RHEOLOGY BULLETIN Publication of the Society of Rheology

Volume 28, No. 3 Fall, 1959

THE BINGHAM MEDAL, 1959 THIRTIETH ANNIVERSARY The Bingham Medal of the Society of Rheology for MEETING — 1959 1959 will be awarded to Dr. Egon Orowan, George Plans are now being completed for the Thirtieth Westinghouse Professor of in Anniversary Meeting of the Society, to be held at the Massachusetts Institute of Technology. The re- Lehigh University on Wednesday, Thursday and Fri- cipient was chosen by a special Bingham Award Com- day, November 4, 5 and 6. A block of rooms has been mittee, consisting of the following members: J. D. reserved for the Society at the Hotel Bethlehem in Dienes (Chairman), T. Alfrey, Jr., H. Leaderman, Bethlehem, Pa., and Society members are strongly A. S. Nowick, and F. D. Dexter. urged to make their room reservations immediately, Dr. Orowan was born in 1902 in , Hungary, if they have not already done so. Bus service will be where he also attended school. He studied at the Uni- available between the Hotel and the Lehigh campus. versity of Vienna for two years, and then transferred A very full program of papers has been scheduled to the Technical University of Berlin-Charlottenburg, by the Program Committee, under the chairmanship of where he obtained an Engineering Diploma and a Doc- J. T. Bergen, as will be seen from the detailed program tor's degree in Applied . which follows. Two special symposia are included. We He then returned to Budapest, and was for a time in are also fortunate to have as a foreign guest Prof. charge of the Krypton Gas Works of the United In- Markus Reiner from Israel, one of the world's dis- candescent Lamp and Electric Company there. tinguished rheologists, who will give an informal talk In 1937, he went to England, and from 1937-39 held at Wednesday's luncheon. Special talks will also be the position of Research Associate in the Physics De- given by John D. Ferry and Melvin Mooney, on Wed- partment of the . During an nesday morning and at Thursday's luncheon, respec- eleven-year period, 1939-50, he was in charge of the tively. Metal Physics Group and was also Reader in the A viscometer exhibit is planned, and there will be Physics of Metals in the Cavendish Laboratory at an opportunity to visit some of the Lehigh laboratories, Cambridge University. including the Fritz Laboratory of Civil Engineering, In September 1950, he moved permanently to the which contains one of the show pieces of the University United States to accept a Professorship at the Massa- —a Universal Testing Machine weighing 5 million chusetts Institute of Technology, following an appoint- pounds, and standing 7 stories tall. ment at M.I.T. in the spring of the same year as Visit- Social activities have also not been neglected. A ing Professor. He was appointed to the George Westing- cocktail party and smoker have been scheduled, as well house Professorship in 1951. as the banquet on Thursday evening, which will feature Professor Orowan's interests have been directed some interesting Pennsylvania Dutch specialties on the toward the general mechanical properties of materials, menu. The ladies' program is given in detail below, and and particularly the underlying physical mechanisms Prof. Raymond R. Myers of the Lehigh Chemistry of deformation and phenomena. He has made Department, Chairman of the Local Arrangements important contributions to this subject from both the Committee, would be interested to know in advance experimental and theoretical aspects, and one of his the number of ladies who will be attending. Attention outstanding contributions was the introduction of the is also drawn to the Lehigh-V.M.I. football game on concept of in metals as a controlling factor Saturday. The Local Committee will attempt to get in their yield and cleavage crack propagation behavior. tickets in advance, if so requested. In 1946, he received the gold medal (Thomas Hawks- ley Award) of the Institution of Mechanical Engineers of London, for his theory of rolling of metals. He has also done important work in interpreting the phenom- Ladies' Program enon of delayed fracture ("static ") in glass, Wednesday Morning, November 4 and in the field of fracture and viscoelasticity of 9:00 Registration begins polymers. 11:00 Guided Bus Tour of Lehigh University He has taken a considerable interest in geological Wednesday Afternoon, November 4 phenomena, as well, and has recently published a 12:30 Luncheon: University Center paper on the mechanism of tectonic earthquakes. In 1:45 Get-acquainted Party: University Center 1958. he was a Visiting Professor in the De- 5:30 Cocktails: Hotel Bethlehem partment at the California Institute of Technology. 7:30 Artistic Program — 1 — or compounded stocks. Typical results for selected elastomers obtained under various operating condi- tions are discussed and compared to data obtained from RHEOLOGY BULLETIN other testing instruments and processing equipment. Inadequacy of single point characterization typical of R. D. Andrews, Jr., Editor widely used tests is emphasized. Results are inter- Plastics Research Laboratory preted with respect to molecular theories of flow for Room 7-006, M.l.T. viscoelastic polymers. Cambridge 39, Mass. The Influence of Viscometer Design on Non-Newtonian Measurements R. MCKENNELL, Ferranti Ltd., Moston, Manchester Thursday Morning, November 5 10, England. 10:00 "Autumn Daze"—a holiday bazaar held in Uncertainty arising from viscometric data obtained the Moravian Christian Education Building from non-Newtonian fluids is minimised by observing (across from Hotel Bethlehem). two principal conditions: the shear rate should be 11:30—2 P.M. Luncheon—cafeteria style (same uniform throughout the measured sample; and a con- location) sistent experimental procedure, including the amount Thursday Afternoon, November 5 and duration of shear, should be adopted. The effect 1:30—3:00 P.M. Old Moravian Area Guided of shear rate variation within the sample fluid is dis- Tour—A glimpse into the life, customs and cussed for some viscometers in common industrial use. architecture of early Bethlehem. An outline is given of the methods available for elim- 7:00 Dinner: Asa Packer Room, University Center inating variations in shear rate, and hence the tedium Friday Morning, November 6 of applying corrections to flow curves for different 9:30 Shopping tour in Hess's—an outstanding types of non-Newtonian behaviour. A viscometer is department store in Allentown. described which combines uniform shearing conditions 11:00 Luncheon and fashion show in the Patio. with a flexible automatic flow curve recorder giving a Friday Afternoon, November 6 wide range of rheological test programs. The recorder Return to Bethlehem enables the duration of shear to be minimised in the (Luncheons, tours and incidental expenses will be higher ranges so that shear-induced heating in the thin borne by the women participants.) layer of fluid is greatly reduced. Comparative data are presented for several rotation viscometers to show this PROGRAM OF MEETING effect.

