Segregation by membrane rigidity in flowing binary suspensions of elastic capsules

Abstract

Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal membrane rigidities. The problem is studied numerically using an accelerated implementation of the boundary integral method. The effect of a variety of parameters was investigated, including the capillary number, rigidity ratio between the two species, volume fraction, confinement ratio, and number fraction of the more floppy particle Xf in the mixture. It was observed that in suspensions of pure species, the mean wall normal positions of the stiff and the floppy particles are comparable. In mixtures, however, the stiff particles were found to be increasingly displaced toward the walls with increasing Xf, while the floppy particles were found to increasingly accumulate near the centerline with decreasing Xf. This segregation behavior was universally observed independent of the parameters. The origin of this segregation is traced to the effect of the number fraction Xf on the localization of the stiff and the floppy particles in the near wall region--the probability of escape of a stiff particle from the near wall region to the interior is greatly reduced with increasing Xf, while the exact opposite trend is observed for a floppy particle with decreasing Xf. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain the contrasting effect of Xf on the near wall localization of the two species. The key observation in these studies is that the stiff particle experiences much larger cross-stream displacement in heterogeneous collisions than the floppy particle. A unified mechanism incorporating the wall-induced migration of deformable particles away from the wall and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.