still preventing the large scale application of cyanobacteria for the production of other commodity chemicals are, (a) the relatively slower growth rates of cyanobacteria and concomitant lower productivity, as compared to heterotrophic bacteria, such as Escherichia coli, (b) the inefficient transformation of light energy into biomass and metabolic products due to phenomena such as self- shading and sub-optimal photosynthetic turn-over rates, and (c) the energetic costs of downstream processing that can nullify any gain obtained from the fixation of COZ [6]. Efforts to overcome these limitations include the development of cyanobacterial strains with optimized product to biomass ratios [11], the design of photobionmctors that control turbulence to optimize gas exchange and light exposure for the organisms []2] and the over expression of product biosynthetic pathways as means of enhancing productivity and C02 fixation rates []3].

~~GENETIC ENGINEERING AND CYANOBACTERIA~~

Genetic analysis and manipulation of a handful of cyanobacteria has been successfully implemented over the last two decades I]4]. Synechocystis sp. has been used as a model organism for photosynthesis research in the past, ~dking advantage of its capability for natural transformation [M]. We have recently described a PCR based transformation method that will facilitate the targeted insertion or deletion of specific genes in Synechocystis sp. []6]. The recent application of Synechocysfis for the improved production of zeaxtmthin and other carotenoids used as coloring agents for food, pharmaceuticals, cosmetics and animal feed, further shows the potential of this species to be used as a “photosynthetic factory” for the manufacture of specialty and commodity chemicals [13]. Genetic transformation of cyanobacteria with the PHA biosynthesis genes from Alcaligenes eutrophus [17] has been successful]y attempted, and PHA accumulations between 1% and 17% Cell Dry Weight (CDW) have been reported 118,19].With the characterization of the PHA biosynthetic pathway in Synechocystis sp. new possibilities are now at hand to geneticallyy manipulate this pathway in cyanobacteria. Finally, an important factor increasing the potential of applying genetic engineering approaches to cyanobacteria is the completion, or near completion of the genome sequencing of several species of cyanobacteria, including unicellular ones (e.g., Synechocystis sp.) and filamentous, diazotrophic representatives of this group (e.g., Anubaena sp.).

~~CYANOBACTERIA AND PHA PRODUCTION~~

The presence of PHA inclusion bodies in cyanobacteria was first reported by Carr in 1966, following the extraction of PHB from Chloroglea fritschii [20]. Since then, the occurrence of PHAs has been shown for several other species of cyanobacteria [2.1].The most common type of PHA synthesized by cyanobacteria is poly-3-hydroxybuty rate (PHB) and, in some cases, also the more flexible poly(3- hydroxyvalerate) (P(3HV)) or the copolymer P(3HB-co-3HV) (Fig. 1; [21]).The biosynthesis of PHAs from acyl-CoA precursors takes place via three steps, as exemplified in Figure 1 for the case of PHB. The first reaction consists of the Claisen-type condensation of two molecules of acetyl-CoA to form

240 acetoacetyl-CoA. This step is catalyzed by a ~-ketothiolase (acetoacetyl-CoA thiolase; EC 2.3. 1.9). Acetoacetyl-CoA is then reduced by an acetoacetyl-CoA reductase (EC 1.1.1,36) to yield D(-)-3- hydroxybutyryl-CoA, followed by the polymerization reaction catalyzed by a PHA synthase (no EC number).

Photosynthesis 1 (reductive pentosephosphate pathway) 3-Phosldloelvccratc I Central Carbon Metabolism 2 [%COA] ~ ‘.v.w ‘- ~ {An N.V-ctlli IIS-CnA Acctvl.CoA Acstmcctvl-CoA Hvdroxvhutvrvl-CoA nNAL)P’ PHB NAIIPII+I1’

~~Figure 1. DiagmmShowingthe Couplingof PhotosyntheticCarbon Dioxide Fixation and PHA production as exemplified for the case of poly-3-hydroxybutyrate (PEIB).~~