All technical sessions will be held in the University Flow Down an Inclined Plane Center. Time for presentation of papers: 30 min. RAY D. HOFFMAN and RAYMOND R. MYERS, Wednesday Morning, November 4 Lehigh University, Bethlehem, Pa. 9:00 Registration Begins: West Foyer, 3rd Floor, The flow of Newtonian and shear-thinning liquids University Center down an inclined plane was studied with the objective 10:00 Opening Remarks: Dr. J. H. Dillon, Presi- of estimating the degree of non-Newtonian behavior dent of the Society. Dr. H. A. Neville, Vice- from a simple test. An empirical relation called the President of Lehigh University flow decay curve was obtained, by means of which a 10:15 Technical Session (J. T. Bergen, Chairman) wide variety of materials was characterized by the de- crease in velocity of the advancing front with distance Rheological Measurements on Elastomers of flow. In general the decrease was an exponential with the Brabender Plastograph function of distance, and the magnitude of the ex- C. C. MCCABE, Elastomer Chemicals Department, ponent provided an index of shear thinning, independ- E. /. du Pont de Nemours and Company, Inc., Wil- ent of viscosity. The flow decay curve was compatible with a theoretical equation based on hydrodynamic mington, Del. flow principles. Rheological properties of elastomers are of primary importance during processing and must be maintained 11:45 "Impressions of Rheological Research in within certain limits for successful operation. The need Europe" for new and improved characterization tests is clearly J. D. Ferry, Department of Chemistry, apparent. The shear stress vs. shear rate relationship University of Wisconsin, Madison, Wis. appears most effective in characterizing elastomers. Wednesday Afternoon, November 4 Because wide variations of these parameters exist in 12:30 Luncheon—University Center processing equipment, it is necessary to determine Informal after-luncheon address: Prof. this relationship over a wide range if processability is Markus Reiner, Israel Institute of Technol- to be predicted. ogy, Haifa, "Reminiscences on the Society's The Brabender Plastograph affords a means of First Thirty Years" measuring rheological characteristics as a function of 1:45 Technical Session (Edward Collins, Chair- shear rate and temperature in either uncompounded man) — 3 —

The Rheology of Asphaltf: Stress Optical Properties of Silicones II. Flow Characteristics of Asphalt W. PHILIPPOFF,* Franklin Institute, Philadelphia, Pa. FREDERICK H. GASKINS,* JOHN G. BRODNYAN,** The stress optical properties of silicone solutions WLADIMIR PHILIPPOFF,*** and EDMUND THELEN, have been reported in previous papers. However, the The Franklin Institute Laboratories for Research and extensive description of the experiments including a Development, Philadelphia, Pa. check of the angle x measured in flow birefringence The rheological behavior of ten asphalts has been and with the one determined by the Weissenberg rhe- investigated. The asphalts were selected by members ogoniometer have not yet been given. This is now of The National Asphalt Research Center to be repre- done. Furthermore, the stress optical properties of sentative of industrial stocks. These were investigated silicone rubber, a transparent polymer cross-linked by under conditions of steady-state shear and laminar atomic radiation, was investigated. The stress optical flow. Two instruments were utilized: a coni-cylindrical coefficients C of the silicone solutions in toluene and (rotational) viscometer and a high-pressure capillary of the cross-linked rubbers are very similar. However, tube viscometer. The results of the investigation show there are significant departures that allow us, accord- that asphalts are visco-elastic bodies, which exhibit ing to the existing theory, to calculate the segment both Newtonian and non-Newtonian flow behavior with length of the silicone rubber which amounts to about no evidence of yield value, structural breakdown or 20 units. This lies between the 2.5 units reported for work-hardening. Thus asphalts, deliberately selected Hevea rubber and 45 for polyethylene at high temper- to represent the extremes of conditions of formation, atures. are similar to concentrated polymer solutions and * Present address: Esso Research and Engineering Co., Linden, N. J. molten polymers in their response to stress. The ex- treme variations noted in the rheological behavior of asphalts can generally be accounted for by the param- Flow Properties of Lithium eters—time, temperature and stress. Stearate-Oil Dispersions t Five-year program conducted by the National Asphalt Research Center at The Franklin Institute from 1951 to WALTER H. BAUER, DUANE 0. SHUSTER, and STEPHEN 1956. E. WIBERLEY, Walker Laboratory, Rensselaer Polytech- * Presently at Aeroprojects, Inc., West Chester, Pa. nic Institute, Troy, N. Y. ** Presently at Rohm and Haas Co., Philadelphia, Pa. *** Presently at Esso Research and Engineering Co., Lin- Lithium stearate-oil dispersions, prepared by cool- den, N. J. ing from 205°C to 25°C, showed initial critical yield The Rheology of Asphalt: stresses, initial creep under stress, and sustained flow III. Dynamic Mechanical Properties of Asphalt stresses which were a function of rate of shear and JOHN G. BRODNYAN, FREDERICK H. GASKINS, WLADI- time of flow at a given shear rate. Measurements in MIR PHILIPPOFF, and EDMUND THELEN, The Franklin capillary viscometers and in a cone-plate viscometer Institute Laboratories for Research and Development, showed that the flow curves