Segregation by membrane rigidity in flowing binary suspensions of elastic capsules

TL;DR

This study investigates how membrane rigidity influences the spatial segregation of elastic capsules in flow, revealing that stiffer particles tend to migrate towards walls while more flexible ones stay near the center, driven by collision dynamics.

Contribution

It introduces a numerical analysis of segregation in binary capsule suspensions considering membrane rigidity, elucidating the mechanisms behind particle distribution in flow.

Findings

Stiff particles migrate towards walls with increasing floppy particle fraction.

Flexible particles tend to accumulate near the centerline as floppy fraction decreases.

Heterogeneous collisions cause larger cross-stream displacements for stiff particles.

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 the number fraction of the more floppy particle $X_f$ 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 towards the walls with increasing $X_f$, while the floppy particles were found to increasingly accumulate near the centerline with decreasing $X_f$. The origins of this segregation is traced to the effect of the number fraction $X_f$ 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 $X_f$, while the exact opposite trend is observed for a floppy particle with decreasing $X_f$. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain this observation. The key result 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 and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.