RecentIy, and as a resuIt of the availability of the fill genome sequence of the cyanobacterium Synechocystis sp. PCC6803 [22], the first complete set of genes coding for the three enzymes involved in PHA synthesis in cyanobacteria has been identified and characterized [23,24] (Fig. 2). The two subunits, phaE.SY,,and phaC,SJ,,,of the type III, two-component PHA synthase are encoded by two open reading frames (ORFS), phm%),,,(slrl829) artdphaC,~y,,(sk1830) respectively, that are located contiguously and in the same orientation on the Synechocystis sp. PCC6803 chromosome (The gene classification and nomenclature used throughout this text is in accordance with the Synechocystis sp. PCC6803 genome project ([http://www.kazusa.or.jp/cyanofl; pz]) (subscripts to the genes refer to the species to which they belong [25]).Type III PHA synthases are characterized by their specificity for short- chain-length hydroxyalkanoic acids (three to five carbon atoms) and the existence of two subunits conforming the active dimer [25,26].The PHA syntha..e activity of the two ORFS, slrl 829 and slrl 830, has been demonstrated by heterologous expression in E.rcherichia coli [23], phenotypic complementation of a PHA-negative mutant of Alcaligenes eutrophus [23]and Pargeteddeletion in Synechocy.stis sp. [16] . Only three other type III PHA synth~ses have been characterized to date (Allochrornatium (Chromatiunz) vinoswn [27], Thiocystis vidacea [28]and Thiocupsa pfennigii [29]).In all three cases the other two biosynthetic genes, phaA and phaB, are clustered with the phuE-phaC genes. The primary annotation of the Synechocystis genome failed to identify any candidates for phaA or phall in the vicinity of the ORF cluster slr1829-slr1830. A directed similarity search of the entire genome of this organism resulted in the identification of two strong candidate ORFS, slr J993 and slrl 994, for the two genes in question, PhaA~Y)t

241 and phaBsYn respectively. Heterologous expression of the two genes together with the PHA synthase genes of Syneckxystis, phaEsYnand phaC$,,,, resulted in PHA biosynthesis in K coli. On the other hand, targeted gene disruption of p/zaA,fY,land phaB.tv,J in Synechocy.rtis caused the 10SSof PHA producing capacity of the organism [24].

~~l19Mmt ().9Mnnll 1..13mnt I .44nmt~~

~~‘I!>=l!= -35 -lo S/D -35 -lo S/D~~

Figure 2. Structure and organization of the four anabolic pha genes in Synwhocystis sp. PCC6803. Locations on the genome (in rent) were determined from CyanoBme [http:/lwww.kazusa. or.jp/cyano/]; hashed bars represent putative promoter regions; bold, cursive letters highlight the only difference between the two promoter regions; -35, -10 and S/l) refer to the -35,-10 and Shine-Dalg~rno consensus regions of cr70in E. coli respectively; lower-case “c” indicates a discrepancy with the CT70consensus region (“c” instead of “A” (-35); “c” instead of “T” (-10)).

~~REGULATION OF PHA PRODUCTION IN Synechocystis SP. PCC6803~~

PHAs fulfill several roles in the physiological balance of prokaryotic cells: They serve as a carbon reservoir, energy storage, or a combination of both in most heterotrophic bacteria [4], or as an electron acceptor or “fermentation product” during glycolysis, as has been proposed in the case of sulfur reducing bacteria such as Chromatium vinosum, or during acetme uptake by activated sludge in the anaerobic phase of the Enhanced Lliological phosphorus ~emoval (EBPR) process [30,31]. Two aspects of carbon metabolism are unique to cytinobacteria. First, alI cyanobacteria accumulate the glucose-polymer glycogen as a carbon and energy reservoir [32]. Glycogen is oxidized via the pentose phosphate pathway and ATP is generated by aerobic respimtion [321.Secondly, the tricarboxylic acid cycle (TCA cycle) is interrupted in cyanobacteria by the lack of the 2-oxoglutarate synthase (EC 1.2.7.3) [33].The implication of this is that PHAs are not an a priori energy storing compound in cyanobacteria, as acetyl-CoA can not be fully oxidized via the TCA cycle and, hence, no energy is produced from their catabolism [21]. A possible carbon storage function can not be ruled out, but the presence of the universal carbon storage compound glycogen undermines this option. In order to gain new insights into the function of PHAs in cyanobacteria, we undertook a series of experiments to determine the effects of nutrient starwtion and the resulting electron imbalances on PHA accumulation, the response of PHA biosynthesis to different carbon sources and the genetic regulation of the PHA synthase and other enzymes involved in acetate uptake in the model organism Synechocystis sp. PCC6803. In a first series of experiments we determined the differential accumulation of PHAs under varying nitrate, phosphorus and combined nitrogen and phosphorus starvation conditions. The results shown in

