Pairwise interactions between deformable drops in free shear at finite inertia

Olapade, Peter; Singh, Rajesh; Sarkar, Kausik

doi:10.1063/1.3153905

Cited by 32 publications

(31 citation statements)

References 35 publications

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“…But since inertia is known to affect hydrodynamic interaction among particles and drops (Feng, Hu & Joseph 1994;Olapade, Singh & Sarkar 2009), we carried out a set of simulations to explore the effect of finite Reynolds numbers. At Re = ρ m u m D/η m = 13, with a drop-to-medium density ratio of 100 and a viscosity ratio of 50, the merging of the two drops happens much more quickly.…”

Section: Coalescence Driven By External Flowmentioning

confidence: 99%

Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow

Ahmadlouydarab

Feng

2014

J. Fluid Mech.

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We report two-dimensional simulations of drop dynamics on a substrate subject to a wetting gradient and an external pressure gradient along the substrate. A phase-field formulation is used to represent the drop interface, and the moving contact line is modelled by Cahn-Hilliard diffusion. The Navier-Stokes-Cahn-Hilliard equations are solved by finite elements on an adaptively refined unstructured grid. For a single drop and a pair of drops, we consider three scenarios of drop motion driven by the wetting gradient only, by the external flow only, and by a combination of the two. Both the capillary force and the hydrodynamic drag depend strongly on the shape of the drop. Since the drop adapts its shape to the local wetting angles and to the external flow on a finite time scale, hysteresis is a prominent feature of the drop dynamics under opposing forces. For each wetting gradient, there is a narrow range of the magnitude of the external flow within which a single drop can achieve a stationary state. The equilibrium drop shape and position depend on its initial shape and the history of forcing. For a pair of drops, the wetting gradient or external flow alone tends to produce catch-up and coalescence. The flow-driven coalescence arises from a viscous shielding effect that relies on the asymmetric shape of the trailing drop once it is deformed by flow. This mechanism operates at zero Reynolds number, but is much enhanced by inertia. With the two forces opposing each other, the external flow favours separation while the wetting gradient favours coalescence. The outcome depends on their competition.

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Section: Coalescence Driven By External Flowmentioning

confidence: 99%

Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow

Ahmadlouydarab

Feng

2014

J. Fluid Mech.

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“…We use a front-tracking finite difference method (Tryggvason et al 2001) that has been used in our lab for a number of viscous (Sarkar & Schowalter 2001;Li & Sarkar 2005a,b,c, 2006Olapade, Singh & Sarkar 2009;Singh & Sarkar 2011) and viscoelastic (Sarkar & Schowalter 2000;Aggarwal & Sarkar 2007, 2008aMukherjee & Sarkar 2009 drop problems. Our previous studies used Oldroyd-B model for viscoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Effects of matrix viscoelasticity on the lateral migration of a deformable drop in a wall-bounded shear

