**Arezoo Motavalizadeh Ardekani**

*Assistant Professor*

School of Mechanical Engineering

585 Purdue Mall

West Lafayette, IN 47907

Dr. Ardekani is currently an assistant professor at the Purdue University. Her expertise is in fluid mechanics, biological and environmental flows. The results of her research have been presented in 130 journal articles and conferences. Prior to joining Purdue, she was an O’Hara, C.S.C., Assistant Professor at the University of Notre Dame and a Shapiro Postdoctoral Fellow at the Massachusetts Institute of Technology before that. She graduated from University of California Irvine with her Ph.D. in 2009. She received the Society of Women Engineers in 2007, Amelia Earhart awards in 2007 and 2008, Schlumberger Foundation faculty for the future grant in 2009 and 2010, NSF CAREER award in 2012, and Presidential Early Career Awards for Scientists and Engineers (PECASE) award in 2016.

*Funded by NSF Grant CBET-1150348-CAREER and CTSI Grant No. TR000006*

We have numerically investigated the effects of non-Newtonian fluid properties, including shear thinning and elasticity, on the locomotion of Taylor’s swimming sheet with arbitrary amplitude. Our findings show that the tiny swimmers are able to increase their speed while consuming less energy because of the shear-thinning behavior of their surrounding fluid. The fluid becomes less viscous very close to the swimmer. So basically there are corridors of low-viscosity fluid that the swimmers are moving inside, allowing them to go faster and also requiring less energy to swim. We have also provided a scaling law for the power consumption of Taylor’s swimming sheet with arbitrary amplitude.

- G. Li, A.M. Ardekani, “Undulatory swimming in non-Newtonian fluids", Journal of Fluid Mechanics Rapids, 784, R4, 2015.

*Funded by NSF CBET-1066545 and CBET-1414581*

The goal of this work is to answer the intriguing question vigorously argued in the literature during the past few years that whether the combined motion of marine organisms contributes to the ocean mixing. In the aphotic ocean (i.e. regions that are 200m beneath the sea surface), zooplankton are the most abundant organisms engaged in the diel vertical migration and their swimming Reynolds number, the ratio of inertial force to viscous force, is in the range of O(1−100). Therefore, it is important to examine the potential contribution of swimming organisms to the ocean mixing in this inertial regime. We utilize the squirmer model to resolve the hydrodynamic interactions of a suspension of swimmers in a density stratified fluid. Our study shows that the diapycnal eddy diffusivity, a measure of vertical mass flux, within a suspension of squirmers increases with Reynolds number and its magnitude is comparable to the value reported for the ocean turbulent mixing. The mixing efficiency, however, is very small in the range of O(0.0001–0.04) when the swimming Reynolds number is in the range of O(0.1–100). For a suspension of squirmers in a decaying isotropic turbulence, we find that the diapycnal eddy diffusivity enhances due to the strong viscous dissipation generated by squirmers as well as the interactions of squirmers with the background turbulence.

- S. Wang, A.M. Ardekani, “Biogenic mixing induced by intermediate Reynolds number swimming in a stratified fluid", Scientific Reports, 5, 17448, 2015.

*Funded by NSF Grant CBET-1150348-CAREER*

Isolating and capturing the least abundant cells play a vital role in diagnosis of some lethal diseases, such as malaria and cancer. Most current technologies can enhance concentration of circulating tumor cells in a sample; however, they face great challenges in their purification from whole blood. In recent years, a hydrodynamic-based cell focusing method has generated considerable interest because of its low price, simplicity and its independence from any electric potential. Despite experimental investigations of cell/particle separation and focusing using microfluidic chips, lack of full understanding of particle migration behavior in complex fluids hinders the clinical application of this technique.

In this work, we developed fully-resolved numerical tools to explore the dynamics of particle migration governed by the interplay of inertia, viscoelasticity and shear-thinning effects in a microfluidic channel flow. Inertial effects push the particle away from the centerline of the channel, while viscoelastic effects drive the particle towards the centerline. Competition between the two effects determines the equilibrium position of the particle. We showed that shear-thinning effects and secondary flows tend to move the particle away from the channel centerline. We introduced a scaling analysis based on the balance of inertial and elastic effects to explain these different behaviors. We illustrated that the particle has a larger transient migration velocity during flow start-up, which can be potentially used to accelerate the particle focusing. The cross streamline migration studied in this work can be used to design microfluidic devices for cell and particle focusing, sorting, separation, enrichment and trapping.

