Abstracts from IUTAM Istanbul

Fiber Suspension Flow in a Converging Channel

Cyrus K. Aidun Georgia Institute of Technology

Mehran Parsheh Univ. of Minnesota

Full text: Not available Last modified: February 28, 2007 Presentation date: 06/12/2007 9:50 AM in ITU Macka Conference Room (View Schedule)

Abstract We have investigated the competing influence of extensional strain and turbulence on the development of the orientation distribution of a dilute density matched suspension of stiff fibers in a planar contraction. Application of a Fokker-Planck type equation is shown to accurately model the development of orientation anisotropy. Nearly isotropic homogenous turbulence with uniform mean velocity profile is introduced at the contraction inlet. Measurement of the downstream fiber orientation distribution shows that the rotational diffusion coefficient decays exponentially with local contraction ratio, C, and is dependent on inlet turbulent characteristics. However, the effect of turbulent energy production in the contraction is observed to be negligible. This is attributed to large streamwise rate of strain at C > 2, which offsets the effect of turbulence, and small production of turbulent energy at C < 2 where turbulence closely follows the decay of grid generated turbulence in a rectangular channel. The development of the orientation distribution function implies a rather weak dependence on the channel Reynolds number. Furthermore, the results show that the influence of turbulence on fiber rotation is negligible when the rotational Peclet number, , which is a measure of the relative influence of the mean gradient component and the rotational diffusion, is less than 10.

I will also discuss the new methods developed in my group for direct numerical simulation of deformable fibers and particles in shear flow.

Point-particle simulations of shear-induced self-diffusion in a wall-bounded dilute suspension

Evgeny S. Asmolov Central Aero-Hydrodynamic Institute, Moscow

Full text: Not available Last modified: March 12, 2007 Presentation date: 06/14/2007 11:10 AM in ITU Macka Conference Room (View Schedule)

Abstract Non-Brownian particles migrate randomly across the streamlines of a carrier flow in sheared suspensions at small Reynolds numbers (Eckstein et al. 1977). A random motion is due to particle hydrodynamic interactions and is characterized by the coefficient of shear-induced self-diffusion which is linear in particle volume fraction in a dilute suspension. The phenomenon was explained by irreversibilities of the two-particle interactions of rough spheres (Da Cunha & Hinch 1996), or by the asymmetry of three-particle interactions (Wang et al. 1996). However, the theories do not predict satisfactorily shear-induced diffusive behavior in the dilute limit. The three-particle mechanism requires the diffusivity to be proportional to volume fraction square. The rough-sphere model gives correct linear dependence, but the values of the diffusivity is an order of magnitude less than the experimental ones (Zarraga & Leighton 2002).

In the present work the mechanism of the self-diffusion is studied due to far-field collective hydrodynamic interactions in a wall-bounded Couette cell. The motion of identical particles distributed randomly in a 3D rectangular cell is simulated. Large-scale density fluctuations induce fluid velocity disturbances with the lengthscale compared to the separation between the walls. The flow disturbances are due to particles freely rotating in a shear flow which can be approximated at large distances by symmetric force dipoles. The boundary conditions are the no-slip conditions on the cell walls, and the periodic boundary conditions in the directions of the undisturbed velocity and vorticity. The particle velocities in a dilute suspension are assumed to be the sum of the undisturbed velocity and the large-scale disturbances. The numerical approach neglecting short-range interactions appears suitable for large dilute systems. The similar model has been used recently (Asmolov 2007) for sedimenting particles when the large-scale fluid flow is due to point forces.

The mean-square displacement curves are quadratic in time initially and show the linear behavior corresponding to the diffusive regime after a time of order unity. The self-diffusivity is determined as the time rate of the change of half the displacements. It is evaluated as a function of initial particle position. The calculated diffusivity is linear in the shear rate and volume fraction. The diffusivity is less for particles close to the walls as the large-scale disturbances are zero on the walls. The theoretical value for particles in the median slice is close to the experimental one (Zarraga & Leighton 2002).

Hydrodynamic interaction of two capsules in simple shear flow

Dominique Barthes-Biesel Universite de Technologie de Compiegne

Etienne Lac Schlumberger Cambridge Research

Abstract We present a numerical model of the hydrodynamic interactions between two identical capsules freely suspended in a simple shear flow (SSF). Each capsule consists of a liquid droplet enclosed by a thin hyper-elastic membrane. The particle Reynolds number is small and a boundary integral formulation is used to represent the fluid motion of the internal and suspending liquids. The particle motion and deformation result from the interaction of viscous deforming stresses balanced by elastic tensions in the membrane. The latter may undergo large shape changes, thus making the problem non-linear. Monitoring the stress level in the membrane is important to predict burst. Two capsules suspended in SSF usually have different velocities and thus eventually overlap and pass each other. The flow is such that the capsules are not subjected to stress levels leading to burst when they are far apart. However, during crossing, the membranes are submitted to extra strains and stresses that may lead to unexpected break-up. Pair interactions also cause an irreversible cross-flow trajectory shift, indicating a self-diffusion effect in dilute suspensions of capsules.

An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid

Arie Biesheuvel University of Twente

*Christian Veldhuis University of Twente

Full text: Not available Last modified: January 5, 2007 Presentation date: 06/14/2007 12:10 PM in ITU Macka Conference Room (View Schedule)

Abstract This paper presents the results of an experimental investigation aimed at verifying some of the interesting conclusions of the numerical study by Jenny, Dušek & Bouchet (J. Fluid Mech. 508 (2004), 201) concerning the instability and the transition of the motion of solid spheres falling or ascending freely in a Newtonian fluid. The phenomenon is governed by two dimensionless parameters: the Galileo number G, and the ratio of the density of the spheres to that of the surrounding fluid rho_s/rho. Jenny et al. showed that the (G, rho_s/rho) parameter space may be divided into regions with distinct features of the trajectories followed eventually by the spheres after their release from rest. The characteristics of these `regimes of motion' as described by Jenny et al. agree well with what was observed in our experiments. However, flow visualizations of the wakes of the spheres using a Schlieren optics technique, raise doubts about another conclusion of Jenny et al., namely the absence of a bifid wake structure.

Shear Rheology and Aging of Soft Particle Pastes

Roger T. Bonnecaze The University of Texas at Austin

Jyoti Seth The University of Texas at Austin

Michel Cloitre ESPCI, Paris

Abstract Soft particle pastes (SPPs) are composed of deformable particles randomly packed into a dense suspension. Examples of the constituent m), polyelectrolytesoft particles include polymer coated colloids (R~100 microgels (R~200 nm) and star polymers (R~10 nm). In spite of the differences in the particle sizes and source of elasticity, all of these materials show similar rheological characteristics and aging behavior. That is, their microstructure and rheological properties change slowly with time without apparent end.

Here we present a numerical simulation of these SPPs to understand the fundamental nature of the observed bulk rheology and aging. The methodology is founded on a Stokesian-dynamics like simulation of the centers of the particles coupled with an additional dynamical equation of the elasto- hydrodynamic contacts between particles. An approximate method is presented for computing the EHD contacts that is accurate and extremely efficient for the simulation of tens of thousands of particles. Predictions of the viscosity and normal stress differences for sheared SPPs of varying concentrations are presented for a variety of packing fractions for mono- and polydisperse soft spheres. The predicted shear viscosity closely matches experimental observations. Further, the normal stress differences observed in the simulation can be used to explain the instabilities observed in coating operations of SPPs.

A pairwise interaction theory is also developed that compares well to the numerical and experimental measurements. As part of this theory we present a methodology to compute a priori the radial distribution function for the quiescent or “equilibrium” glassy SPPs based on free volume considerations and energetic constraints.

Finally, the simulation is used to probe the aging of an initially sheared suspension. It is found that the recovery of the particles after cessation of the flow follows a ballistic path with a power law distribution of recovery times. This observation is seen experimentally in diffuse-wave spectroscopy measurements. The microstructural recovery process is qualitatively related to the aging of the macroscopic properties.

Simulation of Suspensions and Granular Media: Wet vs. Dry

John Brady California Institute of Technology

Abstract Computer simulation of multiphase flows has grown dramatically in the last two decades. Problems as diverse as the Brownian motion of small colloidal particles, the rheology of dense suspensions and emulsions, and the dynamics of bubbly liquids have been addresses by dynamic simulation. This talk will trace the development of the methodologies used to simulate multiphase, particulate systems. A central feature in these systems is properly accounting for the hydrodynamic interactions among particles. Hydrodynamic forces are non-conservative, non-central, couple translational and rotational motion, have distinctive far- and near-field behaviors and are many-body. The incorporation of hydrodynamic interactions has been accomplished rigorously and successfully in the case of small particle Reynolds numbers and in the limit of inviscid flow at high Reynolds numbers. Examples showing how hydrodynamic forces influence suspension structure and determine macroscopic behavior will be given. Of particular interest will be recent work aimed at exploring the similarities and differences between the behavior of low-Reynolds number viscous suspensions and rapid granular flows at high Reynolds numbers: wet vs. dry.

Rheology and structure of concentrated suspensions of non-colloidal particles subject to oscillatory shear Jason Butler University of Florida

*Jonathan Bricker University of Florida

Abstract Non-colloidal suspensions undergoing unsteady shear flows demonstrate unique behaviors not observed under steady flow conditions. To understand the dynamics of suspensions in unsteady shear flow, the rheological behavior under oscillatory flow was examined using experiments and simulations.

Experiments were performed to evaluate the complex viscosity as a function of the total strain. The complex viscosity decreases with total strain for high strain amplitudes and increases for low strain amplitudes. The total strain necessary to attain steady conditions greatly increases as the amplitude decreases and the minimum in the complex viscosity occurs at a strain amplitude of one. The results were independent of the shear cell geometry, suggesting that shear-induced particle migration is unimportant and that the observed behavior results from changes in the suspension microstructure.

Simulations of the oscillating suspensions predict the changes in rheology that occur over large total strains and reproduce a non-monotonic relationship between strain amplitude and the steady value of the complex viscosity. As in the experiments, the minimum in complex viscosity occurs at the strain amplitude of one. The simulations provide insight into the underlying microstructure that generates the macroscopic rheology observed in the experiments. Three distinct phases were identified, with hydroclusters dominating the large amplitude results and ordered microstructures appearing at intermediate and low strain amplitudes.

Shock-bubble interaction near a rigid surface

Michael L. Calvisi School of Mathematics, The University of Birmingham

*Jonathan I. Iloreta Department of Mechanical Engineering, University of California at Berkeley

*John R. Blake School of Mathematics, The University of Birmingham

*Andrew J. Szeri Department of Mechanical Engineering, University of California at Berkeley Full text: Not available Last modified: February 23, 2007 Presentation date: 06/13/2007 10:50 AM in ITU Macka Conference Room (View Schedule)

Abstract In this talk, we present the results of numerical simulations of the nonspherical collapse of bubbles excited by shock waves near a rigid boundary. The waves we consider are representative of those developed by shock wave lithotripsy or shock wave therapy devices. The rigid boundaries we consider are representative of kidney stones and reflective bony tissue. The presence of the boundary causes constructive interference between reflected and incident waves that enhances the expansion and subsequent collapse of bubbles located in a region near the boundary. Quantities such as kinetic energy, Kelvin impulse, and centroid translation are calculated in order to illuminate the physics of the collapse. The main finding is that the dynamics of the bubble collapse depend strongly on the distance of the bubble relative to the wall when reflection is taken into account but much less so when reflection is omitted. The work done by the shock wave on the bubble is shown to predict strongly the maximum bubble volume regardless of the standoff distance and the presence or absence of reflection; furthermore, with appropriate interpretation, these predictions match almost exactly those of a spherical bubble model.

The Role of Particle Shape on Particle-Phase Stress

Jennifer Sinclair Curtis ChE Dept., University of Florida

Benjamin James ChE Dept., University of Florida

Full text: Not available Last modified: March 1, 2007 Presentation date: 06/11/2007 5:00 PM in ITU Macka Conference Room (View Schedule)

Abstract Virtually all solid handling operations involve particles that are non-spherical in shape. However, most fundamental studies of particulates undertaken to date have involved spherical particles. Hence, there is a current significant disconnect between the model particles which are used in fundamental research studies and the characteristics of real particles dealt with in industry. While industrial practitioners comprehend fully that the influence of particle shape on particle flow behavior is significant, the role of particle shape is not understood.

This presentation will discuss the results of DEM simulations of non-spherical particles in planar shear flow. Particles with large aspect ratios and rough particles are simulated. A few of the key conclusions are: • Increases in the particle elongation ratio decreases the kinetic contribution to the particle-phase stress and significantly increases the collisional contribution to the particle-phase stress • There exists a finite maximum collisional stress at a specific degree of particle roughness • Increasing the particle friction and decreasing the particle elasticity increases the collisional stress for elongated particles due to an increase in low velocity collisions

In addition, we show a relationship between the kinetic stress and the projected particle length which is valid for all particle shapes. This relationship forms the basis for a constitutive model for particle- phase stress that can be employed in two-fluid CFD simulations. Direct Numerical Simulation of Emulsion Flow Through Porous Media

Robert H. Davis University of Colorado

Alexander Zinchenko Department of Chemical & Biological Engineering, University of Colorado

Abstract The flow of an emulsion containing drops or bubbles through a porous medium has practical applications in biology, engineering and geology. Of fundamental importance are the relationships between pressure drop and flow rates of the dispersed and continuous phases, and the conditions where the drops or bubbles become trapped within the porous medium. These issues are particularly challenging when the drops or bubbles have sizes close to or larger than the pores, in which case an effective-medium approach fails.

