Volume 18, Issue 12, December 2006
 SPECIAL TOPIC: INTERACTIONS FOR DISPERSED SYSTEMS IN NEWTONIAN AND VISCOELASTIC FLUIDS


Report of the Symposium on Interactions for Dispersed Systems in Newtonian and Viscoelastic Fluids, Guanajuato, Mexico, 2006^{a)}
View Description Hide DescriptionThis report summarizes the issues discussed during a Symposium of the International Union of Theoretical and Applied Mechanics, entitled “Interactions for Dispersed Systems in Newtonian and Viscoelastic Fluids,” which was held in March 2006 in Guanajuato, Mexico.

Clusters of particles falling in a viscous fluid with periodic boundary conditions
View Description Hide DescriptionExemplary dynamics of three point particles falling under gravity in Stokes flow with periodic boundary conditions is presented in a movie. Stable and unstable solutions of the equations of Stokesian dynamics are explicitly shown for two initial configurations: equilateral triangles with side lengths close to a critical size.

The effect of stratification on the wave number selection in the instability of sedimenting spheroids
View Description Hide DescriptionIt is well known that a dilute suspension of spheroids sedimenting under gravity at low Reynolds number is unstable to density fluctuations as a result of hydrodynamic interactions [D. L. Koch and E. S. G. Shaqfeh, J. Fluid Mech.209, 521 (Year: 1989)]. Using a linear stability analysis, it is shown that a vertical density gradient in such a suspension can lead to a wave number selection by damping fluctuations at long wavelengths. A scaling for the most unstable wavelength, or characteristic size of the density fluctuations, is obtained in terms of the background stratification and volume fraction, and is compared to results from numerical simulations in stratified particulate suspensions using methods that we have developed previously. In initially homogeneous suspensions, simulations show a continuous decay of the size of the density fluctuations over time, which we demonstrate can be attributed to the development of stratification inside the suspension.

Dynamics of bidisperse suspensions under Stokes flows: Linear shear flow and sedimentation
View Description Hide DescriptionSedimenting and sheared bidisperse homogeneous suspensions of nonBrownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the threedimensional Stokes equations forced by the presence of the dispersed phase. Multibody hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and nonhydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads to an enhancement of particle fluctuations and selfdiffusion. The velocityfluctuation tensor scales linearly up to 15% concentration. Multibody interactions weaken the correlation of velocityfluctuations and lead to a diffusionlike motion of the particles. Probability density functions show a clear transition from Gaussian to exponential tails while the concentration decreases. The behavior of bidisperse suspensions is more complicated, since the respective amount of small and large particles modifies the overall response of the flow. Our simulations show that, for a given concentration of both species, when the size ratio varies from 1 to 2.5, the fluctuation level of the small particles is strongly enhanced. A similar trend is observed on the evolution of the shear induced selfdiffusion coefficient. Thus, for a fixed and total concentration, increasing the respective volume fraction of large particles can double the velocityfluctuation of small particles. In the second part of the paper, the sedimentation of a single test particle embedded in a suspension of monodisperse particles allows the determination of basic hydrodynamic interactions involved in a bidisperse suspension. Good agreement is achieved when comparing the mean settling velocity and fluctuation levels of the test sphere with experiments. Two distinct behaviors are observed depending on the physical properties of the particle. The Lagrangianvelocity autocorrelation function has a negative region when the test particle has a settling velocity twice as large as the reference velocity of the surrounding suspension. The test particle settles with a zigzag vertical trajectory while a strong reduction of horizontal dispersion occurs. Then, several configurations of bidisperse settling suspensions are investigated. Mean velocity depends on the concentration of both species, density ratio and size ratio. Results are compared with theoretical predictions at low concentration and empirical correlations when the assumption of a dilute regime is no longer valid. For particular configurations, a segregation instability sets in. Columnar patterns tend to collect particles of the same species and eventually a complete separation of the suspension is observed. The instability threshold is compared with experiments in the case of suspensions of buoyant and heavy spheres. The basic features are well reproduced by the simulation model.