- G. Li, G.H. McKinley, A.M. Ardekani, “Dynamics of particle migration in a channel flow of viscoelastic fluids", Journal of Fluid Mechanics, 785, 486-505, 2015.

*Funded by NSF Grants CBET-1066545*

Widespread implications of settling particles in stratified fluids call for accurate assessment of a suspension of particles at pycnoclines. We perform direct numerical simulations of the motion of particles to quantify the effect of density stratification on the settling velocity and microstructure of a suspension of rigid particles. The flow field around particles is fully resolved, and a statistically steady-state condition is obtained after a transient acceleration of particles. Based on the simulation results, we propose a correlation for the mean settling velocity of the suspension as a function of solid volume fraction and background density gradient in a fluid column. The effect of the stratification on the microstructure of the suspension is also investigated by direct comparison of the pair correlation function between homogeneous and stratified fluids. It is shown that the presence of the background density gradient enhances the formation of horizontally aligned clusters in the fluid column.

- A. Doostmohammadi, A.M. Ardekani “Suspension of solid particles in a density stratified fluid", Physics of Fluids, 27, 023302, 2015.
- G. Li, A. Karimi, A.M. Ardekani “Effect of solid boundaries on swimming dynamics of microorganisms in a viscoelastic fluid,” Rheologica Acta, 53(12), 911-926, 2014 (invited paper for special early career issue: Trends and progress in rheology)
- Y. Hu, S. Wang, A. Abbaspourrad, A. M. Ardekani “Fabrication of shape controllable Janus alginate/pNIPAAm microgels via microfluidics technique and off-chip ionic crosslinking", Langmuir, accepted, 2015.
- S. Dabiri, A. Doostmohammadi, S. Bayareh, A.M. Ardekani “Numerical simulation of the buoyant rise of a suspension of drops in a linearly stratified fluid,” International Journal Multiphase Flow, 69, 8–17, 2015.
- Y. Hu, G. Azadi, A.M. Ardekani “Microfluidic fabrication of shape-tunable alginate microgels: Effect of size and impact velocity”, Carbohydrate Polymers, 120, 38-45, 2015.
- A. Doostmohammadi, A.M. Ardekani “Reorientation of elongated particles at density interfaces,” Physical Review E, 90, 033013, 2014.
- A. Doostmohammadi, S. Dabiri, A.M. Ardekani, “A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid,” Journal of Fluid Mechanics, 750, 5-32, 2014.
- G. Li, A.M. Ardekani “Hydrodynamic interaction of micro-swimmers near a wall,” Physical Review E, 90, 013010, 2014.
- M.J. Mercier, A.M. Ardekani, M.R. Allshouse, B. Doyle, T. Peacock, “Self-Propulsion of Immersed Objects via Natural Convection,” Physical Review Letters, 112, 204501, 2014. This work is highlithed on Physical Review Letter website.
- A. Karimi, A.M. Ardekani, “Gyrotactic bioconvection at pycnoclines,” Journal of Fluid Mechanics, 773, 245-267, 2013.
- S.H. Yazdi, A.M. Ardekani, “Bacterial aggregation and biofilm formation in a vortical flow,” Biomicrofluidics, Volume 6, 044114, 2012.
- A. Doostmohammadi, A.M. Ardekani, "Interaction between a pair of particles settling in a stratified fluid," Physical Review E, 88, 023029, 2013.
- A.M. Ardekani, E. Gore, “Emergence of a limit cycle for swimming microorganisms in a vortical flow of a viscoelastic fluid,” Physical Review E, Volume 85, 056309, 2012.
- A. Doostmohammadi, R. Stocker, A.M. Ardekani “Low Reynolds number swimming at pycnoclines,” Proceedings of the National Academy of Sciences, Volume 109, 3856-3861, 2012.
- A.M. Ardekani, R. Stocker “Stratlets: low Reynolds number point-force solutions in a stratified fluid” Physical Review Letters, 105, 084502, 2010.
- A.M. Ardekani, R. Stocker “Swimming at low Reynolds number in a stratified fluid” 16th US National Congress of Theoretical and Applied Mechanics, June 17-July2, 2010, State College, PA.
- A.M. Ardekani, V. Sharma, G.H. McKinley, “Dynamics of Bead Formation, Filament Thinning, and Breakup in Weakly Viscoelastic Jets,” Journal of Fluid Mechanics, Volume 665, 46-56, 2010.
- V. Sharma, A.M. Ardekani, G.H. McKinley “‘Beads on a String’ Structures and Extensional Rheometry using Jet Break-up” 5th Pacific Rim Conference on Rheology, August 1-6, 2010, Japan.
- A.M. Ardekani, V. Sharma, G.H. McKinley “Jetting and breakup of weakly viscoelastic liquids” 16th US National Congress of Theoretical and Applied Mechanics, June 17-July2, 2010, State College, PA.
- [1] A.M. Ardekani, R.H. Rangel, "Unsteady motion of two solid spheres in Stokes flow," Physics of Fluids, Volume 18, Issue 10, 2006.