This talk presents direct numerical simulations of emulsion flows through granular media at low Reynolds number, using boundary-integral methods. A model problem is considered first, where a single drop squeezes between two or more solid obstacles. It is shown that the drop becomes trapped when the capillary number (representing the ratio of viscous and interfacial forces) is below a critical value and the drop is not able to deform sufficiently to pass through the constriction. Subsequently, an efficient, multipole-accelerated algorithm was used for dynamical simulations of many nonwetting deformable drops squeezing through a granular medium comprised of randomly distributed fixed spheres in a periodic box. Simulations are made with typically 50-100 drops and 50-100 particles in a periodic box. A large number of typically 5000 or more boundary elements per surface is needed, because of the lubrication sensitivity of drop-solid interactions. Surprisingly, away from the critical condition, the dispersed phase has higher average velocity than the continuous phase. This result is due to steric exclusion of the drops from the slow-moving streamlines near the solid surfaces. Near the critical condition, however, the average velocity of the dispersed phase is reduced as the drops become trapped (or nearly so) in the narrow spaces between the particles comprising the granular medium.

Cylindrical Bubble Dynamics : Exact and DNS Results

Can F Delale Istanbul Technical University

Gretar Tryggvason Worcester Polytechnic Institute

Selman Nas Istanbul Technical University

Full text: Not available Last modified: February 22, 2007 Presentation date: 06/13/2007 11:50 AM in ITU Macka Conference Room (View Schedule) Abstract The axially symmetric collapse and growth of a cylindrical bubble is considered. In this case a universal law of cylindrical bubble dynamics is obtained when the pressure at the boundary and that inside the bubble satisfy a certain relation. Both vapor bubbles with constant pressure inside and gas bubbles obeying the isothermal law are considered. Moreover, for gas bubbles, the energy equation within the bubble and in the surrounding liquid is considered for the effect of heat conduction through the bubble wall, and an exact particular solution, leading to explicit gas pressure and gas temperature expressions, is obtained. Finally, the results are compared with the DNS results obtained by the front tracking/finite difference method. Good agreement has been achieved.

Two-Dimensional Bubble and Droplet Motion in a Yield-Stress Fluid

Morton Denn City College of New York

*John Singh City College of New York

Full text: Not available Last modified: February 23, 2007 Presentation date: 06/12/2007 3:40 PM in ITU Macka Conference Room (View Schedule)

Abstract Two-Dimensional Bubble and Droplet Motion in a Yield-Stress Fluid John P. Singh and Morton M. Denn CREST Center for Mesoscopic Modeling and Simulation, Benjamin Levich Institute for Physico-Chemical Hydrodynamics, and Department of Chemical Engineering City College of New York, CUNY New York, NY 10031 USA

ABSTRACT Many liquid-like materials exhibit a yield stress. These materials flow above a critical stress, but they deform as linearly elastic bodies below this stress. Yield-stress materials, which are often colloidal suspensions, are commonly experienced in consumer products applications, foodstuffs, etc. The waste sludge tanks at the U.S Department of Energy's Hanford site contain radioactive colloidal suspensions that exhibit a yield stress; the motion of flammable bubbles in these materials is a matter of particular concern. The solution of complex flow problems for yield-stress materials is challenging because of the possible existence of yielded regions in which flow can occur and unyielded regions in which only elastic deformation is possible. The interface between these regions is not known a priori. Constraints imposed by the requirements of stress and velocity continuity at the yield surface are discussed by Lipscomb and Denn [1]. The usual computational approach is to employ a continuously differentiable viscosity function that approaches the discontinuous yield-stress fluid in the limit as a regularization parameter becomes infinite. The regularization approach is discussed in detail by Frigaard and Nouar [2]. The relative motion of solid objects in yield-stress fluids has been studied by many authors, mostly for the Bingham fluid [3,4], in which the stress in excess of the yield stress is linear in the deformation rate. The first accurate solutions for creeping flow of a single sphere in a Bingham fluid were carried out using a regularization method by Beris and coworkers [5]. Convergence of the yield surfaces with respect to the regularization parameter was studied by Liu and coworkers [6, 7] for a single solid sphere and for two identical solid spheres moving along their line of center, respectively. The drag coefficient can be bounded using variational methods and is relatively insensitive to the convergence of the regularization method. Most experiments (e.g., [8]) are not directly comparable to the detailed theoretical calculations because the fluids deviate from Bingham behavior. There are citations to theoretical and experimental studies in papers by Dubash and Frigaard [9] and Tabuteau et al. [10]. The motion of bubbles and drops in yield-stress fluids has received less attention than the motion of solid spheres. Li and Renardy [11] used a volume-of-fluid scheme to study the breakup of a Newtonian drop in a Bingham fluid under conditions where the matrix fluid had yielded everywhere. Dubash and Frigaard [9] used a variational approach to establish the conditions under which bubbles will not rise in a Bingham fluid. Potapov and coworkers [12] studied the detailed motion of single liquid drops and pairs of drops in a Bingham fluid using the FLUENT 6.1 volume-of-fluid code with a bi- linear viscosity function. Both of the latter sets of authors cite prior work that is less relevant to our discussion. We have implemented a finite-element code for a two-phase system consisting of one or more incompressible two-dimensional (i.e., cylindrical) Newtonian bubbles or drops moving in a continuous Bingham fluid. The code employs level-set methods [13, 14] to track the deformable interfaces. The motion is characterized by a Bingham number, defined as , where τy is the yield stress, L is the length scale, ηp is the slope of the linear portion of the flow curve (sometimes misleadingly called the plastic viscosity), and U is the velocity of a single bubble or drop or the initial velocity of the center of mass of an interacting pair. The length scale for a single bubble or drop is the radius, and for interacting pairs it is the initial spacing between the centers. The interfacial effects are characterized by a capillary number, defined as , where σ is the interfacial tension. Converged solutions were obtained for the slow gravitational rising (settling) of single Newtonian fluid bubbles (droplets) through a Bingham fluid in a large closed container. A typical result is shown in Fig. 1 for a rising bubble in which the ratio of inner to outer fluid density is 0.01, the density difference is 0.99, the ratio of inner fluid viscosity to ηp is 0.01, Bn = 1.28, and Ca = 7.8. The unyielded regions are shown in gray and the yielded regions in white. Bold lines define the yield surfaces. The container boundaries are beyond the outer yield surface, and the flow is independent of the container length scale. In addition, there are unyielded “ears” adjacent to the bubble surface on the equatorial axis. A similar structure was observed in unconverged solutions for solid spheres [6] but, unlike the calculations here, the unyielded regions were displaced from the sphere and decreased in size with increasing regularization parameter. Fig. 1. Rising 2-D bubble in a Bingham fluid. Figure 2 shows a time sequence of two rising collinear bubbles of equal size. Here, Bn = 2.67 based on the initial separation and Ca initially equals 1.88 for each bubble. There is an unyielded region that extends between the two equatorial planes, and perhaps initially a very small unyielded region at the facing poles. This configuration is qualitatively different from the inner unyielded regions for two collinear solid spheres [7]. Because of the outer yield surface there is a recirculating flow, which induces a rotation that causes a precession of the unyielded regions along the bubble interfaces. Fore- aft symmetry is also broken. The formation of a cap on the upper bubble and of a teardrop shape on the lower is reminiscent of the droplet calculations reported by Potapov and coworkers [12]. Convergence of the finite-element calculations becomes problematic at longer times because of interface curvature that seems to be tending towards cusps on the upper bubble. Fig. 2. Time sequence of two collinearly rising bubbles of equal size.

The buoyant force must exceed the integrated yield stress for any motion to take place. Bubbles or drops that are too small to overcome the yield stress individually can move as pairs when they are sufficiently close to have overlapping yielded regions around them.

ACKNOWLEDGMENT This work was supported by the National Science Foundation under Grant HRD-0206162. We are grateful to Professor Jeffrey Morris for helpful conversations.

REFERENCES

1. G. G. Lipscomb and M. M. Denn, J. Non-Newtonian Fluid Mech., 14, 337 (1984). 2. I. A. Frigaard and C. Nouar, J. Non-Newtonian Fluid Mech., 127, 1 (2005). 3. J. G. Oldroyd, Proc. Camb. Philos. Soc., 43, 100 (1947). 4. W. Prager, Introduction to Continuum Mechanics, Ginn, Boston, 1961. 5. A. N. Beris, J.A. Tsamopoulos, R.C. Armstrong, and R.A. Brown, J. Fluid Mech., 158, 19 (1985). 6. B. T. Liu, S. J. Muller, and M. M. Denn, J. Non-Newtonian Fluid Mech., 102, 179 (2002). 7. B. T. Liu, S. J. Muller, and M. M. Denn, J. Non-Newtonian Fluid Mech. 113, 49 (2003). 8. D. D. Atapattu, R. P. Chhabra, and P. H. T. Uhlherr, J. Non-Newtonian Fluid Mech., 59, 245 (1995). 9. N. Dubash and I. Frigaard, Phys. Fluids, 16, 4319 (2004). 10. H. Tabuteau, P. Coussot, and J. R. de Bruyn, J. Rheology, 51, 125 (2007). 11. J. Li and Y. Y. Renardy, J. Non-Newtonian Fluid Mech., 95, 235 (2000). 12. A. Potapov, R. Spivak, O. M. Lavrenteva, and A. Nir, Ind. Eng. Chem. Res., 45, 6985 (2006). 13. S. Osher and J. A. Sethian, J. Comput. Phys., 83, 12 (1988). 14. M. Sussman, P. Smereka, and S. Osher, J. Comput. Phys., 114, 146 (1994).

Dynamics of long bubbles at small Eötvös number

Jean Fabre Institut de Mecanique des Fluides de Toulouse

Jean-Rémi Turnau Institut de Mecanique des Fluides de Toulouse

Jean-Baptiste Dupont Institut de Mecanique des Fluides de Toulouse

Abstract The motion of long bubble at small Eötvös number remains an important issue for different practical problems like: the flow of liquid and vapour in space systems, the flow in mini-channels of fuel cells, the filtration with hollow fibres, the film coating in capillary tubes? In the absence of gravity, the shape and the velocity of these bubbles are controlled by viscous, capillary and inertia forces. The bubble dynamics is thus characterized by the Reynolds and the Weber numbers. If the motion of long bubbles in tubes is an old problem, it appears that most of the studies were limited to flow with negligible inertia for which only viscous and capillary forces come into play. We revisited the problem by extending the pioneering investigations of Taylor (1961), Bretherton (1961) and Cox (1964) to large Weber and Reynolds numbers. The shape and velocity of long bubbles pulled by the liquid was investigated both experimentally and numerically. Experiments were carried out in capillary tubes with fluid of various physical properties and numerical simulations were performed with the JADIM code developed at IMFT. When inertia is negligible we recovered that the bubble to fluid velocity ratio V/U is a growing function of the capillary number as shown in previous experiments. However when the capillary number becomes large enough the ratio reaches a constant value that is now clearly established. When inertia is large enough, the velocity ratio does not depend only on the capillary number. To understand the role of surface tension at large Re, an analytical model that predicts the bubble velocity at large Re was developed in the frame of inviscid theory. The solution that compares well with the numerical inviscid solution of Hien et al. (2006) was corrected to take into account the viscous effect.

Bonometti T. & Magnaudet J. An interface capturing method for incompressible two-phase flows. Validation and application to bubble dynamics. Int. J. Multiphase Flow, in press (2006). Bretherton, F.P. The motion of long bubbles in tubes. J. Fluid Mech. Vol. 10, 166-188 (1961). Cox, B.G. An experimental investigation of the streamlines in viscous fluid expelled from a tube. J. Fluid Mech. Vol. 20, 193-200 (1964). Ha Ngoc, H. and Fabre, J. A boundary element method for calculating the shape and velocity of two- dimensional long bubble in stagnant and flowing liquid. Engineering Analysis with Boundary Elements. Vol. 30, 539-552 (2006). Taylor, G. Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. Vol. 10, 161-165 (1961).