based on capillary results, Philadelphia, Pa. corrected for entrance effects, gave flow curves, shear The dynamic mechanical properties of ten asphalts, rate versus shear stress, approximating those obtained representing three major categories, have been deter- from cone-plate results after the dispersions had been mined. During the investigation, four instruments were subjected to high rates of shear. Critical yield stress utilized: the FIL dynamic tester, a torsion crystal, a changes and changes in flow characteristics resulting compression tester and a rebound (impact) tester. from shear were not restored in rest during the time Dynamic measurements were made in shear at 10~6 to of the tests. Original properties were restored when 10' cps and at 20 kc using forced sinusoidal vibra- dispersions were reheated to 205 °C and cooled to 25 °C. tions; in addition, compression and impact tests were Residual critical yield stresses after shearing were performed. The results show that asphalts resemble resored rapidly. At any shear rate, d log D/d log r was concentrated polymer solutions and molten polymers greater for the dispersions prepared by cooling without in that they are visco-elastic bodies. This established stirring than for the stirred dispersions, where D is the validity of the time-temperature superposition prin- shear rate and r is shear stress. ciple by (a) demonstrating that the dynamic proper- Additional lithium stearate-oil dispersions were pre- ties for each type of asphalt can be reduced to one of pared with the addition of a third component. Added a family of three curves, and (b) making measure- components were phenyl alpha naphthyl amine, 2,6 di- ments at ultrasonic frequency which correlated with tertiary butyl paracresol, cyclohexanol, glycerol, meta- those obtained in the sonic range. Later results by Van cresol, diphenyl amine, 2 ethyl-hexanoic acid, and der Poel further confirm these facts. Other bitumens, stearic acid. Principal effects of the third components such as coal tar, cracked asphalt and filled asphalt, were changes in the magnitudes and relative magni- follow the same general characteristics. The frequency tudes of the initial critical yield stress and in the crit- or time-scale and the ranges of temperature involved ical creep stress. Dispersions with glycerine exhibited in the experiments are necessarily extremely wide; for a rapidly restored critical yield stress after sustained example, curves representing the shear moduli of as- flow. phalts at 25 °C were produced which covered twenty- Results are discussed in relation to theories of the five logarithmic decades or more. structure of soap-oil dispersions. Rheology and Dental Materials factors involving pressure and temperature, all of the RICHARD H. ROYDHOUSE, Northwestern University reduced data can be plotted on a single master curve. Dental School, Chicago, HI. Concentration Dependence of the Stress Optical The variety of materials and techniques used by Coefficient in Dilute Solutions dentists and the conditions and requirements for suc- W. PHILIPPOFF,* Franklin Institute, Philadelphia, Pa. cessful use make an analysis of properties in a rheo- In previous papers it could be shown that the stress Iogical sense seem essential. A review of dental and optical coefficient C is reasonably independent of con- other literature reveals the paucity of investigations of centration at high concentrations of polymers. How- this nature. Examples of materials and techniques are ever, existing data on measurements in dilute solu- described. A general basis for the rheological descrip- tions of both birefringence and viscosity at the same tion of dental materials is given in phenomenological rate of shear were not available. Measurements on a terms and as the paper is entirely exploratory in 3% solution of polyisobutylene in "white oil" have nature, criticism and suggestions are invited. been reported. These measurements have now been An investigation into the rheology of impression extended to more dilute solutions. Since the "white oil" materials (sodium-calcium alginate systems) and some itself shows flow birefringence, it is therefore very mathematical derivations show the need for revision of suitable for investigating the superposition of the descriptive equations such as those due to Stefan, Peek, properties (viscosity and flow birefringence) of the and Scott for parallel plate plastometers. Some con- solute polyisobutylene on the properties of the solvent. clusions for dental applications can be made from the The evaluation of the results showed that below a cer- results of this investigation. tain stress all concentrations give a constant stress On Anomalies in the Measurement optical coefficient, as long as the x angle does not of the Complex Modulus depart too much from 45°. This is in agreement with S. R. BODNER, Division of Engineering, Brown Univer- the findings of Peterlin and Signer (P-S). However, sity, Providence 12, R. I. when the angle x assumes lower values than 45° a Resonance tests on aluminum and lead specimens systematic departure from this behavior appears. reveal multiple resonance peaks, i.e., resonances in Using the P-S treatment it is shown that the higher addition to the usual natural frequencies of the sys- concentrations show systematic departures from a con- tem, when the specimens are subjected to uniform stant C. If, on the other hand, one follows Sadron's static stress or contain residual stresses. The multiple suggestion and adds tensorially the properties of the