~~242 figure 3 summarize our findings on the influence of nutrient starvation conditions and balanced,~~

~~PHA Content 10 % ccIhdnr dry wcighi~~

~~n.d 0 BGII BGII 10%N 1O%P IO%N (cont.) (stat.) 10%P~~

Figure 3. PHA content of Synechocystis sp. PCC6803 grown with different carbon sources and under different nutrient limitations in fed-batch or batch culture. The cells were harvested after 8 days of fed-batch culturing (0.D.7S0approx. 0.8)(BG1l(cont.)) or four days in stationary growth phase (all other treatments). (Solid bars indicate no addition of acetate, open bars addition of 10mM acetate to the corresponding medium; labels on abscissa indicate the different nutrient limitation regimes: BGI, (control full medium); cont., continuous growth, stat., stationary growth phme; percentrtges refer to specific nutrient content in the growth medium relative to the base medium BG11 (NuN03, 17.65mM; KzHPOq,O.18mM)(n.d., not detected; error bars show S.E. (n=2)). continuous growth versus stationary phase conditions. PHA accumulation is very low or not detectable under balanced, continuous growth conditions or when carbon becomes limiting at the onset of the stationary phase. The addition of acetiite to the medium increases the biosynthesis of PHA, but the levels still do not exceed 1-270 of the cellular dry weight. In contrast, nitrogen starvation elicits a significant increase in PHA accumulation during the stationary phase, The presence of acetate clearly enhances the effect of nitrogen starvation. Nitrogen limitation induces a characteristic set of physiological responses in cyanobacteria that include cessation of cell division and degradation of the phycobilisomes, pigment-protein complexes that harvest most of the light energy for these organisms [M]. The increased accumulation of PHA observed here is most probably a result of the general imbalance of the carbon to nitrogen ratio in the cells resulting from an excess of carbon skeletons relative to the nitrogen available for amino acid biosynthesis. Phosphate limitation has a more dmrnatic effect on PHA accumulation than nitrogen starvation. Regardless of the nature of the carbon source, inorganic only (COZ) or in combination with an organic source (Na acetate), PHAs were accumulated to high levels. The highest concentration observed was close to 35% cellular dry weight under 6pM K2HP04 (equivalent to 370 of the full medium, data not shown). Similarly to nitrogen starvation, phosphate starvation elicits a set of characteristic responses in the cells that include an increased synthesis of high affinity transport systems for phosphate and the production of hydrolytic enzymes, such as extracellular phosphatases, that allow utilization of alternate forms of phosphate. The effects of the combined nitrogen and phosphate starvation are most similar to those of nitrogen limitation only, because the ovemll effect of nitrogen starvation on the cell’s metabolism is probably more significant than that of phosphate.

243 A second level of our investigation was to determine the actual regulation of the pha synthase in Synechrxystis at the genetic and biochemical levels. The data summarized in table I show the effects of nitrate starwtion and carbon source on the activity in crude extract of the pha synthase and the phosphotransacetylase. The levels of phosphotrmsacetylase are relevant because they reflect the level of acetyl-CoA, the direct precursor of PHA, in the cell, The results show a clear lack of response of the intracellular PHA synthase levels to acevate availability in the medium or acetyl-CoA levels in the cell. While the total transacetylase activity increased predictably with the addition of Na acetate to the medium, the expression levels of the PHA synthase remained constant. Converse]y, nitrogen starvation clearly induced the levels of PHA synthase in the cell, while phosphotransacetylase activities remained constant across treatments.