Rheological Characterization of Extremely Concentrated Suspensions

Francis A. Gadala-Maria Department of Chemical Engineering, University of South Carolina

*James R. Lisk, Jr. Department of Chemical Engineering, University of South Carolina

Abstract Many industrial processes deal with suspensions of solids at such high concentrations that traditional instruments are not suitable to characterize their rheological properties. The behavior of these materials lies somewhere between those of concentrated suspensions and granular materials. Practitioners in industry must often rely on empirical characterization methods or simply test the materials directly in the industrial process. After examining the problems involved and the options available, we turn our attention to a particular type of material consisting of extremely concentrated suspensions of graphite powder in thermoset polymeric resins containing hardeners and other additives. These are the bulk molding compounds used in the manufacture of bipolar plates for fuel cells. They have the consistency of wet sand and their rheological properties cannot be measured using rotational viscometers. Capillary viscometers and extrusion-type extensional viscometers cannot be used either because of particle degradation and because measurements must be performed at the high temperatures at which the thermoset resins harden. Squeeze flow may provide a way of ascertaining the rheological properties of these compounds. In particular, we examine the use of the constant-force squeeze-flow technique described by Meeten (Rheol. Acta 41, 557-566, 2002). Preliminary data using this technique suggests that the test may be fast enough to be unaffected by the curing of the polymer resins and that the compounds remain fairly homogeneous during the molding process. The technique is able to differentiate between various types of compounds and between the same compound at various temperatures. At present the technique provides an effective quality-control test and is able to determine some, but not all, of the parameters in the proposed constitutive equation. The effects of slip and surface roughness on the interpretation of the measurements are also discussed.

Stokesian symmetry - isn't it grand?

Joe Goddard University of California, San Diego

Abstract As a generalization of previous works [1, 3, 4] (and references therein), it is shown that all symmetries of multiparticle, multipolar Stokesian resistances follow from the symmetries of a single grand resistance kernel, which in turn follow from the symmetries of the Stokes equations. As discussed in this article, the combined geometric symmetries of particles and Stokesian kernel serve to confirm previously established symmetries of the resistance tensors for linear and quadratic shear flows. Such symmetries may prove useful in describing the coupling of particle migration to gradients in shear rate [3] or, more generally, in the systematic development of various graded and micromorphic continuum models [2] of Stokesian suspensions and linear-elastic composites.

Literature Cited

1. H. Brenner and M. E. O'Neill. Stokes resistance of multiparticle systems in a linear shear field. Chemical Engineering Science, 27(7):1421?39, 1972.

2. J. D. Goddard. From granular matter to generalized continuum. In P. Mariano, G. Capriz, and P. Giovine, editors, Mathematical models of granular matter, Lecture Notes in Mathematics, page 22 pp. Springer, Berlin, in the press.

3. S. Haber and H. Brenner. Hydrodynamic interactions of spherical particles in quadratic stokes flows. International Journal of Multiphase Flow, 25(6-7):1009?32, 1999.

4. E. J. Hinch. Note on the symmetries of certain material tensors for a particle in stokes flow. Journal of Fluid Mechanics, 54:423?5, 1972.

The analysis of self-diffusion and migration of rough spheres in nonlinear shear flow using a traction-corrected boundary element method

Alan L. Graham Los Alamos National Laboratory

Marc S. Ingber Department of Mechanical Engineering, University of New Mexico

Shihai Feng Los Alamos National Laboratory

Howard Brenner Department of Chemical Engineering, Massachusetts Institute of Technology

Full text: Not available Last modified: January 1, 2007 Presentation date: 06/14/2007 10:50 AM in ITU Macka Conference Room (View Schedule)

Abstract The phenomena of self-diffusion and migration of rough spheres in nonlinear shear flows are investigated using a new traction-corrected boundary element method (TC-BEM) in which the near-field asymptotics for the traction solution in the interstitial region between two nearly touching spheres is seamlessly coupled with a traditional direct boundary element method. The TC-BEM is extremely accurate in predicting particle trajectories, and hence, can be used to calculate both the particle self-diffusivity and a newly-defined migration diffusivity for dilute suspensions. The migration diffusivity is a function of a nonlinearity parameter characterizing the shear flow and arises from the net displacement of the center of gravity of particle pairs. This net displacement of the center of gravity of particle pairs does not occur for smooth particles and does not occur for rough particles in a linear shear flow. An explanation is provided as to why two particle interactions of rough spheres in a nonlinear shear flow results in particle migration Elements of Statistical Bubble Dynamics

Rob Hagmeijer University of Twente

Tim Colonius California Institute of Technology

Keita Ando California Institute of Technology

Abstract We examine models for the statistics of bubble dynamics when the equilibrium radius is a random variable. Such statistics are important in continuum (phase-averaged) bubbly flow models.

For the case of linearized bubble dynamics, the temporal evolution of the moments of the joint probability distribution function of bubble radius, bubble radial velocity, and equilibrium radius is examined. A formula for statistical equilibrium for the case of high Reynolds and Weber numbers is derived. These results are compared to reduced-order polynomial chaos expansions of the Rayleigh- Plesset equation and improved models are suggested. Two formulations are presented, one in terms of bubble radius and another in terms of radius variation. Both formulations lead to closed form expressions for the pdf's. The latter pdf is singular everywhere, but it can still be integrated into moments.

Nonlinear bubble dynamics for high Reynolds and Weber numbers are also studied. Statistical equilibrium is determined by calculation of the time averaged trajectories in phase space. The results are compared with both the results of the linear case and with the temporal evolution of the moments. We also compare the models with direct integrations of an extended Rayleigh-Plesset equation that accounts for compressibility and heat and mass transfer.

Visualization and measurements of explosive boiling in micro-channels

Gad Hetsroni Technion

Full text: Not available Last modified: January 24, 2007 Presentation date: 06/13/2007 11:30 AM in ITU Macka Conference Room (View Schedule)

Abstract "Visualization and measurements of explosive boiling in micro-channels" by G. Hetsroni Department of Mechanical Engineering Technion- Israel Institute of Technology Haifa 32000, Israel

Abstract. We investigate experimentally the instability and heat transfer phenomenon under condition of periodic flow boiling of water and ethanol in parallel triangular micro-channels. Tests were performed in the range of hydraulic diameter 100-220 m, mass flux 32-200 kg/m2s, heat flux 120-270 kW/m2, vapor quality x=0.01-0.08. The flow visualization showed that the behavior of long vapor bubbles, occurring in a micro-channel at low Reynolds numbers, was not similar to annular flow with interposed intermitted slugs of liquid between two long vapor trains. This process may be regarded as explosive boiling with periodic wetting and dryout. In the presence of two-phase liquid-vapor flow in the micro-channel, there are pressure drop oscillations, which increase with increasing vapor quality. This study shows strong dependence of the heat transfer coefficient on the vapor quality. The time when liquid wets the heated surface decreases with increasing heat flux. Dryout occurs immediately after venting of the elongated bubble. The period between successive events depends on the boiling number and decreases with an increase in the boiling number. The initial film thickness decreases with increasing heat flux. When the liquid film reached the minimum initial film thickness CHF regime occurred. Temporal variations of pressure drop, fluid and heater temperatures were periodic. Oscillation frequency is the same for the pressure drop, for the fluid temperature at the outlet manifold, and for the mean and maximum heater temperature fluctuations. All these fluctuations are in phase. The CHF phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and single conventional channel is amplification of parallel channel instability prior to CHF. The dimensionless experimental values of the heat transfer coefficient are presented as the Nusselt number dependence on the Eotvos number and the boiling number.

Corresponding author . Tel.:+972-48-292058; fax: +972-48-238101 E-mail address: [email protected] (G. Hetsroni).

Dynamical simulations of hydrodynamic interactions

Tony Ladd University of Florida Gainesville

Full text: Not available Last modified: December 2, 2006 Presentation date: 06/14/2007 2:00 PM in ITU Macka Conference Room (View Schedule)

Abstract Hydrodynamic interactions are the forces on suspended particles that are transmitted by fluid motion. They play an important role in the rheology of colloidal suspensions and the dynamics of polymer solutions. Since the length-scale and time-scale separations between the suspended particles and solvent molecules are at least one to two orders of magnitude, we can usually treat the solvent as a continuum fluid, whose dynamics are described by the fluctuating Navier-Stokes equations. On sufficiently large scales the effects of molecular-level fluctuations can be ignored entirely, leading to conventional Navier-Stokes fluid dynamics, but at the colloidal scale and below, thermal fluctuations are an essential component. In this talk I will describe different approaches to simulating fluid dynamics incorporating fluctuations.

There are two main approaches to discretizing the continuum fluid equations; one involves particle- based models, including molecular dynamics (MD) and dissipative particle dynamics (DPD), while the other uses grid-based solvers, typically lattice-Boltzmann methods. Finite-element approaches are also possible, but are less popular because the fluctuations do not fit so naturally within this framework. After a brief survey of the various possibilities I will focus on lattice-Boltzmann methods for colloidal suspensions and polymer solutions. We currently use two different methods to couple the solid and fluid phases depending on the particle size. For colloids we implement an explicit no-slip boundary on the particle surfaces, while for polymers we use frictional coupling, similar to that used in many simulations of lightly laden particle-fluid flows. In the low-Reynolds number limit, hydrodynamic interactions can be calculated without explicit reference to the background fluid. These simulations include boundary-element methods as well as Brownian and Stokesian dynamics. Somewhat surprisingly, it is not necessarily true that these methods are faster than an explicit simulation of the fluid motion. In general for dense flows the direct simulation methods are more efficient, while for dilute flows multipole methods are faster. I will discuss computational efficiency in regard to simulations of polymer solutions.

Experimental and numerical techniques in acoustic cavitation

Werner Lauterborn University of Goettingen

Philipp Koch University of Goettingen

Robert Mettin University of Goettingen

Thomas Kurz University of Goettingen

Abstract Intense sound fields in liquids lead to qualitatively new phenomena besides pure propagation of sound, be it linear or nonlinear. One important new phenomenon is the rupture of the liquid (acoustic cavitation) turning it to a two-phase fluid with specific properties: a bubbly liquid with sound driven bubble oscillations and motions. The bubbles in turn alter the sound propagation leading to a complex interaction of the sound field with the bubbly liquid and the individual bubbles. Our knowledge of sound -- bubbly-liquid generation and interaction is still incomplete despite many investigations and approaches to this problem.

The complex problem has been split into a set of subtasks for better handling: (i) the action of a sound field on bubbles, (ii) the action of bubbles on acoustic wave propagation, (iii) interaction of bubbles and of bubbles with boundaries in a sound field, (iv) interaction of acoustic waves in bubbly liquids, and (v) interaction of sound and bubbles in a bubbly liquid, the full problem.

Most work exists on the action of a sound field on bubbles, in particular on single spherical bubbles, notably via the investigations in the context of single bubble sonoluminescence (SBSL). Here also shape, diffusive and chemical stability questions have been addressed. Acoustic wave propagation in bubbly liquids has led to the formulation of new wave equations with the result, among others, of potentially very low sound speeds, as observed. The dispersion relations get very involved. The interaction of bubbles and of bubbles with boundaries in a sound field is essential for the description of bubble clusters and multibubble systems as they occur, for example, in ultrasonic cleaning baths. The investigation of the interaction of acoustic waves in bubbly liquids is part of nonlinear acoustics with wave mixing, up and down conversion and self actions as self focusing or self induced transparency. The full interaction problem with the back reaction of the bubbles on the sound field and on sound propagation needs a new approach beyond the continuum approach so far. The oscillations of the individual bubbles as well as their translational motions, their interactions and clustering have to be included and their action on the sound field to be introduced for sound propagation calculations.

We will report on our efforts on the full problem starting from measurements and calculations on single bubbles (oscillation and translation in an acoustic field) via measurements and calculations on two-bubble interaction in an acoustic standing wave field to measurements and simulations of bubble clusters with several hundred bubbles. Examples of the bubble structures formed in different acoustic fields will be given.

Experimental and Theoretical Studies of the Effects of Surface Active Additives on Coalescence in Immiscible Polymer Blends

Gary Leal University of California, Santa Barbara

Abstract In this talk, I will present a combination of recent experimental and theoretical work on the effects of surface active additives on the coalescence of polymeric drops in a polymeric suspending fluid. The bulk fluid properties are Newtonian. We will consider two types of additives: block copolymers that act as surfactants, and surface functionalized nano-particles. In the case of the copolymer-surfactant, our current focus is on numerical studies that are aimed at understanding the mechanism by which the coalescence process is inhibited. In the case of the nano-particles, the focus is primarily on experimental studies that assess the surface activity when these particles are treated via the adsorption of mixtures of functionalized PDMS and PBd at the particle surface and then added to a PDMS-PBd blend. These latter systems exhibit behavior that is similar to the copolymer-surfactant in some ways, but is also fundamentally different in others.

Determination of the shear-induced diffusion coefficients in a suspension of hard spheres.