resonance peaks can be interpreted in the same man- solvent and solute at constant shear stress, one obtains ner as the resonance dispersions observed by E. R. a constant value for C for the higher concentration Fitzgerald. Experiments have been carried out which and a noticeable levelling off for the lower ones. show that the phenomenon is directly related to the * Present address: Esso Research and Engineering Co., Linden, N. J. presence of either residual or applied static stresses. Related experiments on the variation of the multiple Thermodynamics of Stretching of Nylon Fibers resonance peaks during creep, and on the effect of vi- MALCOLM L. WILLIAMS, Research Center, the Chem- brations of different frequencies on creep rates are strand Corporation, Decatur, Ala. also reported. The application of the thermodynamics of stretching 5:30 Cocktails—Hotel Bethlehem to rubber indicated that the force of extension was 7:30 Smoker—Hotel Bethlehem related to an entropy change. According to the statis- Thursday Morning, November 5 tical theory of rubberlike elasticity, this entropy change was explained in terms of the configuration of a ran- 9:00 Technical Session (F. H. Gaskins, Chairman) dom coil, used as a model for the polymer. In order Dynamic Compressibility of Natural to hypothesize a satisfactory model for a semi-crystal- Rubber-Sulfur as a Function of Pressure, line polymer such as nylon, it is likewise necessary to Temperature, and Frequency know how the force of extension is divided into energy J. E. MCKINNEY, National Bureau of Standards, Wash- and entropy changes. Therefore, stress-temperature ington 25, D.C. data are presented for undrawn, non-spherulitic nylon 66 extended up to 50% at 160°C. That part of the Dynamic compressibility measurements were made extension reversible enough for the application of on 12% vulcanized natural rubber-sulfur, varying the equilibrium thermodynamics is shown to depend pri- static pressure (0-1000 kg/cm2), temperature ( — 30 marily on an entropy change, provided corrections are to 70°C), and frequency (50-1000 cps), using a tech- applied for the effects due to dilation accompanying nique employing piezoelectric volume expander trans- the extension. Nevertheless, the mechanism involved ducers. A structural relaxation was observed whose does not seem to be rubberlike, since use of a random relaxation times varied with temperature in agreement coil model, where the crystallites are assumed to be with the WLF Equation. The glass transition measured merely cross-links, leads to a calculated molecular at 1000 cycles per second (temperature at which a weight between cross-links much too low. The nature maximum in the loss component occurs) was found to of the assumptions involved in the thermodynamic vary linearly with pressure over the above range by treatment will be discussed. .024°C/kg/cm2. With the correct choice of shifting Rupture of Rubber energy of elastic deformation—the rate of shear and L. MULLINS, British Rubber Producers' Research Asso- the amount of deformation in shear; hence, the free ciation, Welwyn Garden City, England energy of a substance is not defined solely by two of The paper describes development of work started the three variables—pressure, temperature and vol- some ten years ago on the application of an energy ume. Two additional variables are required to define criterion to describe the rupture of rubber. It is shown the thermodynamic state of a substance which has that, by the use of an energy balance theory analogous been deformed. This requires that the phase rule be to that proposed by Griffith to explain the fracture of changed to F = C — P + 4, and permits the develop- glass, it is possible to correlate the rupture behaviour ment of a series of partial differential equations in- of rubber samples of widely differing shapes and sizes. volving these five variables. This experimental study provides a stringent test of A perfect viscous fluid is defined as one which has the validity of the energy criterion for the rupture of no elastic component of deformation no matter what rubber and demonstrates the basic significance of the the rate of shear or amount of deformation in shear. value of the rupture energy obtained. Values of this This fluid obeys the phase rule F = C — P + 2 under rupture energy of the order of 106 ergs cm-2, were either static or deforming conditions. obtained. This is considerably in excess of the energy A perfect viscoelastic fluid is defined as one in which required to create new surfaces and indicates that, in the free energy increases with the rate of shear but the rupture of rubber, the irreversible dissipation of for which there exists a condition at each rate of shear energy in highly deformed regions around the rupture such that the free energy does not vary with the path dominate the rupture process. The important role amount of deformation in shear. The phase rule for of these dissipative forces is also demonstrated by a this fluid is F = C — P + 3. Partial differential equa- study of the dependence of rupture energy on rate, tions involving P, V, T and rate of shear are developed temperature and the nature of the rubber polymer. It for this fluid. It is shown that the elastic component of is found that using Ferry's method of reduced variables, the work of deformation must result in a Weissenberg previously applied to viscous and viscoelastic proper- effect. The converse is also true. ties, the rupture energy of all the rubbers examined Any change in molecular orientation caused