~~Table I~~

~~PHA synthase and phosphotransacety lase activities in crude extrrtcts of Synechocystis sp. PCC6803~~

~~Enzyme activity (~ S.E.)” (nmol x rein-i x mg of prot-’) Enzyme assayed and growth conditions” - Acetyl phosphate +Acetyl phosphate~~

~~PHA synthase N,: 321.36 (~ 8.23) 437 (k 32.03) Nl”% 898.8 (~ 42.6) 830.25 (~ 37.3)~~

~~Phosphotransacetylase (EC 2,3. 1.8)~~

~~NF 5762 (~ 258.5) 13755 (~ 632.9) Nit)(k 4783 (~ 1758) 13006 (* 1838)~~

“ Cells were harvested at the beginning of the stationary growth phase; CCIISwere grown in full 13GI,mtxhum (NF)orin BG,,mctlium containing only 10% of the original NaN03 (final N concentration 1.765 mM; NIW,) “ The orgmic carbon source acctyl phosplmtc was acktcclto the mcclium at a final concentration of 10 mM

Previous studies have shown that the control of PHA synthase is mediated by acetyl phosphate in Synechococcu.s sp, [3s]. We conducted a series of analysis to determine the effect of acetyl phosphate on the activity of the Synechocystis sp. PHA synthase and obtained similar results indicating that this enzyme is regulated with substrate inhibition-like kinetics (data not shown). Phosphate concentration has also been shown before to regulate transcription of the PHA biosynthetic genes in Acinetohacter sp. isolated from activated sludge. In this instance, transcriptional activation of the pha~C gene cluster under phosphate starvation conditions is determined by the presence of an 18 bp consensus pho box in the promoter region typical of promoters in the plw regulon [MI.A detailed analysis of the promoter regions of the two pha.~y,,PHA biosynthetic gene clusters reveals the absence of any ph~ box-like sequences but the near identity between the critical -35 and -10 ~7(]-likemotives between both clusters, which raises the possibility of parallel regulation and constitutive expression of the two pha.$},,gene clusters [24].

~~244 The overall regulatory scheme of PHA biosynthesis in Synechocystis sp. PCC6803 that is starting to emerge from this work is represented in figure 4. The direct effects of modulators such as acetyl~~

~~1(,,, A Acctatc o~~

~~‘b P Acctvl-nhossdmtc o+ 0& b 1 PHAsynthase (1 A,$-a)A ➤ LJJil n ACCWLCOA PHB~~

~~0 B~~

~~o i,aA L4 AcctvI-CoA PHBn~~

~~PHAdepolymerase \~~

~~Reducing power/Biomass~~

Figure 4, Conceptual representation of PHA synthase regulation by acetyl-phosphate in Synec/zocystis sp. PCC6803. (A) Activation of the PHA synthase at intracellular concentrations of acetyl phosphate below 3 mM. (B) Inactivation of the PHA synthase at intracellular concentrations of acetyl phosphate in excess of 3 mM resulting from the mobilization of PHAs for the production of biomass and an increase in the NADPH2/NADHz pool available for celhdar metabolism. (“+” and “-” signs denote activation and inhibition respectively)

245 phosphate, an indicator of acetyl-CoA concentrations in the cell, the substrate concentration effects as seen from the influence of acetate concentrations on PHA accumulation, and the global response mechanisms due to nutrient starvation conditions, show that the control of PHA biosynthesis in this organism is multi dimensional and occurring at the physiological as well as biochemical level. Ongoing research in our laboratory is addressing issues such as the influence of physiological imbalances in the intracellular reducing power pools on PHA accumulation patterns.