- [2] A.M. Ardekani, R.H. Rangel, "Numerical investigation of particle-particle and particle-wall collisions in a viscous fluid," Journal of Fluid Mechanics, Volume 596, 437-466, 2008.

- [3] A.M. Ardekani, S. Dabiri, R.H. Rangel, "Collision of multi-particle and general shape objects in a viscous fluid," Journal of Computational Physics, Volume 227, 10094-10107, 2008

- [4] A.M. Ardekani, D.D. Joseph, D. Dunn-Rankin, R.H. Rangel, "Particle-wall collision in a viscoelastic fluid," Journal of Fluid Mechanics, Volume 633, 475-483, 2009

- [5] A.M. Ardekani, R.H. Rangel, D.D. Joseph, "Motion of a sphere normal to a wall in second-order fluid," Journal of Fluid Mechanics, Volume 587, 163-172, 2007.

- [6] A.M. Ardekani, R.H. Rangel, D.D. Joseph, "Two spheres in a free stream of a second-order fluid," Physics of Fluids, Volume 20, Issue 6, 2008.

- [7] A.M. Ardekani, S. Dabiri, R.H. Rangel, "Deformation of a droplet in a particulate shear flow," Physics of Fluids, Volume 21, 093302, 2009

*Funded by NSF Grant CBET-1150348-CAREER and CTSI Grant No. TR000006*

We numerically study the effect of solid boundaries on the swimming behavior of a motile microorganism in viscoelastic media. Understanding the swimmer-wall hydrodynamic interactions is crucial to elucidate the adhesion of bacterial cells to nearby substrates which is precursor to the formation of the microbial biofilms. The microorganism is simulated using a squirmer model that captures the major swimming mechanisms of potential, extensile, and contractile types of swimmers, while neglecting the biological complexities. A Giesekus constitutive equation is utilized to describe both viscoelasticity and shear-thinning behavior of the background fluid. We found that the viscoelasticity strongly affects the near-wall motion of a squirmer by generating an opposing polymeric torque which impedes the rotation of the swimmer away from the wall. In particular, the time a neutral squirmer spends at the close proximity of the wall is shown to increase with polymer relaxation time and reaches a maximum at Weissenberg number of unity. The shear-thinning effect is found to weaken the solvent stress and therefore, increases the swimmer-wall contact time. For a puller swimmer, the polymer stretching mainly occurs around its lateral sides, leading to reduced elastic resistance against its locomotion. The neutral and puller swimmers eventually escape the wall attraction effect due to a releasing force generated by the Newtonian viscous stress. In contrast, the pusher is found to be perpetually trapped near the wall as a result of the formation of a highly stretched region behind its body. It is shown that the shear-thinning property of the fluid weakens the wall-trapping effect for the pusher squirmer.