by de- can similarly be described in a simple unifying way by formation indicates a change in entropy and this two basic curves relating its dependence on rate, and implies a change in free energy and elastic deforma- the interdependence of rate and temperature. tion. These ideas are extended to other conditions of Dynamics of Frictional Compressible Fluids — equilibrium and to a limited extent to the general case. Application to Plastico-Dynamics Thursday Afternoon, November 5 12:30 Luncheon—University Center C. TORRE, Research and Development Laboratory, Informal remarks by Dr. Melvin Mooney M. r. Kellogg Co., Jersey City, N. J. 1:45 Technical Session (H. Markovitz, Chairman) The dynamics of frictional compressible fluids is Symposium on Mechanics of Continua formulated mathematically by eleven equations. There are three equations of motion of a continuum: the Modern Theories of Materials continuity equation, the "specifying" equation and six C. TRUESDELL, University of Indiana, Bloomington, Ind. stress-rate of strain relations. The eleven unknowns Theoretical work on rheological materials shows are: six stresses, three velocities, pressure and density. three distinct phases: The system contains eleven quasi-linear partial dif- 1. Early work, to 1945. Simple models, mainly one- ferential equations. To obtain the real characteristics dimensional and linear, are constructed by analogy to (hyperbolic case) which are different from zero, we discrete systems. Various coefficients are named. have to complete Stokes' stress-rate of strain relations 2. Intermediate period, 1945-1955. Ideal materials by stress and pressure derivatives with respect to time exhibiting non-linear response are defined explicitly as and space (methods of rheology). exact mathematical realizations of a simple idea. Their Assuming a density which is a given scalar function properties are studied by means of general theorems of space and time or a constant density, we shall re- and special exact solutions. late our system of equations to the plastico-dynamics 3. Current phase, from 1955. The most general con- of a solid body. The governing differential equations stitutive equations consistent with the observed phe- are of the Hamilton-Jacobi type, while the charac- nomena are determined. teristic directions are expressed in Hamilton's or Work of the second and third kinds is summarized, canonic differential equations. Results describing the with particular reference to the different roles of motion of plastic mass have been obtained. methods of invariance. Open problems are stated. A Thermodynamic Approach to Rheology HARRY H. HULL, R. R. Donnelley and Sons Co., Chi- Stress Analysis for Viscoelastic Bodies cago, III. Subject to Temperature Variation The elastic component of the work of deformation L. W. MORLANI) and E. H. LF.E, Division of Applied is equal to that portion of the work which has not been Mathematics, Brown University, Providence, R. I. converted into heat. This is an available or thermo- The temperature-frequency shift concept is used to dynamic free energy. Two variables control this free formulate the stress-strain-time-temperature relation — 6 —

for a linear viscoelastic body with varying temperature. to simple fluids and general isotropic materials to illus- This is combined with the strain compatibility rela- trate the physical significance of these results. Stabil- tions, the equilibrium equations, and the boundary ity questions and the relationship of the present work conditions to formulate the mathematical system for to Gibb's thermostatics of fluids are also discussed. determining stress distributions. Use of a pseudo-time 5:00 Business Meeting based on the temperature-time shift concept is tried in 7:00 Dinner — Asa Packer Room, University order to simplify the constitutive equations, but it leads Center to serious complications in the equilibrium equation 8:00 Presentation of Bingham Medal, by Dr. C. and in the expressions for strain components. Exam- Richard Soderberg, former Dean of Engi- ples are shown of stress analysis with a non-homog- neering and Institute Professor, M.I.T. eneous temperature field, and the marked influence of Medalist's Address, by Dr. Egon Orowan the temperature variation on the stress distribution is Friday Morning, November 6 demonstrated. 9:00 Technical Session (E. H. Lee, Chairman)

Hypo-elasticity and Elasticity Rheological Properties of Molecules in Fibers BARRY BERNSTEIN, U.S. Naval Research Laboratory, FRANCIS H. REE, SEIHUN CHANG, TAIKYUE REE and Washington, D.C. HENRY EYRING, Department of Chemistry, University The equations of hypo-elasticity are not in general of Utah, Salt Lake City, Utah sufficient to define a material. It is necessary in addi- Using an extensometer, the stress-relaxation curves tion to indicate one stress-strain configuration. Con- and the elongation-contraction curves for nylon 66, ditions may be written which test whether any or all nylon 6 and dacron were obtained. We found the fol- materials satisfying a given set of hypo-elastic equa- lowing experimental facts: (1) The simple Eyring- tions are elastic in the sense of Cauchy or in the sense Halsey three-element model (Text. Res. J. 15, 451 of Green. If the hypo-elastic material is a work hard- (1945)) holds only over the range of relatively small ening material, it must be elastic in the sense of Green. stresses and strains. (2) The elongation-contraction curves for all samples are similar in form. (3) An Theory of Anisotropic Fluids elongation curve has an inflection