~~REFERENCES~~

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~~246 Final List of Participants~~

~~18th Symposium on Energy Engineering Sciences~~

~~May 15-16,2000~~

~~Argonne National Laboratory Argonne, Illinois~~

.. . 247 Bassem Armaly Harvey W. Blanch Division of Materials Sciences and Engineering, SC 131 Department of Chemical Engineering U.S. Department of Energy University of California-Berkeley Office of Basic Energy Sciences Tan Hall 19901 Germantown Road Berkeley, CA 94720 Germantown, MD 20874-1290 Phone: 510.642.1387 Phone: 301.903.4062 Fax 510.643.1228 Fax: 301.903.0271 E-Mail: [email protected] E-Mail: [email protected]

S. George Bankoff Yehuda Y. Braiman Chemical Engineering Department Ctr. for Eng. Sci. Adv. Res./Comp. Sci. & Mathematics Northwestern University Oak Ridge National Laboratory Evanston, IL 60208 P.O. BOX 2008 Phone: 847.491.5267 1000 Bethel Valley Road Oak Ridge, TN 37831-6355 Fax: 847.491.3728 E-Mail: [email protected] Phone: 865.241.2065 Fax: 865.574.0405 E-Mail: [email protected]

Jacob Barhen Frederick W. Brust, Jr. Center for Engineering Science Advanced Research Department of Engineering Mechanics Oak Ridge National Laboratory Battelle Memorial Institute P.O. BOX 2008 505 King Avenue, Rm. 11-4-122 1000 Bethel Valley Road Columbus, OH 43201 Oak Ridge, TN 37831-6355 Phone: 614.424.5034 Phone: 865,574.7131 Fax: 614.424.3457 Fax: 865.574.0405 E-Mail: [email protected] E-Mail: [email protected]

Gabriel Bitton Raffi Budakian Ctr. for Eng. Sci. Adv. Res./Computer Sci.& Mathematics Department of Physics Oak Ridge National Laboratory University of California-Los Angeles P.O. BOX 2008 Los Angeles, CA 90095 1000 Bethel Valley Road Phone: Oak Ridge, TN 37831-6355 Fax: Phone: 865.241.2065 E-Mail: [email protected]. edu Fax: 865.574.0405 E-Mail; bittong@ornLgov

John Blair [van Catton Council on Energy Engineering Research (CEER) Department of Mechanical and Aerospace Engineerin University of California-Los Angeles 25 Moore Road Wayland, MA 01778 405 Hilgard Avenue Los Angeles, CA 90095-1597 Phone: 508.358.7568 Phone: 310.825.5320 Fax 508.358.7568 Fax: E-Mail: [email protected] 310.206.4830 E-Mail: [email protected]

248 Yok Chen Xinyu Fu Department of Materials Sciences School of Nuclear Engineering US. Department of Energy Purdue University 19901 Germantown Road 1290 Nuclear Engineering Building Germantown, MD 20874-1290 West Lafayette, IN 47907 Phone: 301.903.4174 Phone: 765.494.5759 Fax: Fax 301.903.9513 765.494.9570 E-Mail: yok,[email protected] E-Mail: [email protected]

Michael Cross Henry S. Greenside Department of Physics Department of Physics California Institute of Technology Duke University MS 114-36 P.O. Box 90305 Pasadena, CA 91125 Durham, NC 27708-0305 Phone: 626.395.4320 Phone: 919.660.2548 Fax 626.683.9060 Fax: 919.660.2525 E-Mail: [email protected] E-Mail: [email protected]

James R, Fincke Daniel D. Joseph Department of Optical and Plasma Physics Department of Aerospace and Mechanics INEEL University of Minnesota P,O. BOX 1625 110 Union Street, SE Idaho Falls, ID 83415-2211 Minneapolis, MN 55455 Phone: 208.526.2031 Phone: 612.625.0309 Fax 208.526.5327 Fax: 612.626.1558 E-Mail: jfl @ineLgov E-Mail: [email protected]