Elisabeth Lemaire Laboratoire de Physique de la Matiere Condensee

Dima Merhi Full text: Not available Last modified: February 28, 2007 Presentation date: 06/14/2007 11:30 AM in ITU Macka Conference Room (View Schedule)

Abstract We report some experimental and numerical results on the behaviour of a macroscopic monomodal suspension undergoing shear rates in various curved flow geometries. For the first time, we show that shear-induced migration takes place when the suspension is subjected to a torsional flow between two rotating plates. The time evolution of the particles concentration profiles are obtained thanks to an experimental technique based on the detection of tracers by measurement of light absorption The outward shear-induced migration is confirmed by viscometric measurements where an increase in the apparent viscosity of the suspension has been observed for long periods of shear. Moreover, this increase is found to depend solely on the value of the applied strain, which is consistent with a shear- induced migration phenomenon. Experimental results are reproduced using a semi-quantitative model involving the balance of three diffusion fluxes induced respectively by the gradient of viscosity (Jh), the gradient of the collision rate between particles (Jc), and the flow curvature (Jr). Steady and transient numerical profiles are obtained using a finite volume approach. The coefficients of the diffusion fluxes (Kh, Kc, Kr) are determined by optimising the numerical profiles to fit the experimental data. The ratios of these coefficients (Kh/Kc and Kr/Kc) are found to be independent of the flow geometry while their absolute values strongly depend on the direction of particles drift. Furthermore, we present some experimental results dealing with the direct measurement of the hydrodynamic diffusion coefficients. Indeed, we show that, under some special conditions, the application of an electric field to a suspension undergoing a creeping flow results in a gathering together of the particles in a small region of the shear flow. When the field is cut off and the flow maintained, the evolution of the concentration profile of particles allows us to determine the diffusion coefficient of the particles in the vorticity direction.

Clustering of microbubbles and particles in turbulent flow

Detlef Lohse University of Twente

T. H. van der Berg

E. Calzavarini

D. Lohse

F. Toschi

Full text: Not available Last modified: May 24, 2007 Presentation date: 06/11/2007 3:00 PM in ITU Macka Conference Room (View Schedule)

Abstract Lagrangian dynamics of inertial particles in turbulence has recently become the subject of experimental investigations and massive numerical calculations. The relevant parameters are the particle-fluid density ratio and the particle dimension with respect to the smallest scale of turbulence. We present a study primarily focused on the case of micro-bubbles, i.e. $rho_p ll rho_f$, in a turbulent flow. Our investigation is based both on the analysis of experimental and numerical results.

First, single-point hot-wire measurements in the bulk of a turbulent channel have been performed in order to detect and quantify the phenomenon of preferential bubble accumulation. We show that a statistical analysis of the bubble-probe colliding-times series can give a robust method for investigation of bubble clustering in the bulk regions of a turbulent flow where, due to the opacity of the flow, no imaging technique can be employed. We demonstrate that micro-bubbles ($R_0 simeq100 mu m$) in a developed turbulent flow, where the Kolmogorov length-scale is $eta simeq R_0$, display preferential concentration in small scale structures. In particular, it is found that the clustering process is enhanced by increasing the turbulence intensity. Next, a comparison with Eulerian-Lagrangian numerical simulations has been performed and arising similarities and differences with the experimental results will be discussed.

An attempt to better characterize the morphological features of bubble/particle clusters is considered, too. For this, we employ a family of descriptors, known as Minkowski functionals, that have been shown capable to extract geometrical as well as topological features of a spatial distribution of points. These tools and techniques are borrowed from cosmology.

Silver Street vs. Pembrooke Street: The transition from spherical cap to toroidal bubbles

Jacques Magnaudet Institut de Mecanique des Fluides de Toulouse

Thomas Bonometti Dpt of Aerospace Engineering, Florida State University

Abstract Large gas bubbles rising under buoyancy adopt either a spherical cap shape or undergo a topological transition after which they become toroidal. We carry out a numerical investigation of the evolution of such large bubbles in presence of both capillary and viscous effects using a VOF-like technique. The transition from spherical cap to toroidal bubbles is studied in the parameter space built on the Bond (Bo) and Archimedes (Ar) numbers. Two markedly different transition scenarios, corresponding to the limit of large Ar and large Bo, respectively, are identified. In the first case, the front of the bubble is pierced by an upward jet coming from the rear of the bubble. In contrast in the limit of large Bo, a downward jet develops at the front and pierces the rear of the bubble, unless viscous effects are sufficient to stabilize the front. We also determine the position of the transition for intermediate values of Bo and Ar and discuss the connection between present axisymmetric results and experimental situations in which the bubble is followed by a turbulent wake. We finally examine why, given an initial gas volume, the final bubble topology observed in experiments appears to depend on the initial conditions. Indeed, we find that initially oblate bubbles may result in stable spherical cap bubbles for values of Bo and Ar well beyond those for which initially spherical bubbles of similar volume undergo the topological transition. This remarkable influence of the initial shape is shown to be due to the influence of the oblateness on both the bubble acceleration and the hydrostatic pressure head around the bubble.

Numerical based prediction of three-phase bubble column reactor operation

Dieter Mewes Universitaet Hannover

Dierk Wiemann Universität Hannover

Abstract A population balance model is applied to calculate the mass transfer in bubble columns with and without suspended solids. For the calculation of the three-dimensional flow fields in bubble columns a multi-fluid model is used. In addition to the balance equations of mass and momentum a transport equation for the mean bubble diameter is solved. This transport equation is based on a population balance equation and considers the coalescence and break-up of bubbles in dependence of the local flow field. Thus for the homogeneous and the heterogeneous flow regime the local interphase transfer terms for mass and momentum are calculated in dependence of the local bubble size distribution. For the consideration of chemical reactions both the local interfacial area density and the back mixing properties must be reasonably predicted. The local interfacial area density is obtained from the transport equations for the mean bubble volume. For the determination of the dispersion in the gas and liquid phase an ideal tracer is injected. As a result the time-dependent tracer concentration is obtained. The fluctuations of liquid vortices influence the axial and radial spreading of the tracer. For comparison with experimental results the axial dispersion coefficients are calculated. The multi-fluid model predicts the interfacial area density and the dispersion in the gas and liquid phase in good agreement with experimental observations. Therefore the model is extended to include mass transfer between the gaseous and liquid phase due to physical absorption and chemical reactions. In comparison with inert gas-liquid flow the resulting flow pattern is significantly changed in dependence of the mass transfer rate. For certain applications a particulate solid phase is added which represents the catalyst for a homogeneous chemical reaction. In these cases a three-phase gas-liquid-solid flow arises. For the calculation the suspended solids are described by an individual Eulerian phase using the theory of granular flow. Numerical calculations result in the instantaneous as well as the time-averaged fields of the volume fractions, velocities and concentrations for the homogeneous and the heterogeneous flow regimes in cylindrical bubble columns for two and three-phase gas-liquid-solids particulate flow

Inclusion of Heat/Mass Transfer Computations in DNS Studies for Particle Laden Flows Efstathios E. Michaelides Mechanical and Energy Engineering, University of North Texas

Zhi-Gang Feng Mechanical and Energy Engineering, University of North Texas

Abstract Direct Numerical Simulation (DNS) methods have focused on the motion, mechanical interactions and hydrodynamic interactions of suspended particles in isothermal fluids. Thus, typical DNS studies involve the solution of the continuity and momentum equations as well as the force-coupling between the particles and the fluid. Thermal interactions of particles and energy exchange between the particles and the fluid are normally dealt with by solving independently the heat or mass diffusion equation of particles.

This presentation introduces a novel DNS method that computes both the momentum and heat or mass interactions between particles and fluid. The method is implemented using a finite difference numerical scheme in combination with the Immersed Boundary (IB) concepts. The latter facilitate the handling of both the velocity and temperature boundary conditions on the surface of the particles. An integral part of the method is the adoption of the Boussinesq assumption to resolve the coupling of velocity and temperature fields. Thus, the Navier-Stokes equation and energy equation are solved simultaneously for the entire fluid. In the region occupied by solid particles, a force density function and a heat flux density function have been used to represent the momentum interaction and energy exchange, respectively. The heat flux density function has been computed by an iteration technique, which accounts for the different boundary conditions at the particle-fluid interface.

Bubble behavior in a molten metal pool

Kaichiro Mishima Research Reactor Institute, Kyoto University

*Yasushi Saito Research Reactor Institute, Kyoto University

*Masahito Matsubayashi Japan Atomic Energy Agency

Abstract This paper presents the behavior of gas bubbles and water droplets injected into a molten metal pool. Bubbles and droplets were visualized by neutron radiography. Images taken by neutron radiograpy were processed to obtain the bubble shape, size, interfacial drag coefficient, void fraction and the velocity vector in the molten metal pool. The results were compared with existing correlations obtained for conventional gas-liquid systems. The interfacial heat transfer coefficient of a steam bubble was also measured during direct contact evaporation of water in the pool. Water droplets were injected into the pool which was heated at the top and cooled at the bottom so that the pool had a large temperaature gradient in the vertical direction. A water droplet was introduced near the bottom where the temperature was below the boiling point of water but above the melting point of the metal, and the droplet began to evaporate when it rised to reach the upper region where the temperature was high enough to initiate evaporation of water droplet. Images of the evaporating droplets and bubbles were analyzed to obtain the interfacial drag and heat transfer coefficients.

Hydrodynamics of interacting particles in finite-inertia shear flow

Jeffrey F. Morris City University of New York

*Pandurang Kulkarni City University of New York

Abstract Numerical simulation and experiments on the interaction of neutrally-buoyant spherical particles in finite-inertia shear flow are reported. The pair interaction is the primary focus of the work. The numerical approach is the lattice-Boltzmann method, simulated in a wall-bounded geometry with periodic boundary conditions in the flow and vorticity directions; simple shear is driven by the walls and the motions of the particles are studied for varying initial separations. The Reynolds number is defined in terms of the shear rate \gamma, particle radius a, and kinematic viscosity \nu as Re = \gamma a^2/\nu.

Reynolds numbers from Re = 10^{-2} - O(1) will be discussed, with attention restricted to pairs symmetrically placed relative to the midpoint of the computational domain. For all Re in this range, the simulated trajectories exhibit qualitative, and in fact topologically distinct, differences from the Stokes flow trajectories. Recall that in Stokes flow, a pair of spheres is predicted to move relative to one another either on a passing trajectory in which the pair begin and end at infinite separation, or on a permanently bound ("closed") orbit; all of these trajectories exhibit fore-aft symmetry consistent with linearity of the motion. For two equal spheres at finite Re, the spheres show no closed trajectories, but instead are found to follow one of three types of trajectories: passing, reversing, or spiralling. The passing trajectories occupy the bulk of the pair space as in the Stokes flow, but are fore-aft asymmetric with the pair generally displaced to a larger offset in the velocity direction by the interaction. The reversing trajectories occupy a range of initial conditions in which the particles move toward one another due to the shear, then move across the zero-velocity line of the bulk shear flow, reverse their direction and move away. The spiralling trajectories occupy the region which brings the particles into closest interaction, and includes an extended zone with initial separation primarily along the vorticity axis as well as a zone within the plane of shear. The zone within the plane of shear is very small at Re>0.1 for equal sized-spheres. The interactions of spheres of unequal size has also been studied and select results will be presented to illustrate the full variable range from a tracer to equal radius. Solid and periodic boundary influence has been considered by varying the domain size, and in all cases the role of inertia is established to play a key role in the trajectories described.

Experimental analysis of trajectories in a cylindrical Couette geometry by a stereoscopic particle- tracking technique will be reported. Certain of the features noted in simulation have been observed and these will be described. The interactions seen in a many-particle system, i.e. a true suspension, at finite inertia will also be presented, with a focus on observable structures due to the non-Stokes conditions.

The insight the work provides on the influence of inertia upon dispersion and the stress in the mixture will be considered if time permits. Recent Developments in Multiphase Flow Algorithms for the Numerical Simulation of Droplet Mixing and Evaporation

Fadl Moukalled America University, Beirut

*Marwan Darwish America University, Beirut

Abstract This paper reports on recent developments in the numerical simulation of a special type of polydisperse flows, namely the evaporation and mixing of droplets sprayed into a supersonic stream; a situation similar to that in the combustor of a scramjet engine. During this work a number of numerical methods were investigated and developed namely: (i) The full multiphase flow model; (ii) The Multi-Size-Group model (MUSIG); (iii) The Heterogeneous Multi-Size-Group model (H-MUSIG). In general, particles in a dispersed phase can be divided into several size classes and each of these size classes can be treated as a separate phase in a multiphase flow calculation. Thus, the multiphase flow model has N+1 set of coupled equations (continuity and momentum) to be solved, where N is the number of size groups. Because of the large number of equations involved, the number of size groups that can be used in practical calculations is limited. As a result, the size distribution of the particles is inadequately represented. MUSIG assumes that all particle classes share the same velocity field so that it is only necessary to solve one set of momentum equations for all the particles. Essentially reducing the multiphase approach described above back to a two-fluid approach with one velocity field for the continuous phase and one for the dispersed phase. However, the continuity equations of the particle size groups are retained and solved to represent the size distribution. With this approach, it is possible to consider a larger number of particle size groups (say 10 to 20 particle phases) to give a better representation of the size distribution. The shortcoming of this approach is related to the droplet class velocity. It is well known that larger droplets do not follow the flow and smaller droplets do. By considering one average velocity for the droplets, a stratification of droplet sizes from normal fuel injection occurs with larger droplets penetrating further into the flow. The larger droplets transport more fuel mass than may be expected. To alleviate this problem, the MUSIG model is extended into an H-MUSIG model. In the extended model, rather than assigning one velocity for all droplet classes, groups of classes are considered with droplet classes in a group sharing the same velocity. This is a blend between a full multi-phase approach and a two-phase approach. If a group is composed of one droplet class, then the full multiphase approach is obtained, whereas if a group is composed of all droplet sizes, then the original MUSIG is recovered. Results generated using the three models will be presented and a comparative assessment of their performance will be provided.