A novel method to fabricate shape controllable alginate/pNIPAAm complex microgels is reported. Monodisperse alginate/pNIPAAm droplets are created via microfluidics and crosslinked in different concentrations of hot glycerol/barium acetate water solutions. By changing the initial droplet size and glycerol concentration of the collecting solution, the resultant microgel shape and surface details can be systematically tuned. High-speed imaging is used to visualize and explain the microgel formation process.

*Funded by NSF Grants CBET-1066545*

Direct numerical simulations of a swarm of deformable drops rising in density stratified fluids are presented at intermediate Reynolds numbers. All flow scales are fully resolved using front-tracking/finite-volume method. The average rise velocity and velocity fluctuations of the swarm are reduced in the presence of density stratification. The isotropy in velocity fluctuations is enhanced as the volume fraction increases. The higher likelihood of the cluster formation is illustrated in the presence of density stratification and is explained by quantitative assessment of the microstructure using radial and angular pair probability distribution functions. The combined effect of the drop deformability and density stratification on the average deformation of the drops is investigated.

We report on a capillary-based microfluidic platform for the fabrication of non-spherical sodium alginate microgels. The sodium alginate droplets were crosslinked off-chip in a mixture of barium acetate and glycerol solution. Novel morphologies such as tear drop, lamp-like, mushroom-like, double-dimpled and bowl-like microgels were fabricated by controlling the size, impact velocity (at the crosslinking solution/oil interface), and concentration of sodium alginate solution. We monitored the microscale deformation process in situ at the interface and proposeed a deformation mechanism resulting in unique morphologies. Additionally, we constructed microgel superstructures by assembling the non-spherical alginate microgels to spherical poly(N-isopropylacrylamide) (pNIPAAm) microgels via electrostatic interaction.

*Funded by NSF Grants CBET-1066545 and CBET-1414581*

Density interfaces in the water column are ubiquitously found in oceans and lakes. Interaction of settling particles with pycnoclines plays a pivotal function in nutrient transport between ocean layers and settling rates of marine particles. We perform direct numerical simulations of an elongated particle settling through a density interface and scrutinize the role of stratification on the settling dynamics. It is found that the presence of the density interface tends to turn the long axis of an elongated particle parallel to the settling direction, which is dramatically different from its counterpart in a homogeneous fluid. Although broadside-on settling of the elongated particle is enhanced upon approaching the interface, the long axis rotates toward the settling direction as the particle passes through the interface. We quantify turning couples due to stratification effects, which counteract the pressure-induced torques due to the fluid inertia. A similar behavior is observed for different initial orientations of the particle. It is shown that the reorientation of an elongated particle occurs in both sharp and linear density stratifications.

*Funded by NSF Grants CBET-1066545 and CBET-1414581*

The transient settling dynamics of a spherical particle sedimenting in a linearly stratiﬁed ﬂuid is investigated by performing fully resolved direct numerical simulations. The settling behaviour is quantiﬁed for different values of Reynolds, Froude and Prandtl numbers. It is demonstrated that the transient settling dynamics is correlated to the induced Lagrangian drift of ﬂow around the settling particle. The peak velocity of the particle can be followed by the oscillation of the settling velocity and the particle can even reverse its direction of motion before reaching to its neutrally buoyant level. The frequency of oscillation of settling velocity scales with the Brunt–Väisälä frequency and the motion of the particle can lead to the formation of secondary and tertiary vortices following the primary vortex.

*Funded by NSF Grant CBET-1150348-
CAREER*

Organisms swimming at a low Reynolds number regime near a no-slip wall is a subject of growing interest in recent years for its importance in many health and environmental problems. For example, accumulation of bacteria near the surface and the formation of biofilms are closely related to many types of microbial infections. Here we focus on the near-wall swimming of an archetypal low-Reynolds number swimmer, called ``squirmer" . For a single squirmer, depending on the swimming mechanism, three different modes are distinguished: (a) the squirmer escaping from the wall, (b) the squirmer swimming along the wall at a constant distance and orientation angle, and (c) the squirmer swimming near the wall in a periodic trajectory. Near-wall accumulation in a suspension of squirmers is observed. In the near-wall region, pullers repel each other, while pushers are attracted to each other and form clusters.

