(79c) Suspensions of Elastic Capsules In Polymer Solutions

Suspensions of fluid-filled elastic capsules in a Couette flow in Newtonian fluids and dilute solutions of high molecular weight (drag-reducing) polymers are investigated. A simple model is presented to describe the cross-stream migration of deformable capsules in suspensions which comes from a balance of shear-induced diffusion and wall-induced migration due to capsule deformability. The model provides an explicit theoretical prediction of the dependence of capsule-depleted layer thickness on the shear rate. A computational approach is then used to examine the motion of elastic capsules in polymer solutions. Capsule membranes are modeled using a neo-Hookean constitutive model and polymer molecules are modeled as bead-spring chains with finitely extensible non-linearly elastic (FENE) springs; parameters were chosen to loosely approximate $4000$ kD poly(ethylene oxide). Simulations are performed with a novel Stokes flow formulation of the Immersed Boundary Method (IBM) for the capsules, combined with Brownian dynamics for the polymer molecules. Results for an isolated capsule near a wall indicate that the wall-induced migration depends strongly on the capillary number, expressing capsule deformability. Numerical simulation of suspensions of capsules in Newtonian fluid illustrates the inhomogeneous distribution of capsules at steady-state with the formation of capsule-depleted layer near the walls. The thickness of this layer is found to be strongly dependent on the capillary number. The shear-induced diffusivity, on the other hand, show a weak dependence on capillary number. These results indicate that the mechanism of wall-induced migration is the primary source for determining the capsule-depleted layer thickness of capsules in suspensions. Numerical simulation results on the effect of polymer show that both the wall-induced migration and the shear-induced diffusive motion of the capsules are suppressed under the influence of polymer. Results on suspensions of capsules illustrate that the net effect of polymers is to reduce the thickness of the capsule-depleted layer resulting in a redistribution of capsules at steady state. The results are in qualitative agreement to the experimental observations.