A Front-Tracking Method for Computation of Interfacial Flows withSoluble Surfactants

Metin Muradoglu Koc University, Istanbul

Abstract A finite-difference/front-tracking method is developed for computations of interfacial flows with soluble surfactants. The method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations using a non-linear equation of state that relates interfacial surface tension to surfactant concentration at the interface. The method is validated for simple test cases and the computational results are found to be in a good agreement with the analytical solutions. The method is then applied to study the cleavage of drop by surfactant---a problem proposed as a model for cytokines (Greenspan 1977, 1978). It is also used to model the effects of soluble surfactants on the buoyancy-driven motion of viscous drops in a circular capillary tube. It is shown that the terminal velocity of bubble reduces significantly as surfactant accumulates at the bubble interface and the terminal velocity of a contaminated bubble approaches to that of a solid sphere in the limit of creeping flow regime.

Paradoxes in Bubbly Liquids and Bubble Thermonuclear Fusion

Robert I. Nigmatulin Russian Academy of Sciences

Full text: Not available Last modified: February 14, 2007

Abstract A paradox is a real phenomenon, which contradicts ordinary insights and human intuition. Paradoxes are milestones of science. Two-phase bubbly fluids manifest a number of paradoxical properties. In spite of the 10-5) the thermo-physicalnegligible amount of the gas (mass concentration properties of the gas in the bubbles exert a significant influence on the shock and acoustic wave attenuation. At the same time the variation in viscosity and other thermo-physical properties of the liquid, which composes almost all of the bubbly liquid mass has little influence on wave attenuation. It is common for the bubbly liquid to damp the shock, but for some regimes the shock waves can be strongly amplified by bubbly liquids. The basis for this phenomenon is determined by a very specific property of the bubbly liquid known as a local ,volume deformation inertia when the pressure depends not only on the density, but on the acceleration of compression, . The third paradox of bubbly liquid is connected with the bubble motion in a vertical column with a bottom subjected 10 Hz). For specific regimes gas bubbles to intensive vertical vibration ( can be entrained on the upper surface of liquid and move down forming a gas cushion on the bottom of the column. This cushion may initiate additional . Interaction of these two frequenciesvertical oscillations with frequency, may be resonant and initiate motion of the bubbles down and up. This phenomena can be used for very effective mixing of two liquids which normally are mixed poorly. Many paradoxes are manifested in sonoluminescence and bubble fusion experiments (Taleyarkhan, West, Cho, Lahey, Nigmatulin, Block, 2002, 2004). The last experiments showed that neutron emission and tritium formation may occur in deutorated acetone under acoustic cavitation conditions. Intensity of the fast neutron (2.5 MeV) emission and tritium nucleus production is 5´105 s-1. This suggests ultrahigh compression of the matter produced inside the bubbles during their collapse. Systematic research is being carried out on vapor bubble implosion in intense acoustic fields in D- acetone (C3DO6) to provide the observed effect theoretical confirmation and explanation. The dynamics of the bubbles formed during maximum rarefaction in the liquid is numerically studied on the basis of the models developed for a single bubble and bubble clusters. It is assumed that during their growth the bubbles coagulate and form a few bigger bubbles, which then collapse under the additional pressure pulses produced in the liquid through the amplification of compression waves within the cluster. A shock wave is shown to be formed inside the bubble during the latter’s rapid contraction. Focusing of this shock wave in the bubble center initiates dissociation and ionization, results in violent increases (0.77×105 times) in density (104 kgm3), pressure (1010-1011 bar) and temperature 108-109 K), high enough to produce nuclear fusion reactions. The bubble looks like a micro-hydrogen bomb. The diameter of the neutron emission zone is about 100 nm. The highest neutron emission is recorded at about 25 nm from the bubble center. 10The number of neutrons emitted during the implosion of a single bubble is neutrons per implosion, and the number of tritium nuclei is the same. It is found out that the intensity of bubble implosion and the number of neutron emitted increase with variations in nucleation phase, positive half-wave amplitude, and liquid. Some important features of the process were: 1. The cold liquid effect, where relatively small variations of the liquid pool temperature strongly influence the acceleration of the liquid and intensity of the thermonuclear fusion reaction. 2. The bubble cluster effect, where multi-bubble cluster dynamics produce an amplification of compression compared with the incident pressure of acoustical field 3. Non-dissociation of the liquid, where, in spite the high pressures and temperature experienced on the interface (105 – 106 bar, 2500 K) the liquid has insufficient time for dissociation during 10 ns. That is why the liquid is much less compressible than implied by the equilibrium adiabat which corresponds to more than a microsecond of compression. Thus only the extrapolation of first part of D-U shock adiabat should be used for the estimation of compressibility of the liquid. 4. “Cold” electrons. During the extremely short time of the compression (10-13 – 10-12 s) the electrons have no time to be heated by ions. Thus the heat capacity of the gas/vapor is ~ 2,000 J/kg instead of the equilibrium heat capacity of fully ionized plasma, ~ 8,000 J/kg. This allows the temperature of ions to be four times higher than for an equilibrium plasma which results in conditions suitable for thermonuclear fusion. Moreover the “cold” electrons do not produce intensive energy losses by photon emissions. 5. Intensive collapse of the bubble is a multi-scale phenomena with the final sharpening. During the different stages the different physical phenomena, spatial and time scales dominate the process. These physical processes are: heat transfer, evaporation, condensation, transition from two phase to supercritical fluid, transition from a non-compressible liquid and a homobaric pressure distribution in the vapor (this stage takes almost all the time of the process (41.5 μs from 42 μs) to high compression of the liquid and to shock wave phenomena in gas (0.5 μs), dissociation, ionization and finally to nuclear fusion). The spatial scales are the following: acoustical field scale is ~ 10-2 m, cluster scale is ~10-3 m, bubble scale is ~ 10-5 – 10-4 m, dissociation and ionization cores scale is ~ 10-7 - 10-6 m, thermonuclear core scale is 10-8 – 10-7 m. The time scales are the following: evaporation and condensation scale is ~ 10-5 s, compression wave scale is ~10-6 s, dissociation and ionization scale is ~10-9 s, and thermonuclear time scale is 10-13 s. The numerical code needs to vary the equations to accommodate the different physical phenomena and different sizes of the grid and different time steps form Dt = 10-7 s to 10-14 s. To clarify the process in the tiny central thermonuclear core this zone should be considered by the cell size Dr = 10-10 m in the bubble with radius 10-5 m. The same problem exists with the thin boundary layers near the interface. 6. Three-dimensional analysis for the shape of the bubble supports the assumption of a spherically symmetrical flow to produce the concentration of the energy in the tiny core. All these effects are crucial for the prediction of the thermonuclear reaction intensity.

Dynamics of non-Newtonian slender drops in viscous flow

Avinoam Nir Department of Chemical Engineering, Technion

*Moshe Favelukis

*Olga Lavrenteva Department of Chemical Engineering, Technion

*Dina Tsemakh Department of Chemical Engineering, Technion

Abstract We have studied the dynamics of slender drops of power-law fluids embedded in immiscible Newtonian viscous fluids, subject to linear flows such as extensional and simple shear. The analyses consider stationary states, inertia effects in the ambient fluid, bifurcation of the states, stability of the slender shapes, dynamics of unstable deformation and possible mechanisms for break-up of the drops. While the analyses and formulations follow the approach of earlier works on the dynamics of Newtonian drops in such flows, the resulting dynamics for the non-Newtonian drops suggest that it is not a regular extension of this particular case. The slender body analysis exists only for Newtonian and shear thinning drops. We present various results and compare it to those obtained in the case of Newtonian drops by Acrivos and co-workers.

The Collective Dynamics of Self-Propelled Particles

Prabhu Nott India Institute of Science

Abstract We present a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. Most swimming microorganisms that abound in nature possess these characteristics. They display several intriguing features in their collective motion, such as the spontaneous formation of spatio-temporal patterns, coherent clusters and convection cells. In this study we have proposed a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector, whose locomotion is driven by the action of a force dipole of constant magnitude at a point slightly displaced from its centre. In isolation, it would move at constant velocity set by the magnitude of the force dipole and its orientation. When many such particles coexist, their hydrodynamic interaction alters their velocity and, more importantly, their orientation. As a result, the motion of the particles is chaotic.

We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, and find several interesting features in the microstructure and statistics. There is a continuous process of breakage and formation of the clusters, as observed in previous experimental studies. We find that the probability distribution of particle velocity exhibits interesting behaviour - at low particle concentration, it differs qualitatively from the equilibrium distribution in a colloidal suspension (i.e. a Gaussian), or the distribution in a sheared suspension. However, the velocity distribution resembles the Gaussian at large particle concentration. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing particle concentration. The microstructural indicators, such as the pair correlation function and the orientation correlation, show interesting anisotropic features, which are again quite different from that of sheared suspensions.

Erosion and dune formation on particle beds submitted to shearing flows

*Malika Ouriemi IUSTI, UMR CNRS 6595, Polytech'Marseille Pascale Aussillous IUSTI, UMR CNRS 6595, Polytech'Marseille

*Elisabeth Guazzelli IUSTI, UMR CNRS 6595, Polytech'Marseille

Abstract When particle beds are submitted to shearing flows, the particles at the surface of the bed can move as soon as hydrodynamic forces acting on them exceed a fraction of their apparent weight. The common way of representing this incipient motion of the particles is to use a dimensionless number, the Shields number, which is constructed as the ratio of the shear stress to the apparent weight of a single particle and which exceeds a critical value at motion threshold. This situation occurs in a wide variety of natural phenomena, such as sediment transport in rivers or by air, and in industrial processes, such as hydrate or sand issues in oil production and granular transport in food or pharmaceutical industries. A very common feature that arises is the formation of ripples, i.e. small waves on the bed surface, or of dunes, i.e. larger mounds or ridges. The widely recognized mechanism for dune or ripple formation is the fluid inertia or more precisely the phase-lag between the bottom shear stress and the bed waviness generated by the fluid inertia, see e.g. Charru and Hinch 2006 and references therein. In that case, the shear stress, the maxima of which are slightly shifted upstream of the crests, drags the particles from the troughs up to the crests. However, a complete description of the bed instability is still lacking as the coupling between the granular media and the fluid is poorly understood. Empirical or phenomenological laws relating the particle flux to the bottom shear stress have been used in the literature. In the past decade, advances has been made in the understanding of granular flows. In particular, it has been shown that a simple rheological description in terms of a friction coefficient may be sufficient to capture the major properties of granular flows, see GDR MiDi 2004. This description has been found to be also successful when an interstitial fluid is present, see Cassar, NIcolas, and Pouliquen 2005. We propose the use of a two phase model having this rheology for the particulate phase to describe the bed-load transport as well as the erodible-bed instability. Calculations are performed numerically but also analytically in asymptotic cases. These predictions are compared to experimental results obtained in laminar flow above a bed composed of spherical particles in a pipe.

References Charru, F. and Hinch, E.J., "Ripple formation on a particle bed sheared by a viscous liquid. Part One: steady flow", Journal of Fluid Mechanics (2006), vol. 550, pp. 111-121. MiDi GDR, "On dense granular flows", European Physical Journal (2004), E 14 (4), pp 341-365. Cassar C., Nicolas M., Pouliquen O., "Submarine granular flows down inclined planes", Physics of Fluids (2005), 17 (10) 103301.

Accurate adaptive Volume-Of-Fluid using Gerris

Stephane Popinet National Institute of Water and Atmospheric Research, Wellington

Full text: Not available Last modified: March 12, 2007 Presentation date: 06/12/2007 4:40 PM in ITU Macka Conference Room (View Schedule) Abstract I will present recent developments in the quad-octree Gerris Flow Solver (http://gfs.sf.net) which allow adaptive simulations of interfacial flows. In contrast to previously published techniques, Gerris allows for mass-conserving adaptivity along the interface (i.e. the spatial resolution can vary along the interface).

Accurate surface tension representation is still an important issue for interfacial flow calculations, especially when the interface is represented implicitly (e.g. in VOF or levelset formulations). I will present how a combination of different curvature estimation schemes and "balanced-force" formulation of surface tension lead to highly accurate results for classical surface tension test cases. The results are better than previously published results using either continuum formulations or explicit formulations (marker techniques) while preserving the robustness and generality of the VOF technique.

I will conclude with a selection of applications illustrating the capabilities of the Gerris solver for difficult interfacial flow problems.

Experimental Methods for the Study of Multiphase Materials

Robert Powell UC Davis

Abstract This talk will review experimental techniques for studying the dynamics of multiphase fluids. We wil focus on magnetic resonance imaging (MRI), ultrasonic pulsed Doppler Velocimetry (UPDV) and include other techiques such as Electrical Impedance Tomography. The systems that we consider consist of either a solid particle or a liquid drop suspended in a continuous fluid. A core requirement is the ability to work with concentrated opaque systems. The view taken in this talk is that while ideal multiphase systems can be designed that allow for important fundamental measurements for concentrated suspensions, techniques that do not have this requirement permit working with a wider range of model multiphase fluids as well as with fluids found in real processes.