Natural convection of a fluid due to a heated or cooled boundary has been studied within a myriad of different contexts due to the prevalence of the phenomenon in environmental and engineered systems. It has, however, hitherto gone unrecognized that boundary-induced natural convection can propel immersed objects. We experimentally investigate the motion of a wedge-shaped object, immersed within a two-layer fluid system, due to a heated surface. The wedge resides at the interface between the two fluid layers of different density, and its concomitant motion provides the first demonstration of the phenomenon of propulsion via boundary-induced natural convection. Established theoretical and numerical models are used to rationalize the propulsion speed by virtue of balancing the propulsion force against the appropriate drag force.

*Funded by NSF Grant No. CBET-1066545*

Bioconvection is a complex biological phenomenon causing spontaneous pattern formation and self-organization in the suspensions of motile bacteria and algae. It occurs as a result of the collective behavior of up-swimming microorganisms in response to the certain types of physical stimuli. We are interested in the special case of gyrotaxis where the swimming is directed by the balance of the viscous and gravitational torques. We investigate gyrotactic bioconvection in presence of stratification arising from thermal or solutal gradients in aquatic environments. Using large-scale numerical simulations, we explore different regimes of the flow by varying the boundary conditions and the strength of stratification. Also, we discuss the inhibition threshold of bioconvection in light of a linear stability analysis. The result can shed light on the characteristics of double-diffusive convection engendered by active swimmers in a stratified environment.

*Funded by NSF Grant No. CBET-1150348-
CAREER*

Microbial habitats are rarely at rest (e.g. ocean, blood stream, flow in porous media and flow through membrane filtration processes). In order to study the hydrodynamics of bacterial response in a vortical flow, we utilize a microfluidic system to mimic some of the important microbial conditions at ecologically relevant spatiotemporal scales. We experimentally demonstrate the formation of “ring”-shaped bacterial collection patterns and subsequently the formation of biofilm streamers in a microfluidic system. Acoustic streaming of a microbubble is used to generate a vortical flow in a microchannel. Due to bacteria’s finite-size, the microorganisms are directed to closed streamlines and trapped in the vortical flow. The collection of bacteria in the vortices occurs in a matter of seconds and, unexpectedly, triggers the formation of biofilm streamers within minutes.

*Funded by NSF Grant No. CBET-1066545*

The anisotropic structure of fluidized suspensions is governed by their microstructures which are in turn determined by the dynamics of particle pair interactions. In this study, we present numerical simulations of particle interaction in linearly stratified fluids. It is shown that unlike homogeneous fluids, stratification results in attraction of particles settling abreast. The interaction of the particles settling in tandem can be fundamentally altered due to the presence of the background density gradients and the drafting-kissing-tumbling behavior in a homogeneous fluid can be replaced by drafting-kissing-separation or drafting-separation phenomenon depending on the strength of the stratification. In case of weak stratification, drafting-kissing-tumbling occurs, however, a prolonged kissing time is observed and the rate of change of the orientation of particles is reduced. Attraction of particles settling side-by-side and prolonged kissing time for particles settling in tandem can lead to accumulation of particles and aggregation of organisms at local hot spots in aquatic environments characterized by density stratification.

*Funded by NSF Grant No. CBET-1150348-
CAREER*

Spatial distribution of
microorganisms

in a vortical flow of a complex fluid.

We have shown that the rheological properties of exopolysaccharides secreted by microorganisms play an important role in their interaction with background flow field. The normal stresses generated due to the presence of polymer molecules lead to aggregation of microorganisms in a vortical flow field. The shape and formation rate of these aggregation patterns depend on motility, vorticity, and rheological properties of exopolysaccharides. Given the viscoelastic nature of extracellular polymeric substances, these results suggest new mechanisms for ubiquitous processes among microorganisms, such as bacterial aggregation and biofilm formation.

*Funded by NSF grant No. CBET-1066545*

Propulsion speed of small organisms is strongly

affected by unsteady hydrodynamic forces.