Interaction of cavitation bubbles on a wall
View Description Hide DescriptionWe report experimental and numerical investigations on the dynamics of the cavitation of bubbles on a solid surface and the interaction between them with the help of controlled cavitation nuclei: hemispherical bubbles are nucleated from hydrophobic microcavities that act as gas traps when the substrate is immersed in water. The expansion of these nuclei is triggered by an impulsive lowering of the liquidpressure. The patterning of the substrate allows us to control the number of bubbles and the distance between them. Each hemispherical bubble experiences the effect of its mirror image. Correspondingly, an isolated hemispherical bubble together with its mirror image behaves like a free spherical bubble, i.e., its dynamics is well described by the RayleighPlesset equation. We employ the setup to study the dynamics of two and more bubbles in a row at controlled and fixed distances from each other. For weak interaction, namely when the maximum size of the bubbles is smaller than the bubble distance, the dynamics of the system is well captured by an extended RayleighPlesset equation, where mutual pressure coupling through sound emission is included. Bubble pairs last longer than an isolated bubble as neighboring bubbles modify the surrounding pressure and screen each other. For strong interaction, obtained by increasing the tensile stress or decreasing the bubble distance, the bubbles eventually flatten and form a liquid film between each other which can rupture, leading to coalescence. The film thinning is inertia dominated. A potential flow boundary integral simulation captures the overall shape evolution of the bubbles, including the formation of jets horizontal to the wall. These horizontal jets are caused by symmetry breaking due to the neighboring bubbles.

Dynamics of particleparticle collisions in a viscous liquid
View Description Hide DescriptionWhen two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquidimmersed headon and oblique collisions, which complements previously investigated particleonwall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particlewall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects.

Collapse and growth of cavity regions in granular media due to viscous flow
View Description Hide DescriptionExperimental studies of viscousflow are made on the effect of macroscopic cavity regions in an otherwise homogeneous granular material. The presence of such cavity regions enhances local velocity, which can accelerate the collapse of their boundaries. At the same time, the mobilized regions grow toward the upstream direction. In a continuation of our previous paper [Kaneko and Sano, Phys. Fluids17, 033102 (2005)], we focus our attention on the latter processes in this paper. For a certain configuration of two interacting cavities, mobilized regions spread faster and in larger scale, which is likely to play an important role in the network formation of a water channel and the onset of a landslide. A numerical simulation based on the twofluid model is also performed, and is compared with our experimental results.

Selection of the ripple length on a granular bed sheared by a liquid flow
View Description Hide DescriptionThe stability of a granular bed sheared by a liquid flow is investigated using an erosiondeposition model for the moving grains. Extending to arbitrary wave number a previous long wave analysis [F. Charru and E. J. Hinch, J. Fluid Mech.550, 111 (2006)], this study shows that short waves are stabilized by a cresterosion mechanism that is absent when the local particle flux is assumed to be in equilibrium with the local bed shear stress. The cutoff length associated with this mechanism scales on a deposition length of the particles. This characteristic length is similar, although of a different physical nature, to the inertial length involved in relaxation models of dune dynamics under the wind. Two stabilizing mechanisms cooperate for the most amplified wave number: the new cresterosion mechanism and the gravity force parallel to the local slope of the inclined bed. The predictions of this model are compared to observations, showing better agreement than previous stability analyses, which strongly underpredict the observed lengths.

On velocity profiles and stresses in sheared and vibrated granular systems under variable gravity
View Description Hide DescriptionWe employ discrete element threedimensional simulations that include realistic modeling of physical system boundaries to determine the influence of gravity on velocity profiles and stresses for frictional inelastic particles that are confined in an angular Couette cell, and sheared by a rotated upper wall. In addition to Earth gravity, we consider other gravitational fields, in particular those of the Moon and Mars. The computational techniques are based on hardsphere simulations of polydisperse particles at relatively high volume fraction (50–55%). We find that the presence of gravity induces significant changes of the velocity profiles and stresses. One important nondimensional parameter in the problem is shown to be , where is the imposed shear rate, is the weight of the system per unit area due to gravity, and is the solid density. We also consider systems that are vibrated in addition to being sheared, since vibrations are one of several important methods for agitating (e.g., fluidizing and/or unjamming) granular systems. We find that the introduction of nondimensional acceleration , where are the amplitude and frequency of oscillations, and the acceleration of gravity, explains novel features that develop in these complex granular systems.