Daniel Frederick David L. Jung Department of Engineering Science and Mechanics CESAR, Computer Science and Mathematics Division Virginia Polytechnic Institute and State University Oak Ridge National Laboratory MC 0219 P.O. BOX 2008 Blacksburg, VA 24060 1000 Bethel Valley Road Oak Ridge, TN 37831-6355 ~~$ne: 540,231.3270 540.231.6903 Phone: 865.241.2985 E-Mail: [email protected] Fax: 865.241.0381 E-Mail: jungdl@ornLgov

L. B. Freund Seungjin Kim Division of Engineering School of Nuclear Engineering Brown University Purdue University 182 Hope Street Hangar No. 3, Purdue Airport Providence, RI 02912 West Lafayette, IN 47906 Phone: 401.863.1476 Phone: 765.494.5759 Fax: Fax: 401.863.2857 765.494.9570 E-Mail: [email protected]. edu E-Mail: [email protected]

249 Gunol Kojasoy Francis C. Moon Department of Mechanical Engineering Department of Mechanical and Aerospace Engineerit University of Wisconsin-Milwaukee Cornell University P.O. Box 784 204 Upson Hall Milwaukee, WI 53201 Ithaca, NY 14853-7501 Phone: 414.229.5639 Phone: 607.255.7146 Fax: 414.229.6958 Fax: 607.255.1222 E-Mail: [email protected] E-Mail: [email protected]

Katja Lindenberg Chris D. Muzny Department of Chemistry and Biochemistry 0340 National Institute of Standards and Technology University of California-San Diego MS 838.07 9500 Gilman Drive 325 Broadway La Jolla, CA 92093-0340 Boulder, CO 80303 Phone: 858.534.3285 Phone: 303.497,5549 Fax: 858.534.7244 Fax: 303.497,5224 E-Mail: [email protected] E-Mail: chris.muzny@nist. gov

Uwe Lommatzsch N. Sri Namachchivaya Department of Chemistry Department of Aero & Astro Engineering Stanford University University of Illinois Mudd Building, MC 5080 306 Talbot Laboratory Stanford, CA 94305-5080 Urbana, IL 61801 Phone: 650.723.4332 Phone: 217.244.0683 Fax: 650.725.0259 Fax: 217.244.0720 E-Mail: [email protected] E-Mail: [email protected]. uiuc.edu

Arun Majumdar Joseph J. O’Gallagher Department of Mechanical Engineering Department of Physics University of California-Berkeley The University of Chicago 6185 Etcheverry Hall Enrico Fermi Institute Berkeley, CA 94720 5640 South Ellis Avenue Phone: 510.643.8199 Chicago, IL 60637 Fax: 510.642.6163 Phone: 773.702.7757 E-Mail: [email protected] .edu Fax: 773.702.6317 E-Mail: [email protected]

Mark J. McCready Alfonso Ortega Department of Chemical Engineering Dept. of Aerospace and Mechanical Engineering University of Notre Dame The University of Arizona 182 Fitzpatrick Hall P.O. Box210119 Notre Dame, IN 46556 1130 North Mountain Phone: 219.631.7146 Tucson, AZ 85721 Fax 219.631.8366 Phone: 520.621.6787 E-Mail: [email protected] Fax: 520.621.8191 E-Mail: [email protected] .edu

~~250~~

,. ., :,’ . . ..- -., ,. ‘. Lynne E, Parker Seth J. Putierman Center for Engineering Science Advanced Research Department of Physics Oak Ridge National Laboratory University of California-Los Angeles P,O, BoX 2008 Los Angeles, CA 90095 1000 Bethel Valley Road Phone: 310.825.2269 Oak Ridge, TN 37831-6355 Fax: 310.206.5668 Phone: 865,241.4999 E-Mail: [email protected] Fax: 865,574,0405 E-Mail: [email protected]