Small planktonic organisms ubiquitously display unsteady or impulsive motion to attack a prey or escape a predator in natural environments. Despite this, the role of unsteady forces such as history and added mass forces on the low Reynolds number propulsion of small organisms, e.g. Paramecium, is poorly understood. In this paper, we derive the fundamental equation of motion for an organism swimming by the means of surface distortion in a nonuniform flow at a low Reynolds number regime. We show that the history and added mass forces are important as the product of Reynolds number and Strouhal number increases above unity.

*Funded by NSF grant No. CBET-1066545*

Flow field generated by small organisms is

markedly affected by stratification.

Swimming of microorganisms, a topic of long-standing interest for both biologists and physicists, has been mostly studied in homogeneous fluids. However, many aquatic environments, including oceans, lakes and the interstitial fluid in sea ice, are routinely stratified, due to salt- or temperature-induced variations in fluid density. We have analytically showed that stratification dramatically alters the flow field induced by the organism, generating recirculation cells in the velocity field. The size of these cells scales with Ra^{-1/4} where the Rayleigh number, Ra, measures the relative importance of buoyancy and diffusion. For stronger stratification, cells are more compressed and the velocity field decays faster with distance from the organism. These less conspicuous flow fields could affect those predator-prey interactions based on sensing of hydromechanical signals, potentially acting as a ‘silencer’ for swimming prey or a ‘stealth’ mechanism for approaching predators. We use a combination of methods that range from simple scaling laws to detailed computational models and sophisticated experimental equipments to explore the effects of stratification on swimming of small organisms.

*Funded by Schlumberger*

Jet Extensional Rheometry enables evaluation of

transient extensional rheological properties for even

very weakly elastic fluids.

Understanding the instability and breakup of polymeric jets is important for a wide variety of applications including inkjet printing, and spraying of fertilizers and paint. Such fluids are typically only weakly viscoelastic and the jetting/breakup process involves a delicate interplay of capillary, viscous, inertial and elastic stresses. The initial growth of disturbances can be predicted using linear instability analysis for small perturbations. A viscoelastic jet is initially more unstable when compared to a Newtonian fluid of the same viscosity and inertia. As the radius of the jet thins under the action of surface tension, elastic stresses grow and become comparable to the capillary pressure, leading to formation of a uniform thread connecting two primary drops. This beads-on-a-string structure can be captured by the Oldroyd-B model, and the radius of the thin cylindrical ligament connecting the beads necks down exponentially in time. The finite time breakup of the jet observed experimentally can be captured using the nonlinear Giesekus model. We show that by understanding the physical processes that control each phase of the temporal evolution in the jet profile it is possible to extract transient extensional viscosity information even for very low viscosity and weakly-elastic liquids. This is especially useful since filament-stretching and capillary breakup elongational rheometers face challenges for low-viscosity elastic polymer solutions.

*Funded by NSF grant No. CBET-0828104*

The motion of solid particles in fluids plays an important role in sedimentation, crystal growth, filtration, suspension rheology, microfluidic devices such as cell lysis method and several other natural and industrial applications. In mechanical cell-lysis method, interaction and collision between cells and glass beads in liquids are used to break cells and release DNA as a part of sample-to-answer nucleic acid analysis.

In order to study this complex problem which involves particle-cell interaction in a viscous fluid, initially the effect of cells is neglected and the particle interaction in a particulate flow is investigated. First, the theoretical analysis of dilute particulate flow is carried out. Using the method of reflections in Laplace space, the equation of motion for two particles moving in a Stokes flow is explicitly derived. The results indicate that the Basset force corresponding to the motion of two spheres is larger than the solitary-particle Basset force [1].

To accurately predict the behavior of particulate flows, fundamental knowledge of the mechanisms of single-particle collision is required. More specifically, the study of particle-wall collision provides deeper insight into modeling particle-laden flows when particle interaction is important. In order to elucidate the basic physics of the particle interaction and collision processes, a Distributed-Lagrange-Multiplier-Based computational method for colliding particles in a solid-fluid system is developed. The Navier-Stokes equations are directly solved and no model is used for solid phase. The collision between particles is simulated by taking into account the effect of particles roughness and the Stokes number [2]. Comparison of the present methodology with experimental studies for the bouncing motion of a spherical particle onto a wall shows very good agreement and validates the collision strategy (figure 1). This collision strategy is extended for systems of multi-particle and general shape objects in a viscous fluid [3]. There has been a need for a good collision scheme for particulate flow simulations. This approach can be used in engineering applications and commercial CFD codes in addition to academic use.