Mukherjee

Sarkar

2013

J. Fluid Mech.

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The dynamics of a drop deforming, orienting and moving in a shear flow of a viscoelastic liquid near a wall is numerically investigated using a front-tracking finitedifference method and a semi-analytic theory. The viscoelasticity is modelled using the modified FENE-CR constitutive equation. In a Newtonian system, deformation in a drop breaks the reversal symmetry of the system resulting in a migration away from the wall. This study shows that the matrix elasticity reduces the migration velocity, the reduction scaling approximately linearly with viscoelasticity (product of the Deborah number De and the ratio of polymer viscosity to total viscosity β). Similar to a Newtonian system, for small Deborah numbers, the dynamics quickly reaches a quasisteady state where deformation, inclination, as well as migration and slip velocities become independent of the initial drop-wall separation. They all approximately scale inversely with the square of the instantaneous separation except for deformation which scales inversely with the cube of separation. The deformation shows a non-monotonic variation with increasing viscoelasticity similar to the case of a drop in an unbounded shear and is found to influence little the change in migration. Two competing effects due to matrix viscoelasticity on drop migration are identified. The first stems from the reduced inclination angle of the drop with increasing viscoelasticity that tries to enhance migration velocity. However, it is overcome by the second effect inhibiting migration that results from the normal stress differences from the curved streamlines around the drop; they are more curved on the side away from the wall compared with those in the gap between the wall and the drop, an effect that is also present for a rigid particle. A perturbative theory of migration is developed for small ratio of the drop size to its separation from the wall that clearly shows the migration to be caused by the image stresslet field due to the drop in presence of the wall. The theory delineates the two competing viscoelastic effects, their relative magnitudes, and predicts migration that matches well with the simulation. Using the simulation results and the stresslet theory, we develop an algebraic expression for the quasi-steady migration velocity as a function of Ca, De and β. The transient dynamics of the migrating drop is seen to be governed by the finite time needed for development of the viscoelastic stresses. For larger capillary numbers, in both Newtonian and viscoelastic matrices, a viscous drop fails to reach a quasi-steady state independent of initial drop-wall separation. Matrix viscoelasticity tends to prevent drop breakup. Drops that † Email address for correspondence: sarkar@gwu.edu Near-wall migration of a viscous drop in a sheared viscoelastic matrix 319 break up in a Newtonian matrix are stabilized in a viscoelastic matrix if it is initially far away from the wall. Initial proximity to the wall enhances deformation and aids in drop breakup.

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“…The crossing events occur when DY o is above a critical separation DY o;crit , and the turning events occur when DY o is below DY o;crit . Similar crossing and turning events have been observed during the interaction of two identical (homotypic) red blood cells and liquid drops in shear flow [37,57,58]. The present work deals with heterotypic particles.…”

Section: Discussionmentioning

confidence: 55%

Hydrodynamic Interaction Between a Platelet and an Erythrocyte: Effect of Erythrocyte Deformability, Dynamics, and Wall Proximity

Vahidkhah

Diamond

Bagchi

2013

Journal of Biomechanical Engineering

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We present three-dimensional numerical simulations of hydrodynamic interaction between a red blood cell (RBC) and a platelet in a wall-bounded shear flow. The dynamics and large deformation of the RBC are fully resolved in the simulations using a fronttracking method. The objective is to quantify the influence of tank treading and tumbling dynamics of the RBC, and the presence of a bounding wall on the deflection of platelet trajectories. We observe two types of interaction: A crossing event in which the platelet comes in close proximity to the RBC, rolls over it, and continues to move in the same direction; and a turning event in which the platelet turns away before coming close to the RBC. The crossing events occur when the initial lateral separation between the cells is above a critical separation, and the turning events occur when it is below the critical separation. The critical lateral separation is found to be higher during the tumbling motion than that during the tank treading. When the RBC is flowing closer to the wall than the platelet, the critical separation increases by several fold, implying the turning events have higher probability to occur than the crossing events. On the contrary, if the platelet is flowing closer to the wall than the RBC, the critical separation decreases by several folds, implying the crossing events are likely to occur. Based on the numerical results, we propose a mechanism of continual platelet drift from the RBC-rich region of the vessel towards the wall by a succession of turning and crossing events. The trajectory deflection in the crossing events is found to depend nonmonotonically on the initial lateral separation, unlike the monotonic trend observed in tracer particle deflection and in deformable sphere-sphere collision. This nonmonotonic trend is shown to be a consequence of the deformation of the RBC caused by the platelet upon collision. An estimation of the platelet diffusion coefficient yields values that are similar to those reported in experiments and computer simulations with multicellular suspension.

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Pairwise interactions between deformable drops in free shear at finite inertia

Cited by 32 publications

References 35 publications

Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow

Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow

Effects of matrix viscoelasticity on the lateral migration of a deformable drop in a wall-bounded shear

Hydrodynamic Interaction Between a Platelet and an Erythrocyte: Effect of Erythrocyte Deformability, Dynamics, and Wall Proximity

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