point at a definite J. L. ERICKSEN, Johns Hopkins University, Baltimore, point of stress and strain. (4) All elongation curves M aryland of a sample, which were obtained by pulling at a con- stant rate after letting the fiber relax for a given time, Almost no research has been done on properly in- variant theories of anisotropic fluids. Preliminary At, between successive elongation-contraction experi- researches on anisotropic viscoinelastic fluids have ments, pass through the inflection point. Above the in- suggested that simpler theories of this type are better flection point, the smaller the value of At, the steeper able to describe some observations on high polymer the slope of the elongation curve, while the reverse is solutions than comparably simple theories of isotropic true below the inflection point. (5) The inflection point fluids. Such theories seem not to be included as special is a function of the structure of the sample, the rate of cases of very general theories of fluids which now elongation, and the ambient temperature. exist. After briefly clarifying these points, we discuss From the above experimental facts, it is concluded the formulation and some predictions of a rather that below the inflection point thixotropic breakdown simple theory of transversely isotropic viscoelastic of structure occurs while above the inflection point fluids. hydrogen bond formation is accompanied by the usual flow mechanism. The relaxation curves obtained under various condi- On the Concepts of Equilibrium in Continua, tions give interesting information concerning the struc- Part I ture of fibers and rheological properties of high poly- BERNARD D. COLEMAN, Mellon Institute, and WALTER meric molecules. The experimental results and detailed NOLL, Carnegie Institute of Technology, Pittsburgh, Pa. discussion will be given in the paper. This paper deals with bodies B which are regarded as smooth manifolds of material points. We attempt The Significance of Rheology in the to develop a rigorous theory of thermostatics for such Making and Using of Paper bodies in arbitrary states of finite strain. The concepts ALFRED H. NISSAN, H. G. HIGGINS and A. LAGANI, JR., of mechanical and thermal equilibrium are given pre- Dept. of Chemical Engineering, Rensselaer Polytechnic cise definitions. Two physical postulates are assumed Institute, Troy, N. Y. which imply restrictions on the constitutive equations A brief review of paper making indicates that rhe- of thermostatics. ology is an important factor at many points. The most significant are (1) rheology of fiber suspensions; (2) On the Concepts of Equilibrium in Continua, rheology of wet webs of fibers with 1:4 to 1:2 solid Part II to water ratios and (3) rheology of air-dry paper in BERNARD D. COLEMAN, Mellon Institute, and WALTER use. The first two subjects are briefly reviewed. NOLL, Carnegie Institute of Technology. Attempts at fitting mechanical models of springs The results presented in Part I are here specialized and dashpots to represent paper behaviour are sum- — 7 —

marised and reasons for their rejection advanced. In- In addition to the conventional rheological approach, stead, interpretations based on molecular and thermo- measurements were made of the electrical conductiv- dynamic parameters are advanced as a basis for a ities and dielectric constants in quiescent dispersions theory of the rheological behaviour of hydrogen-bonded as well as in dispersions deflocculated by shear or by solids. Predictions of the theory appear to be con- chemical means. firmed not only by paper but also by ice, cellulose A detailed picture of the structural involvement sheets, nylon and other hydrogen-bonded materials. could be derived from conductivity data, such as the Attempts are made to explain by means of this theory minimum in the conductivity-shear rate relation, the the influences of water, chemical substitution, time and induction period and the rate of rebuilding of destroyed other factors on the rheological constants of paper. structures as well as the magnitudes of minimum and The essential contribution of the theory is that it re- maximum conductivities. These conclusions are sup- lates these behaviours to an important parameter, n, ported by dielectric data and can be explained from the number of hydrogen-bonds per unit volume of mate- the standpoint of potential energy curves representing rial. Thus, changes in rheological behaviour reflect particle interaction. changes in n; these changes can be treated by methods Rheological data, however, do not allow straight- of chemical kinetics. forward conclusions about the structure. Yield values, derived either from a rheological diagram, obtained A Re-Interpretation of the Rouse-Bueche with the aid of a high-shear rotational viscometer, or Theory of Viscoelastic Behavior* by means of a parallel plate viscometer fail to show a R. S. MARVIN, National Bureau of Standards, correlation with actual structures. Oil adsorption data, Washington 25, D.C. when obtained under carefully controlled conditions, The Rouse and Bueche theories of the viscoelastic show a limited correlation with structure. A somewhat response of a rubberlike polymer were derived con- better correlation was found to exist for the specific sidering the response of a single polymer molecule to plastic viscosity. force, displacement, or velocity fields resulting from macroscopic forces or deformations applied to a bulk sample. From this point of view, Ferry and Bueche The Behaviour of Particles in Laminar Shear have derived