The Average Stress in Fluid-Particle Flows

Andrea Prosperetti Johns Hopkins University and University of Twente

Quan Zhang Mechanical Engineering, Johns Hopkins University

Abstract This paper presents an analysis of the average stress in a disperse fluid-particle flow. It is shown that, in addition to the well-known stresslet contribution to the symmetric mixture stress, other contributions arise whenever the disperse-phase volume fraction or the particle-fluid relative velocity is non-uniform. Furthermore, even in the absence of external couples acting on the particles, in general the stress also acquires a non-symmetric contribution. The analysis is general and applicable in any Reynolds number regime. As an example, the general expressions are evaluated for the case of particles in Stokes flow. The dilute limit is treated by extending to the non-uniform case Batchelor's renormalization procedure, while computational ensemble averaging is used for dense systems. Estimates of the importance of the new terms are presented.

Agglomeration and breakup of solid particles in a random symmetric shear

Michael Reeks School of Mechanical and Systems Engineering, University of Newcastle

*Yasmine Ammar School of Mechanical Systems Engineering, University of Newcastle

*David Swailes School of Mechanical & Systems Engineering, University of Newcastle

Abstract When particles are released into a turbulent flow, they segregate into the regions of straining between regions of vorticity in the flow. This process of demixing by the turbulence among other things, leads to enhanced agglomeration of the suspended particles and in some cases to the break up of agglomerates as they are formed.

The work reported here is concerned with the development and validation of a simple Lagrangian model for agglomeration and break-up involving the trapping and release of particles from a random sequence of straining and vortical structures that simulates the Kolmogorov small dissipating scale motion of the turbulence responsible for particle pair dispersion. In particular we measure the flux of particles colliding with a test particle at the centre of a symmetric straining flow and examine the build up of the particle concentration in the vicinity of the test particle arising from a uniform continuous source of particles injected at the boundaries of the flow field, the size of the straining region being typical of the Kolmogorov length scale η of the turbulence. The collision kernel determined from the flux of particles colliding with a test particle is much higher than the prediction of Saffman and Turner (1956) for intermediate Stokes number due to both particle segregation and velocity decorrelation (Sundaram and Collins, 1996).

The straining flow is described with respect to its principla axes with the strain rate and position normalized on the Kolmogorov timescale and length scales respectively. This flow persists for an eddy life time T lected from an exponential distribution with a decay time constant = 1. Then a new flow field is generated with a new value of T and a new value of the strain rate selected from a Gaussian distribution of unit variance and at the same time the principal axes of the pattern are rotated by an angle selected from a uniform distribution of width 2/pi will generate a Gauusian radial velocity distribution whose RMS is independent of the azimuthal coordinate.

The particle equations of motion is based on Stokes drag and refer to the principal axes of the straining flow (which rotate depending on the angle) and have a simple analytic solution, which is used to construct a final solution in a fixed frame of reference. A uniform flux of particles corresponding to a constant half Gaussian velocity distribution identical to that of the local fluid at the boundaries is obtained by selecting particles with Gaussian distribution and injecting them with a time delay inversely proportional to their velocity. The particle flux and concentration are calculated when equilibrium in particle concentration is obtained, the flow field containing a sufficiently large number of particles to achieve statistical stationarity. Result are presented for the agglomeration kernel as a function particle Stokes no for perfectly absorbing surfaces and compared with the result for particles which follow the flow precisely (Saffman & Turner). A simple model is constructed based on simple gradient two-particle dispersion and turbophoretic drift and the predictions compared with those of the simulation.

References Crowe C.T., Chung J. N. and Troutt T. R. (1993), Particulate Two phase Flow, Butterworth, Heinemann Sundaram S. and Collins L.R. (1996) Collision statistics in an isotropic particle-laden turbulent suspension. Part1. Direct numerical simulation J. Fluid Mech., 335 Saffman P.G. and Turner J. S. (1956) On the collision of drops in turbulent clouds J. Fluids Mech., 1, 16-30

Capillary interactions among particles protruding from a gas-liquid interface

Ashok S. Sangani Biomedical and Chemical Engineering, Syracuse University

Abstract This talk will consist of two parts. The first part will be concerned with the so-called problem of coffee- ring formation. When a drop of suspension containing particles evaporates from a substrate, higher evaporation rates near the drop edge compared with the drop center drives an outward flow advecting thereby particles to the drop edge. If the substrate-liquid-air contact line remains pinned as the evaporation continues, more particles will buildup near the drop edge resulting in the formation of particle-rings. Experiments show that while suspensions of small particles (about 1 micron diameter) do form rings, larger particles (5 micron or larger) move toward the center of the drop. To understand this phenomenon we analyze the problem of determining capillary forces on particles partially protruding from a gas-liquid interface and the influence of the protruding particles near the drop edge on the contact angle at the gas-liquid-substrate line. A criterion is derived for predicting conditions under which the particles will form the ring pattern.

The second part is concerned with the calculation of capillary interactions among many protruding particles and the resulting self-assembly of particles either resting on a substrate or floating at a gas- liquid interface. We consider both cylindrical and spherical particles. It is shown that the capillary interactions among spherical particles are screened so that the rate of self-assembly is considerably smaller than for cylindrical particles.

3-D Wave Dynamics driven by Cavitation - Equilibrium Phase Transition versus Disperse Bubbly Non-equilibrium Modelling

*Guenter H. Schnerr Technical University of Munich

Ismail H. Sezal Technical University of Munich *Steffen J. Schmidt Technical University of Munich

Abstract The aim of the present investigation is modelling and analysis of complex, 3-D cavitating, compressible liquid flows, especially the detection of shock waves and their interaction with collapsing vapour clouds.

Therefore, we recently developed a Riemann problem based finite volume solver, CATUM (CAvitation Technical University Munich), to simulate unsteady 3-D liquid flows with phase transition. The full compressible formulation enables the resolution of all scales of unsteady pressure, density and temperature fields by using time steps down to Δt≤10^(-9) s. This high temporal resolution is necessary to resolve wave dynamics that leads to acoustic cavitation and to detect regions of instantaneous high pressure loads.

The first part presents results of highly unsteady two-phase flow around a 3-D twisted hydrofoil. This specific hydrofoil allows the detailed study of sheet and cloud cavitation patterns, together with 3-D shock dynamics, emerging from collapsing vapour regions. The time dependent development of vapour clouds and the resulting unsteady variation of lift and drag are discussed in detail and are compared with experimental data.

Subsequently, potential and limitations of the actual equilibrium two-phase model of CATUM are discussed and compared with solutions of dispersed bubbly liquid models with respect to its application to cavitating flows. Therefore, dependent on spatial and temporal discretization, we compare the dynamics of collapsing bubbles based on the Rayleigh-Plesset equation with solutions of the equilibrium phase transition model.

Finally, we discuss the extension of CATUM for inclusion of non-equilibrium phase transition models with focus on theoretical and numerical requirements for their implementation in compressible liquid flows. Here we regard the models of Rayleigh, Rayleigh-Plesset, empirical rate equations for growth and collapse and extended models for bubble clouds.

Concentration distribution, recirculation length, and pressure drop for a concentrated suspension flowing through an abrupt contraction-expansion

Nina Shapley Department of Chemical Engineering, Columbia University

*Tracey Moraczewski Department of Chemical Engineering, Columbia University

Abstract Our research aims to enhance the fundamental understanding of the flow of a concentrated suspension through an abrupt contraction-expansion, which can be encountered in such applications as materials processing or flow in the circulatory system. The abrupt, axisymmetric contraction- expansion is a classic flow geometry that has been utilized in many flow studies of Newtonian fluids and single-phase, non-Newtonian materials. However, contraction-expansion flows of concentrated suspensions have received less attention in the literature. Of particular interest is the relationship of the particle concentration distribution, which can be spatially nonuniform, to the length of recirculating regions in the expansion and to the total pressure drop.

In this study, suspensions of neutrally buoyant, noncolloidal spheres in viscous, Newtonian liquids undergo steady, pressure-driven flow in an abrupt, axisymmetric 1:4 contraction-expansion. Nuclear magnetic resonance imaging (NMRI) is used to measure the steady-state particle concentration and velocity profiles. Wall-mounted pressure transducers record the pressure drop across the contraction- expansion tube section. The effect of shear-induced particle migration on the concentration, velocity, and pressure fields in the system is investigated, and the role of particle and flow properties (e.g. particle volume fraction, particle size, flow Reynolds number, and inlet conditions) is examined. Comparison of experimental results with continuum model functions can provide further insight into suspension flow behavior in a complex geometry.

The dynamics of colloidal rod suspensions under induced-charge electrophoresis

Eric S.G. Shaqfeh Stanford University

*David Saintillan Courant Institute

*Brendan Hoffman Stanford University

*Eric Darve Stanford University

Full text: Not available Last modified: December 1, 2006 Presentation date: 06/14/2007 3:00 PM in ITU Macka Conference Room (View Schedule)

Abstract It is now well-known (see Squires & Bazant 2005) that, in a polarizable, colloidal suspension, under application of an external electric field, the phenomenon of induced-charge electrophoresis (ICEP) occurs. We present theory and large scale numerical simulations to study the collective dynamic effects associated with this phenomenon in dilute and non-dilute colloidal rod suspensions. In the ICEP phenomenon, using a new multi-particle formulation of slender-body theory for the suspension interactions, we demonstrate that the field causes both alignment of the rods as well as ion migration in the solvent bath as a result of the particle polarization. Thus the field drives an induced stresslet flow in the vicinity of the particles, and, in the thin EDL limit, the hydrodynamic interactions created by these induced flows can be exactly captured within slender body theory. We demonstrate that these induced flow interactions cause “particle pairing” much like that in the swimming interactions of biological organisms, as well as diffusive center of mass motion. These induced flow interactions are then examined in light of their effect on two classic suspension problems: sedimentation and shear flow. In the sedimentation of colloidal rods under ICEP, strong particle alignment in the direction of the electric field tends to stabilize the now well known suspension concentration instabilities that result from the coupling of particle orientation and the sedimentation velocity. The suspension is shown to be stable to concentration fluctuations for sufficiently strong fields. Upon stabilization, the average sedimentation velocity of the particles is hindered, and we present calculations of both the stability boundary in terms of the dimensionless applied field, as well as a theory for the hindered setting function. Our results have direct application to microfluidic technology associated with nanobarcodes, where micron sized rods encode reactant information and where the codes are scanned in a microbarcode reader. We shall discuss our findings in light of this technology.

From DNS to LES of heavy particle dispersion in wall-bounded turbulent flows

Alfredo Soldati Dipartimento di Energetica e Macchine and Centro Interdipartimentale di Fluidodinamica ed Idraulica, Universita' di Udine

*Maria Vittoria Salvetti Dipartimento di Ingegneria Aerospaziale, Universita' di Pisa

*Cristian Marchioli Dipartimento di Energetica e Macchine and Centro Interdipartimentale di Fluidodinamica ed Idraulica, Universita' di Udine

Abstract The dispersion of particles with finite inertia in wall-bounded turbulent flows is characterized by phenomena such as non-homogeneous distribution, large-scale clustering and preferential concentration in the near-wall region due to the inertial bias between the denser particles and the lighter surrounding fluid [1]. Both Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) together with Lagrangian particle tracking have been widely used to investigate and quantify these macroscopic phenomena, for instance in vertical turbulent pipe and channel flows [1,2]. While DNS is able to capture particle preferential distribution in the proximity of the wall leading to locally non-uniform deposition rates, LES has proven inadequate to predict particle accumulation in the wall region and, in turn, particle deposition [3]. To circumvent this problem, Sub-Grid Scale (SGS) models to recover the influence of the filtered scales on particle motion have been recently developed and validated [3,4]. Development and validation of these models require accurate and reliable databases to perform rigorous, systematic analyses of the SGS effects on particle motion under different flow conditions. The present work represents a contribution in this direction by studying the closure problem in Lagrangian particle tracking one-way coupled with LES. To this purpose, a well validated and tested numerical set-up is used, namely a pseudo-spectral code for the Eulerian simulation of the plane channel flow coupled with a Lagrangian tracking algorithm [1]. Objectives of the present study can be itemized as follows. 1) Create a database for the benchmark case of particle-laden turbulent channel low in which different values of the flow Reynolds number and of the particle relaxation time are considered. In this paper, we will show fluid velocity and particle velocity statistics reported from databases with grid resolution up to 512^3, shear Reynolds number equal to 150, 300 and 600 [5] and non-dimensional particle relaxation time [6] equal to 0.2, 1, 5, 25 and 125. 2) Use this database to investigate on the importance of the SGS velocity fluctuations in predicting the statistical properties of the dispersion process. We will focus on the effects due to changes in particle inertia (obtained by tuning of the particle size with respect to the filtered spatial scales) or in grid resolution as well as on possible flow Reynolds number scaling properties of particle preferential concentration. 3) Provide subsidies for the development of new SGS models for particles which can account for the abovementioned effects properly. 4) Based on these subsidies, derive closure models for the equations of particle motion and evaluate their performance through real DNS, filtered DNS in a-priori tests and real LES in a-posteriori tests. One idea we are currently validating is to reconstruct the SGS fluid velocity fluctuations by means of the fractal interpolation technique [7] to develop a SGS model for the Navier-Stokes equations.

