Pair collisions of fluid-filled elastic capsules in shear flow: Effects of membrane properties and polymer additives

The dynamics and pair collisions of fluid-filled elastic capsules during Couette flow in Newtonian fluids and dilute solutions of high-molecular weight (drag-reducing) polymers are investigated via direct simulation. Capsule membranes are modeled using either a neo-Hookean constitutive model or a model introduced by Skalak et al. [Strain energy function of red blood-cell membranes, Biophys. J. 13, 245 (1973)], which includes an energy penalty for area changes. This model was developed to capture the elastic properties of red blood cells. Polymer molecules are modeled as bead-spring trimers with finitely extensible nonlinearly elastic springs; parameters were chosen to loosely approximate 4000 kDa poly(ethylene oxide). Simulations are performed with a novel Stokes flow formulation of the immersed boundary method for the capsules, combined with Brownian dynamics for the polymer molecules. The results for isolated capsules in shear indicate that at the very low concentrations considered here, polymers have a little effect on the capsule shape. In the case of pair collisions, the effect of polymer is strongly dependent on the elastic properties of the capsules' membranes. For neo-Hookean capsules or for Skalak capsules with only a small penalty for area change, the net displacement in the gradient direction after collision is virtually unaffected by the polymer. For Skalak capsules with a large penalty for area change, polymers substantially decrease the net displacement when compared to the Newtonian case and the effect is enhanced upon increasing the polymer concentration. The differences between the polymer effects in the various cases are associated with the extensional flow generated in the region between the capsules as they leave the collision. The extension rate is highest when there is a strong resistance to a change in the membrane area and is substantially decreased in the presence of polymer. (C) 2010 American Institute of Physics. [doi:10.1063/1.3524531]