expressions for the response of a bulk sample containing a distribution of molecular weights, S. G. MASON, Physical Chemistry Division, Pulp & finding the equilibrium compliance proportional to Paper Research Institute of Canada, Montreal and MZMHI/M». Department of Chemistry, McGill University, Montreal, An alternative point of view for the derivation is pre- Canada sented here, in which the form of the function can be Particles suspended in a liquid subjected to a veloc- shown to be equivalent to the empirical Voigt or Max- ity gradient undergo rotational and translational move- well representations. From this point of view the ex- ments and, when they are deformable, changes in pressions of these theories (or the equivalent model) shape. The general behaviour of solid spheres, fluid correspond to the response of the bulk sample rather drops, rigid and flexible rods and fibres will be de- than that of a single chain. scribed with the aid of cine photomicrographs. The constants are calculated from the equilibrium The relevance of these phenomena to theories of kinetic theory, the resistance per unit length of the viscosity of dilute suspensions will be discussed. particular polymer, the critical molecular weight where the dependence of viscosity on molecular weight under- goes an abrupt change in form, and the molecular Heat Transfer to Non-Newtonian Fluids weight of the sample. They are calculated entirely Under Laminar Flow Conditions from measurements of molecular weights and steady- A. B. METZNER and D. F. GLUCK*, University of Dela- flow viscosities, and represent very well the response ware, Newark, Del. over the whole time scale of interest. Also the effect of Rates of heat transfer to non-Newtonian fluid sys- entanglements is introduced in a more direct fashion tems passing through smooth round tubes under than in previous work. laminar flow conditions have been studied both experi- Results for steady-state dynamic response are pre- mentally and theoretically, for the case in which vis- sented, and the problem of the calculation of transient cous heat generation may be neglected. The data of response (creep and stress relaxation) discussed. three independent investigators have been correlated * Supported in part by the Office of Naval Research. with an average deviation of 12%. The final equation contains the conventional Grashof number type of Rheology in Search of Structures, Part II correction to account (empirically) for natural con- ANDRIES VOET and WM. N. WHITTEN, JR., J. M. Ruber vection effects. It was interesting to note that up to Corporation, Borger, Texas 30% of the total heat was transferred by natural con- An investigation was made of the structures in dis- vection even in systems which were highly non-New- persions of carbon blacks in white mineral oil. A selec- tonian, hence viscous, in nature. tion of twelve blacks was made, representative of the * Present address: National Aeronautics and Space Admin- commercially available types. istration, Cleveland, Ohio. — 8 —

Friday Afternoon, November 6 Experiments on Peeling 12:30 Luncheon—University Center J. J. BIKERMAN, Dept. of Civil and Sanitary Engineer- 1:45 Technical Session (R. R. Myers, Chairman) ing, Massachusetts Institute of Technology, Cambridge Symposium on Adhesion 39, Mass. The force Wo required to peel an aluminum or nickel ribbon glued to a rigid glass plate with a polyethylene or a poly (vinyl acetate) was determined and com- pared with the theory (partly new). The experimental force was smaller than the calculated (often in a ratio Mechanism of Peeling between 2 and 5), and the difference was due to two YUKIHIKO INOUE and YONOSUKE KOBATAKE, Tokyo distinct stress concentrations. For highly extensible Institute of Technology, Ookayama, Meguro, Tokyo, adhesives, their elongation in the pull direction was Japan associated with Poisson's contraction in a direction Taking into consideration both the pulling and normal to the pull; the stress distribution caused by bending actions of the external force, the differential this lateral contraction made Wo a linear function of equations for bending of a partly attached tape in a ribbon width w instead of being proportional to w. peeling test have been derived. The equations relating For near-Hookean adhesives of a low total elongation, the peeling load to the adhesive force were derived Wo was found proportional to w; the stress concentra- under the assumption that the peeling may proceed tion dangerous for these materials occurred at the step by step from the attached end when the adhesive boundary between the adhesive and the ribbon at the force is overcome by either the tensile stress along the sharp bend of the latter. The postulated damage to interface (shearing peeling) or that which is perpen- brittle adhesives caused by the ribbon deformation dicular to the interface (tensile peeling). To verify the could be reproduced without bending, namely by validity of the equations obtained, the dependence of stretching the ribbon beyond its yield stress. the peeling load, P, on the angle, a, between the direc- tion of the action of the load and the adhering surface The Peeling Force of Adhesive Joints has been investigated using plasticized polymer films. FRANKLIN S. C. CHANG, Mystik Adhesive Products, Furthermore, the temperature dependence of the peel- Inc., Northfield, III. ing resistance of adhesive tapes stuck onto a glass During the peeling of adhesive joints the strained surface has been studied. In the case of a stiff adhesive region is bounded by either one curve and one straight having a glass transition temperature higher than room line or two curves. The latter case has been discussed temperature, the plots of the peeling load against temp- in a previous paper. In the former case, applying to erature show a curve with a maximum, notwithstand- the bent adherend the theory of beams on elastic foun- ing that adhesion should decrease with temperature. dations, after modification to allow for large bending On the contrary, in the case of a pressure sensitive angle, it can be readily shown that the vertical dis- tape, the peeling resistance lessens with temperature. placement y of the adherend is y = aL2 — a3L4/3,