References [1] Marchioli C, Soldati A (2002) Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech., vol. 468, pp. 283--315. [2] Uijttewaal WSJ, Oliemans RVA (1996) Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows. Phys. Fluids, vol. 8, pp. 2590--2604. [3] Kuerten JGM, Vreman AW (2005) Can turbophoresis be predicted by large-eddy simulation? Phys. Fluids, vol. 17, pp. 011701. [4] Fevrier P, Simonin O, Squires KD (2005) Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially-uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech., vol. 528, pp. 1--46. [5] The shear Reynolds number of the flow is defined as $Re_{tau} = h u_tau /nu$ where $h$ is the channel half height, $nu$ is the fluid kinematic viscosity and $u_{tau}$ is the shear velocity, defined as $u_{tau}=sqrt{tau_{w} / rho}$, where $tau_{w}$ is the wall shear stress and $rho$ is the gas density. [6] The particle relaxation time is defined as $tau_{p}=rho_{p}d^{2}_{p}/18mu$ where $rho_p$ is the particle density, $d_p$ is the particle diameter and $mu$ is the fluid dynamic viscosity. The non- dimensional particle relaxation time, namely the particle Stokes number, is defined as $St=tau_{p}/tau_{f}$ where $tau_{f} = nu / u_{tau}^2$ is the characteristic time-scale of the flow. [7] Salvetti MV, Marchioli C, Soldati A (2006) On the closure of particle motion equations in large-eddy simulation.In Direct and Large-Eddy Simulation, Ed by E. Lamballais, R. Friedrich, B.J. Geurts, O. Metais (Springer Netherlands) vol. 6, pp. 311--318.

Simulation and modelling of aggregate behaviour

Martin Sommerfeld Martin-Luther-Universitaet

Sebastian Stübing Martin-Luther-Universitaet

Mathias Dietzel Martin-Luther-Universitaet

Stefan Blei BASF

Abstract The agglomeration of particles is of great importance for numerous industrial processes, such as vapour condensation in combustion synthesis, crystallisation, precipitation and spray drying. The major objective in most of these processes is the design of the particles (i.e. agglomerates) in order to yield desired product properties, as for example structure or shape, porosity and number of primary particles involved. Such a product design is nowardays usually done experimentally by try and error. However, this approach is quite time consuming and costly. Therefore, in recent years CFD is increasingly applied also in the above mentioned industrial areas for process optimisation. Besides population balances also the two-fluid approach or the Euler/Lagrange method are being used for predicting such very complex two-phase flows. All of these methods however require detailed information on the production of agglomerates through inter-particle collisions and the transport of the agglomerates in the reactor for deriving appropriate models. For allowing numerical computations of spray dryers the Euler/Lagrange approach was further extended to account for collisions between particles with different properties (Blei & Sommerfeld 2004 and 2006). These different particle properties result from the evaporation of solvent and the associated increase of the solids content in the droplet. Hence, collisions between surface tension and viscous dominated droplets as well as dry particles were identified and for each type of collision an appropriate collision model was derived on the basis of a stochastic modelling frame proposed by Sommerfeld (2001). Especially the collision of viscous droplets is essential for the agglomerate structure due to the partial penetration of colliding droplets in such a situation. A typical result for particle agglomeration in a defined homogeneous isotropic turbulence is shown in Fig. 1, where the PDFs of the penetration depth are plotted for different droplet viscosity, i.e. solids content. It is clear from this result that high viscous droplets yield only small penetration and hence weaker agglomerates. For low viscosity droplets the penetration depth is much higher whereby strong agglomerates are generated. Based on these inter-particle collision models also the development of the particle size distribution in a spray dryer was calculated (Blei & Sommerfeld 2006). The results provide information on the volume equivalent agglomerate size, the number of primary particles and the distributions of the penetration depth. For a further characterisation of the agglomerates the collision models were extended and for each agglomerate (in the computations still treated as a Lagrangian point particle) the position vectors of the primary particles in the agglomerate are stored for a representative agglomerate number. By applying a convex hull to the agglomerates also their porosity could be estimated which is an important property of the aggregates. In all these computations the agglomerates are still treated as solid spheres with the adequate volume equivalent diameter. This is however a crude assumption in calculating the fluid dynamic forces acting on agglomerates. Therefore, the Lattice-Boltzmann method was applied to calculate resistance coefficients of aggregates in dependence of their fractal dimension. These results will be used to derive appropriate correlations for the drag, lift and moment coefficients to be used in Lagrangian computations. A typical result of the the flow field around an agglomerate is shown in Fig. 2. References Blei, S. and Sommerfeld, M.: Computation of agglomeration for non-uniform dispersed phase properties – an extended stochastic collision model. 5th International Conference on Multiphase Flow, ICMF`04, Yokohama, Japan, Paper No. 438 (2004) Blei, S. and Sommerfeld, M.: Consideration of particle interactions in spray dryer modelling: An extended Euler-Lagrange approach. 15th International Drying Symposium (IDS 2006), Budapest, Hungary, August 2006. Sommerfeld, M.: Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. International Journal of Multiphase Flows, Vol. 27, 1828-1858 (2001)

Surfactant effect on the lift force acting on a bubble and bubble clustering phenomenon

Shu Takagi The University of Tokyo

Toshiyuki Ogasawara The University of Tokyo

Masato Fukuta The University of Tokyo

Yoichiro Matsumoto The University of Tokyo

Abstract Bubble clustering phenomenon in an upward turbulent channel flow and the effect of surfactant on the structure are discussed. 3-Pentanol and Triton-X100 are used as surfactant. Experiments are conducted under the condition of void fraction less than 1%. Surfactant concentration is set in 20- 170ppm in the case of 3-Pentanol and 2ppm Triton-X100. Under the condition of 20ppm 3-Pentanol, highly accumulated bubbles near the wall form crescent-like shape bubble cluster. The bubble cluster increases its horizontal size with the increase of surfactant concentration and maximum size becomes larger than an interval of coherent structure of the single-phase turbulence. Further increase of surfactant concentration, then, reduces the cluster size and the clusters disappear in the case of 168ppm concentration. In surfactant solution, boundary condition of bubble surface is changed by Marangoni effect due to the surface concentration distribution of surfactant along the bubble surface. Around Re=100, as are shown by Legendre & Magnaudet(1998) and Bagchi & Balachandar(2002), clean bubble (free-slip bubble) feels much stronger shear-induced lift than freely rotating rigid sphere (no-slip bubble). Because of surfactants presence, the surface velocity is retarded and the boundary condition approaches from free-slip to no-slip. This change affects the lift force on bubbles and the spatial distribution of the bubbles in upward channel flow is altered drastically. Numerical simulations are also conducted to study quantitatively the effect of surfactant adsoption / desorption kinetics on the lift force acting on a bubble. It has been shown that the Marangoni effect produces the retarded surface velocity profile and this gives the rapid reduction of the shear-induced lift force with the increase of bulk surfactant concentration. All of these results lead the conclusion that the lift force is the dominant factor of bubble clustering phenomena in upward bubbly channel flows.

Large Scale Multiphase Flow Analysis by an Immersed Boundary Technique Coupled with FEM and VOF for Incorporating Deformable Objects and Multiple Species of Fluids

Shintaro Takeuchi Osaka University

*Takeo Kajishima Osaka University

*Ryuichi Iwata Osaka University

*Yoshihiko Yuki Osaka University

Abstract Interaction problem of rigid/deformable solid objects with multiple fluids system is often observed in nature, industry and biological systems. The examples include bubbly flows in boiling-water reactor, petroleum industry, combustion system, water purification system and blood-borne micro-bubbles for angiography. A common problem in analysing the behaviour of the dispersed phases in those systems is that it is difficult to model the dynamics of the inter-phase interaction and clustered behaviours. In the present study, the authors will show recent attempts for the problems with our immersed boundary technique coupled with volume of fluid (VOF) method and finite element method (FEM) for incorporating rigid/elastic solid objects in a single or multiple immiscible fluids.

The above systems commonly involve solid surfaces in fluid. Implementation of moving rigid surface (moving boundary problem) in a fluid is based on an immersed boundary method (IBM) of body-force type by the author [1,2]. In this method, the inter-phase momentum exchange is calculated through the distributed interaction-force field shared by both Eulerian and Lagrangian references, rather than a coupling of phases by cross-interpolation of physical properties between the two references. This interaction algorithm offers a considerably efficient computation, and it has enabled direct numerical simulation (DNS) of interaction problem between a fluid and rigid spherical particles of a total number of O(1000) [1,2].

For simulation of behaviours of rigid body in a multiple immiscible fluids system, volume of fluid (VOF) method[4] is applied. The authors show that the treatment for moving solid boundary in a single fluid established in the above IBM is fully applicable to the system involving multiple fluids interface. In this approach, a volume averaged velocity field (hereafter, integrated velocity field) of the existing solid and fluids phases is governed by the equation of continuity and the Navier-Stokes equation with the above interaction force and surface tension. The velocity and pressure fields are apparently time- advanced by the SMAC procedure, irrespective of the substances (fluids or rigid object) occupying the cell. The rigid particles undergo the same interaction force with the opposite sign, and time- advancement of the solid phase is completed by integrating the forces multiplied by the local- averaged fluid’s density over the volume of the particle. The use of the same interaction force for all the existing phases in a shared cell guarantees the momentum preservation between the phases. Applicability of the present method is demonstrated in 2-D flow fields under the effect of gravity. In the present work, a total of O(100) monosized particles are employed allowing three degrees of freedom (translation and rotation). Particle suspension in the multiple-fluid flow will be studied in a wide range of conditions for volume and density ratios. Figure 1 (omitted) shows a snapshot of descending particles in the flow field. The two species of fluids are found to be affected by the movements of the particles, and vise versa.

The second attempt with our IBM approach is coupling with finite element method (FEM) for deformable object in a single fluid. The difficulty lies in the way of incorporation of elastic effect into the dynamics of the fluid. In the present study, the interaction force appeared in the IBM is incorporated into FEM through a superposition of the interaction-force field with the solid internal force field. This process does not cause any changes in algorithm for the time-advancement of the integrated velocity field, and therefore, the efficient computation (for the above fluid-rigid interaction problems) also applies here again. The surface digitiser[3] is found to be essential for identifying time- dependent geometry of the deformable solid interface. With this approach, the full-scale simulation of interaction between multiple elastic objects and a fluid is attempted in 2-D open space under gravitational force. A total of O(100) elastic particles are employed. The bulk solid volume fraction is found to be below 0.5%, where the effect of collisions on the whole flow field remains negligible. Figure 2 (omitted) shows snapshots of the flow field. The particles are confirmed to deform due to the hydrodynamic forces as the particles descend, and some particles are observed to be trapped in the wake of the predecessors. In the present work, the deformable effect on particle clustering and lubrication will be studied.

References [1] Kajishima, T., Takiguchi, S., Hamasaki, H. and Miyake, Y., "Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding", JSME Int. J. Ser. B, 44-4, pp.526-535, 2001 [2] Kajishima, T. and Takiguchi, S., "Interaction between particle clusters and fluid turbulence", Int. J. Heat and Fluid Flow, 23-5, pp.639-646, 2002 [3] Yuki, Y., Takeuchi, S. and Kajishima, T. "Efficient Immersed Boundary Method for Strong Interaction Problem of Arbitrary Shape Object with the Self-Induced Flow" J. Fluid Science and Technology, 2-1, pp.1-11, 2006 [4] Hirt, C.W. and Nichols, B.D. "Volume of fluid (VOF) method for the dynamics of free boundaries" J. Comput. Phys. 39-1 pp.201-225, 1981

Interfacial Instabilities and Breakup in Intense Multiphase Interactions Theo Theofanous University of California, Santa Barbara

Abstract We are interested in particle-size distributions, and “equilibrium-cloud” dimensions resulting from liquid masses released at supersonic speeds in the atmosphere. In this presentation I will discuss progress on experimental, theoretical, and computational issues that arise in inception and early growth of interfacial instabilities—this is a key ingredient of our overall strategy [1].

Our methods include:

(a) A large-scale pulse, supersonic (Mach 3) wind tunnel, providing 100 ms flows at pressures from ¼-atmosphere down to 10 Pa (~80 km atmospheric altitude); a shock tube equipped with a large- scale catch chamber, providing dynamic pressures of up to 2 MPa; visualization with time resolutions of 15 ns at rates of up to 50 kHz, and of 3 ns on a single-pulse, 16-beam (essentially full-flow field coverage) digital recording system, in shadow or Laser-Induced Fluorescence (LIF) operating modes;

(b) A linear stability analysis code for multiphase systems with sharp and/or diffuse interfaces, multilayer configurations, pressure and/or shear driven, with density/viscosity ratios and molecular diffusivities that reach up to those of gas-liquid properties (all-regime Orr-Sommerfeld, AROS). In the mathematical formulation the constitutive law is consistently applied to the base-flow and the disturbance equations. Key ingredients of the code are quadruple precision arithmetic, and the Chebyshev collocation method with domain decomposition, allowing for the resolutions necessary to obtain convergent solutions even at exceedingly high Schmidt numbers and as the diffuse layer thickness is let approach zero.