A study of velocity discontinuity for single air bubbles rising in an associative polymer
View Description Hide DescriptionThe motion of air bubbles in aqueous solutions of a hydrophobic alkaliswellable associative polymer is studied in this work. The associative nature of these polymer systems dictates their rheological properties: for moderate values of the shear rate, the formation of structure can lead to a shearthickening behavior and to the appearance of first normal stress difference. For larger shear rates, the polymer associations can be broken, leading to shear thinning. In general, these fluids show a Newtonian behavior for small values of the shear rate, but behave as viscoelastic liquids for large shear rates. Experimental results show the appearance of a critical bubble volume at which a discontinuity in the relation velocityvolume occurs; however, the velocity increase found in this case is not as large as that previously reported for the case of shearthinning viscoelastic fluids. The discontinuity is associated with a significant change of the bubble shape: before the critical volume, the bubbles are convex spheroids, while past the critical volume a sharp cusped end appears. The appearance of the tail is also associated with the appearance of an inflection point (change of curvature) on the bubble surface. Moreover, since the rheology of the liquids is measured it was found that the discontinuity, and hence the change of shape, occurs when the elastic nature of the liquid first manifests itself (appearance of a first normal stress difference). A comparison of the measured velocities for small bubbles with predictions from a StokesHadamard law shows a discrepancy. The Newtonian viscositymeasured in a viscometric flow was smaller than that determined from a fallingball arrangement. Considering the viscositymeasured under this nonviscometric flow, the comparison between theory and experiments was very good for bubbles having volumes lower than the critical one. Moreover, due to the importance of the elasticity, and due to the change of the shape of the bubble, a dimensionless number formed as the ratio of elastic to surface tension forces clearly defines the change of the behavior for the bubbles rising in these fluids. Finally, a photographic study of the peculiar shapes of the bubble tails, tip, and edgestreaming phenomena is presented. To our knowledge, experiments in this class of fluids have not been reported to date.

Entrapped air bubbles in piezodriven inkjet printing: Their effect on the droplet velocity
View Description Hide DescriptionAir bubbles entrapped in the ink channel are a major problem in piezodriven inkjet printing. They grow by rectified diffusion and eventually counteract the pressure buildup at the nozzle, leading to a breakdown of the jetting process. Experimental results on the dropletvelocity as a function of the equilibrium radius of the entrained bubble are presented. Surprisingly, shows a pronounced maximum around before it sharply drops to zero around . A simple onedimensional model is introduced to describe this counterintuitive behavior which turns out to be a resonance effect of the entrained bubble.

Microscale tipstreaming in a microfluidic flow focusing device
View Description Hide DescriptionA microfluidic flowfocusing device is used to explore the use of surfactantmediated tipstreaming to synthesize micrometerscale and smaller droplets. By controlling the surfactant bulk concentration of a soluble nonionic surfactant in the neighborhood of the critical micelle concentration, along with the capillary number and the ratio of the internal and external flow rates, we observe several distinct modes of droplet breakup. For the most part, droplet breakup in microfluidic devices results in highly monodisperse droplets in the range of tens of micrometers in size. However, we observe a new mode of breakup called “thread formation” that resembles tipstreaming and yields tiny droplets in the range of a few micrometers in size or smaller. In this work, we characterize the growth of the thread and its maximum length as a function of flow variables and surfactant content, and we also characterize the period of droplet breakup as a function of these variables. Our results suggest possible methods for controlling the process. Using a simple flow visualization experiment as the basis, we report on preliminary efforts to model the thread formation process.