Tomio Y. Petrosky Nageswara S.V. Rao Center for Statistical Mechanics and Complex Systems Computer Science and Mathematics Division The University of Texas-Austin Oak Ridge National Laboratory RLM 7.220 P.O. BoX 2008 Austin, TX 78712 1000 Bethel Valley Road Phone: 512.471.7253 Oak Ridge, TN 37831-6355 Fax: 512.471.9621 Phone: 865.574.7517 E-Mail: [email protected] Fax: 865.241.0381 . E-Mail: raons@ornLgov

Robert Price Walter G. Reuter Division of Materials Sciences and Engineering, SC 131 Materials Department U.S. Department of Energy INEEL Office of Basic Energy Sciences P.O. BOX 1625 19901 Germantown Road Idaho Falls, ID 83415-2218 Germantown, MD 20874-1290 Phone: 208.526.1708 Phone: 301.903.3565 Fax: 208.526.0690 Fax: 301.903.0271 E-Mail: [email protected] E-Mail: [email protected]

Vladimir A, Protopopescu Hermann Riecke Computer Science and Mathematics Division Department of Applied Mathematics Oak Ridge National Laboratory Northwestern University P.O. BOX 2008 2145 Sheridan Road 1000 Bethel Valley Road Evanston, IL 60208 Oak Ridge, TN 37831-6355 Phone: 847.491.3345 Phone: 865,574.4722 Fax 847.491.2178 Fax: 865.574.0405 E-Mail: [email protected] E-Mail: vvp@ornLgov

David Y. H. Pui Herschel B. Smartt Department of Mechanical Engineering Industrial and Material Technologies Department University of Minnesota INEEL 111 Church Street, SE P.O. BOX 1625 Minneapolis, MN 55455 Idaho Falls, ID 83415-2210 Phone: 612,625,2537 Phone: 208.526.8333 Fax 612.625.6069 Fax: 208.526.0690 E-Mail: [email protected] E-Mail: [email protected] Todd R. Smith Charles R. Tone School of Nuclear Engineering Industrial and Material Technology Department Purdue University INEEL West Lafayette, lN 47907 P.O. BOX 1625 Phone: 765.494.5759 Idaho Falls, ID 83415-2210 Fax: 765.494.9570 Phone: 208.526.1895 E-Mail: [email protected] Fax: 208.526.0690 E-Mail: [email protected]

Pol D. Spanos Jack C. Wells Dept. of Civil & Mechanical Engineering Computer Science and Engineering Division Rice University Oak Ridge National Laboratory MS-321 , P.O. BOX 1892 P.O. BOX 2008 Houston, TX 77251 1000 Bethel Valley Road Phone: 713.348.4909 Oak Ridge, TN 37831 Fax: 713.348.5191 Phone: 865.241.2853 E-Mail: [email protected] Fax: 865.241.0381 E-Mail: [email protected]

Gregory Stephanopoulos Roland Winston Department of Chemical Engineering Department of Physics Massachusetts Institute of Technology The University of Chicago Building 56, Rm. 469 Enrico Fermi Institute 77 Massachusetts Avenue 5640 South Ellis Avenue Cambridge, MA 02139 Chicago, IL 60637 Phone: 617.253,4583 Phone: 773.702.7756 Fax 617.253.3122 Fax 773.702.6317 E-Mail: [email protected] E-Mail: winston@rainbow. uchicago.edu

Xiaodong Sun Lei Zhang School of Nuclear Engineering Ctr. for Eng. Science & Advanced Research Ctr. Purdue University Oak Ridge National Laboratory 1290 Nuclear Engineering Building P.O. BOX 2008,6010, MS 6355 West Lafayette, IN 47906 1000 Bethel Valley Road Phone 765.494.5759 Oak Ridge, TN 37831-6355 Fax: 765.494.9570 Phone: 865.241.2061 E-Mail: [email protected]. edu Fax: 865.241.0381 E-Mail: [email protected]

Yupin Sun Department of Physics The University of Chicago Enrico Fermi Institute 5640 South Ellis Avenue Chicago, IL 60637 Phone: 773.702.7759 Fax 773.702.6317 E-Mail: yupinsun@midway .uchicago.edu 252

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