(c) A sharp-interface method (SIM) for direct numerical simulation of interfacial flows implemented in our MuSiC code [2,3]. The method is based on the Level Set approach and Structured Adaptive Mesh Refinement, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to 3rd-order spatial accuracy. Key in this regard are: avoidance of numerical mixing, and a Least- Squares interpolation method that is supported by irregular datasets distinctly on each side of the interface.

With LIF, at very high Weber numbers, we show strong interaction/competition between Rayleigh- Taylor (R-T) instability and shear-induced flow, and thus a completely different drop-breakup regime than that found in previous experimental and theoretical works. With AROS we show that the Yih instability can be approached monotonically in high-Sc shear flows as the diffuse layer thickness is let approach zero. With AROS we also show that that MuSiC-SIM converges at near theoretical rates to the correct results for viscous Kelvin-Helmholtz (vK-H) flows. With MuSiC-SIM we show prediction of growth factors in the linear regime for both R-T and vK-H flows, of neutral-stability maps for the Yih instability in vK-H flows, and self-selection of the most unstable wave in multimode R-T flows. These provide the essential basis for numerical simulation of the complex, non-linear interactions found in exquisite clarity and detail in our experiments.

1. Theofanous, T.G., et al, “Compressible Multi-Hydrodynamics (CMH): Breakup, Mixing, and Dispersal, of Liquids/Solids in High Speed Flows”, in Proceedings of an IUTAM Symposium on Computational Approaches to Disperse Multiphase Flow, S. Balachandar and A. Prosperetti (eds.), Springer, pp.353-369, Dordrecht, 2006. 2. Nourgaliev, R.R., Dinh, T.N., and Theofanous, T.G., “Adaptive Characteristics-Based Matching for Compressible Multifluid Dynamics”, Journal of Computational Physics, 213(2), 220–252, 2006. 3. Nourgaliev, R.R., and Theofanous, T.G., “High-Fidelity Interface Tracking in Compressible Flows: Unlimited Anchored Adaptive Level Set”, Journal of Computational Physics (in press), doi:10.1016/j.jcp.2006.10.031, 2007.

Coating Flow of viscous liquids on a rotating vertical disc

Mahesh Tirumkudulu Chemical Engineering, Indian Institute of Technology-Bombay

Abstract We report the formation of a ring like structure (donut shaped) in the flow of particular non-Newtonian liquids coating a rotating vertical disc. Experiments were performed with a known volume of the liquid and at varying rotation rates such that the inertial effects were negligible. Liquid injected on the rotating disc initially coats the surface uniformly, which then redistributes itself such that at steady state a significant amount collected into a circular ring, off center with the axis of rotation. Beyond a critical rotation speed and for a given liquid volume, the ring formation did not occur. The ring formation was not observed in the case of Newtonian liquids. In order to better understand the ring formation phenomenon, detailed experiments with viscous Newtonian liquids were performed at varying disc rotation speeds and liquid volumes, and the thickness profile at steady state was measured as a function of the spatial coordinates. A lubrication analysis for Newtonian liquid resulted in a time evolution equation for the film thickness that accounted for gravity, surface tension and viscous forces. The predicted thickness profiles are in good quantitative agreement with those obtained experimentally for moderate volumes of silicone oil. Experiments also showed that though the maximum liquid supported by the rotating disc varied with rotation rate and liquid viscosity, the numerical value of the dimensionless number signifying the ratio of gravity to viscous force was same in all the cases. Shear rate calculations for the Newtonian liquid along with the rheological measurements for the non-Newtonian liquids suggest that the shear thinning nature of the non- Newtonian liquids may be the cause for the observed ring formation.

Lift force acting on single fluid-particles in simple shear flows

Akio Tomiyama Kobe University

*Shigeo Hosokawa Kobe University

Full text: Not available Last modified: February 20, 2007

Abstract Trajectories of single drops and bubbles in linear shear flows of glycerol-water solutions were measured to evaluate lift forces acting on single fluid-particles. Experiments on drops were conducted under the conditions of -6.0 < logM < -4.7, 0 < Re < 19 and 3.2 < G < 6.0 [1/s] where M is the Morton number, Re the Reynolds number and G the velocity gradient of a linear shear flow. Those for bubbles were -5.1 < logM < -3.7, 0 < Re < 30 and 3.3 < G < 9.1 [1/s]. Lift coefficients CL were evaluated using measured trajectories, measured liquid velocity profiles and an equation of fluid- particle motion. As a result, the following conclusions were obtained: (1) for Re < 20, CL of spherical fluid-particles monotonously decreases to an asymptotic value as Re increases, (2) the asymptotic value is about 0.5 for bubbles and 0 for drops, (3) CL of deformed fluid-particles changes its sign from positive to negative as Re increases, and (4) further increases in Re results in further decreases in CL. Comparison between available theoretical models, interface tracking simulations and measured data will be also presented.

Direct Numerical Simulations of Bubbly Channel Flows

Gretar Tryggvason Worcester Polytechnic Institute

Abstract Direct numerical simulations are used to examine the behavior of relatively high void fraction bubbly flows in vertical channels. The results show that when the bubbles remain nearly spherical, the flow has a particularly simple structure, induced by lateral migration of the bubbles due to lift. At steady state the flow consisting of a homogeneous core in a hydrostatic balance and a wall-layer whose composition depends of whether the liquid is flowing upward or downward. For downward flow the wall-layer is bubble free, but for upward flow the bubble concentration in the wall-layer is higher than in the core. This simple structure leads to a very simple analytical model for the void fraction as well as the velocity for down flow. This simple structure seems to hold both for laminar and turbulent flows. We have also examined the effect of bubble deformability, which results in a completely different, yet relatively simple, flow structure. We will also discuss how the results compare with modeling using a two-fluid model. At high void fractions the probability of bubble coalescence increases and we will show a few results for the transient evolution of disperse bubbly flows as it transitions into annular and slug flows.

Steady bubble rise and deformation in Newtonian and Bingham fluids and conditions for their entrapment

John Tsamopoulos University of Patras

Yannis Dimakopoulos University of Patras

Abstract We examine the buoyancy-driven rise of a bubble in a Bingham fluid assuming axial symmetry and steady flow. Bubble pressure and rise velocity are determined, respectively, by requiring that its volume and center of mass remain constant. The continuous constitutive model suggested by Papanastasiou is used to describe the viscoplastic behavior of the material. The flow equations are solved numerically using the mixed finite-element/Galerkin method. The nodal points of the computational mesh are determined solving a set of elliptic differential equations to follow the often large deformations of the bubble-surface. The accuracy of solutions is ascertained by mesh refinement and by predicting very accurately previous experimental and theoretical results for Newtonian fluids. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties. Besides the yield surface away from the bubble which surrounds it, unyielded material can arise either behind the bubble or around its equatorial plane in contact with the bubble. As the Bingham number increases, the yield surface at the equatorial plane and away from the bubble merge and the bubble gets entrapped. When the Bond number is small and the bubble cannot deform from spherical the critical Bingham number is 0.143, i.e. it coincides with the critical Bingham number for the entrapment of a solid sphere in a Bingham fluid. As the Bond number increases allowing the bubble to squeeze through the material easier, the critical Bingham number increases as well.

The role of inertial waves in the pattern formation of a suspension in a cylinder rotating about a horizontal axis at small Ekman and Rossby numbers

Marius Ungarish Dept. Computer Science, Technion, Haifa, Israel

Seiden Gabriel Physics Dept., Technion

Lipson Steve G. Physics Dept., Technion

Abstract Non-Brownian particles suspended at low volume concentration in a rotating horizontal cylinder filled with a low-viscosity fluid tend to segregate into well-defined periodic vertical bands. We consider the interpretation of an experimental investigation in which we collected data concerning the dependence of the phenomenon on particle characteristics (i.e. size, shape and specific gravity), tube length to diameter ratio, and fluid viscosity. These observations reveal a robust phenomenon, which is independent to a large extent on particle characteristics. A theoretical explanation of the phenomenon is given along the following backbone: the segregation occurs as a result of the interaction between the gravity-induced motion of the particles and the inertial modes excited in the bounded rotating fluid. The theory assumes small Ekman and Rossby numbers, which is consistent with the parameter regime of our experiments. The inertial waves are expected to decay in general on the spin-up time interval, but the modes which are in resonance with the excitation of the particles prevail. The resulting flow field in the fluid carries the particles to the nodal planes and keeps them in the segregated quasi-steady-state pattern. Comparisons of the predicted and experimental positions of the bands show good agreements. Some considerations for improved simulations will also be presented and discussed.

References [1] S. G. Lipson, J. Phys. Condens. Matter 13, 5001 (2001). [2] G. Seiden, S. G. Lipson & J. Franklin, Phys. Rev. E 69, 015301 (2004). [3] G. Seiden, M. Ungarish & S. G. Lipson, Phys. Rev. E 72, 021407 (2005).

Forces and shape oscillations on ellipsoidal bubbles rising in water.

Christian Veldhuis University of Twente

*Leen van Wijngaarden University of Twente Full text: Not available Last modified: January 8, 2007 Presentation date: 06/14/2007 9:50 AM in ITU Macka Conference Room (View Schedule)

Abstract Both experimentally and by numerical simulation it has been shown in the recent past that small air bubbles rising in water bifurcate from a rectilinear path at a Reynolds number somewhere between 600 and 700. Beyond this the path may assume various shapes, among which the spiral and the zigzag are archetypes. With still larger bubbles, Reynolds numbers above 900, roughly, shape oscillations appear on the interface with the fluid. In the first part of our talk we present experimental results on the various bubble trajectories, the orientation of the bubbles along these, and the forces experienced. A new method is presented to measure accurately the minor axis of the bubbles under the assumption that these have an oblate ellipsoidal shape. This method means an improvement on the technique to calculate the forces applied in a recent paper by Shew et al. ( 2006) . As is well-known the wake consists of a pair of helicoidal line vortices with circulation of opposite sign. At a certain distance behind a bubble they become unstable and break up in vortical structures. Through the fluid dynamics of the trailing vortices, forces(and a torque) are exerted on a bubble. Since we could accurately measure the velocity of the bubbles, their shape, as well as properties of the vortices among which their circulation,we could measure the forces. This was done by establishing a force balance in a Frenet frame of reference and using known expressions for the added mass contributions. We compare the results obtained by us in this way with the simulation results by Mougin & Magnaudet (2006), and with the force measurements reported by Shew et al (2006). It appears from our measurements that the forces in normal and binormal direction are the same for pure spiraling motion. Our analysis of the wake structure and orientation confirms this equality and a simple general relation can be derived, giving the relation between spiral radius, pitch, and frequency. In the second part we pay attention to bubbles large enough for the appearance of surface oscillations. In particular the 2,0 and 2,2 modes, in the language of surface harmonics, are prominent. We paid a lot of effort in investigating the connection between on one hand the measured frequencies of these modes and on the other hand frequencies of changes in bubble velocity, changes in aspect ratio and frequencies connected with dynamics of the wake, such as vortex shedding. This was done both with purified water and with tap water which can be considered in this connection as contaminated. Several interesting conclusions are reported. For example, it appears that with purified water there is a clear correspondence between the 2,0 mode and the oscillations of tangential velocity, aspect ratio, and of the wake. This is no longer true for tap water. Another conclusion is that the 2,2 mode is strongly coupled with zigzag bubble motion. A comparison is made between our results and those obtained by,in particular, Lunde & Perkins (1998).

References Lunde , K. & Perkins, R.J., 1998 Shape oscillations of rising bubbles. Appl.SciRes.58, 387-408 Shew, W.L..Ponçet, S, & Pinton, F.,2006 Force measurements on rising bubbles. J.Fluid Mech. 569, 51-60 Mougin, G.& Magnaudet, J., 2006 Wake-induced forcesand torqueson a zigzagging/spiraling bubble. J.Fluid Mech. 567,185-194

Simulations of jet and droplet formation in droplet impacts and atomizing jets

Stephane Zaleski Universite Pierre et Marie Curie - Paris 6 Full text: Not available Last modified: March 6, 2007 Presentation date: 06/13/2007 9:50 AM in ITU Macka Conference Room (View Schedule)

Abstract Recent Volume of Fluid simulations of atomization and droplet impact will be discussed. Increased resolution allows to approach experimentally realistic parameter ranges, such as the high speed impacts of glycerine droplets on liquid layers photographed by S. Thoroddsen. Three dimensional simulations of free edge liquid sheets are shown and discussed in connection with the recent theory of I. Roisman. They offer a tentative mechanism for droplet formation in splash, sheet and jet breakup experiments.