*Figure 1 - Coefficient of restitution normalized by that for dry collision as a function of St. Present results are shown using solid circles and experimental measurements for different materials by Gondret et al. (2002) are shown using open symbols. Lubrication theory of Davis et al. (1986)(-). *

*Movie 1 - Collision of a sphere onto a wall. *

In the above investigations, particle interaction and collision in a Newtonian fluid was considered whereas the suspensions of cells and DNA molecules exhibit both viscoelastic and shear thinning characteristics. Thus, particle-wall interaction in viscoelastic fluids is experimentally investigated. A sphere is released in a tank filled with polyethylene-oxide (PEO) mixed with water with varying concentrations up to 1.5%. The effect of Stokes and Deborah numbers on the rebound velocity when a spherical particle collides onto a wall is considered [4]. Higher rebound occurs for higher poly(ethylene-oxide) concentration at the same stokes number (figure 2a). However, the results for the coefficient of restitution in polymeric liquids can be collapsed together with the Newtonian fluid behavior if one defines the Stokes number based on the local shear rate (figure 2b). This implies that the shear-thinning behavior of these liquids is more important than their viscoelasticity during the collision process.

*Figure 2 - Collision in a polymeric liquid. Present results are shown by solid symbols. Experimental measurements for Newtonian liquids by Gondret et al. (2002) are shown by open symbols. Lubrication theory of Davis et al. (1986) (-).*

Particle-particle interactions in viscoelastic fluids are dramatically different than in Newtonian fluids: particles disperse in the flow of Newtonian fluids and they aggregate in the flow of viscoelastic fluids. Our analyses based on second-order fluid model suggest that the chaining of particles in viscoelastic liquids is the result of local effects and is due to three fundamental causes: (1) a viscoelastic ``pressure'' generated by normal stresses due to shear; (2) the total time derivative of the Stokes pressure; and (3) the change in the sign of the normal stress, which is a purely extensional effect. In order to study the effect of viscoelasticity of the fluid on the particle interaction, the following problems are studied: 1) The motion of a sphere normal to a wall in a second-order fluid is investigated. The normal stress at the surface of the sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analyzed [5]. For small separation distances, when the particle is moving away from the wall, a tensile normal stress exists at the trailing edge if the fluid is Newtonian, while for a second-order fluid a larger tensile stress is observed. When the particle is moving towards the wall, the stress is compressive at the leading edge for a Newtonian fluid whereas a large tensile stress is observed for a second-order fluid. The contribution of the second-order fluid to the overall force applied to the particle is an attractive force towards the wall in both situations. 2) The forces acting on two fixed spheres in a second-order uniform flow are investigated [6]. For flow along the line of centers or perpendicular to it, the net force is in the direction that tends to decrease the particle separation distance. For the case of flow at arbitrary angle, unequal forces are applied to the spheres perpendicularly to the line of centers. These forces result in a change of orientation of the sedimenting spheres until the line of centers aligns with the flow direction. The results explain the experimentally observed chaining of sedimenting particles in a viscoelastic fluid.

Finally, we have developed numerical tools to understand the interaction of rigid and deformable droplets (simplified cell) in a viscous fluid. A level-Set method is used to represent the interface and surface tension. The results show that the presence of particles leads to larger droplet deformation, and a perforation in the center of the droplet which facilitates droplet breakup (figure 3). It is found that the critical Stokes number above which a perforation occurs increases linearly with the inverse of the capillary number and viscosity ratio (figure 4) [7].

*Figure 3 - Deformation and breakup of a droplet in a particulate shear flow. a) Ca=30, Re=100. b) Ca=0.025, Re=80. A perforation in the center of droplet is generated as the particles collide.*

*Movie 2 - Deformation and breakup of a droplet in a particulate shear flow at Ca=30, Re=100. *

*Figure 4 - The critical Stokes number above which a perforation occurs linearly changes with the inverse of the capillary number and the viscosity ratio.*