From these results, the mechanism of peeling is dis- where a = (3Ei/4Ey<>53) Ei, E, y0 and 8 being the cussed in connection with the physical and rheological Young's Moduli and the thicknesses of the adhesive properties of the adhesive tapes. film and the adherend, respectively, and L the length of adherend. The peeling force, generally known as adhesion strength, is numerically equal to the sum of resistance to peeling offered by individual strings, of Theory and Analysis of Peel Adhesion: which the maximum value allowed is limited by the Bond Stresses and Distributions adhesion between the adhesive and the adherend. When a 3-element model, consisting of an elastic D. H. KAELBLE, Minnesota Mining and Manufacturing spring Ei in series with a parallel combination of a Co., St. Paul, Minn. second Hookean spring E2 and a dashpot v, is used to Previous theory is extended to provide expressions, represent the mechanical behavior of the adhesive, the general with respect to stripping angle, for the bound- peeling force is calculated as ary stresses and bond stress distributions. The treat- ment is developed in terms of two stress mechanisms. WaE 2Elfl F =- ^[foL3+ 3 Boundary cleavage involves tension-compression stress (EI + E2)b and predominates at high angles of peel. At some low b2L2 b3L3 range of peel angles, predicted from theory, boundary 1 - bL + -exp(-bL)}] shear provides the controlling mechanism. Measure- ment of peel force as a function of angle of peel and where b = (Ei -f E2)/w, v being the peeling speed, rate identify the transition in failure mechanism from W the width of the joint, and f» and fi functions of L cleavage to boundary shear and provide comparison showing the geometry of the strained region. The first data for theoretical force-angle functions. The results term of the expression gives the peeling force at very of direct measurement of the internal cleavage stresses, high peeling speed where the adhesive acts like a by means of a new experimental device termed the Hookean solid. The rest of the expression is the correc- "split-beam transducer", further characterize this bond tion terms for the peeling speed used. The application failure mechanism. of this force equation to actual cases is discussed. — 9 —

The Tensile Strength and Tacky Behavior Effect of Viscosity on the Penetration of of Polymeric Liquids Adhesives into Paper

ROBERT A. ERB, The Franklin Institute Laboratories, Miss R. M. KARAPETOFF COBB, Lowe Paper Co., Ridge- Philadelphia, Pa., and ROBERT S. HANSON, Drexel field, N. J. Institute of Technology, Philadelphia, Pa. (To be read in summary by R. R. Myers) End of Symposium The tensile strength of liquids appears to have con- siderable importance in describing tacky behavior in Fluid Mixing in Agitated Vessels unfilled systems. An apparatus is described whose A. B. METZNER, K. W. NORWOOD* and J. S. TAYLOR**, operation involves the rapid separation of flat plates University of Delaware, Newark, Del. between which the liquid is contained, the bottom plate Fluid motion in an agitated tank has been studied by being a block of known mass whose vertical motion following the motion of tracer particles, in both New- is followed by a high speed motion picture camera tonian and non-Newtonian fluid systems. Measured (4000 frames per second), permitting measurement velocity distributions were differentiated to obtain local of the instantaneous forces operating across the liquid shear rates and local rates of power dissipation. coupled with a simultaneous recording of the events The above analysis indicated that the contents of an occurring during the plate separation. Five high molec- agitated vessel may be considered as consisting of two ular weight liquids, with viscosities in the Newtonian portions: a small region near the impeller which is flow range of from 60 poises to 1.2 x 106 poises, were nearly "perfectly-mixed", and a surrounding region in studied. Photographic sequences showing seven differ- which the rates of turbulent mixing are nearly zero. ent types of tacky behavior are shown; viscous and The equation describing mixing rates which was based elastic deformations, cohesive and adhesive breaks, on this model has been experimentally verified in New- and single and multiple filament formation (the latter tonian fluids. While no experimental verification has with cavitation) are distinguishable in the various as yet been obtained in non-Newtonian systems, the modes of failure. Stress analyses of the several types tracer-particle work indicates that in this case the of film failure reveal liquid tensile strengths in the model would be obeyed even more closely than in New- range from about ten to several hundred bars. tonian fluids.

* Present address: General Electric Company, Hanford, Wash. ** Present address: Continental-Diamond Fibre Division, The Budd Company, Newark, Del.