The dynamics of a capsule in a wall-bounded oscillating shear flow

TL;DR

This study investigates the motion and deformation of capsules in wall-bounded oscillating shear flows, revealing optimal migration conditions, deformation behavior, and the influence of flow parameters through boundary integral simulations.

Contribution

It provides a detailed analysis of capsule dynamics in oscillating shear flows using an accelerated boundary integral method, highlighting the effects of oscillation frequency and membrane elasticity.

Findings

Maximum wall-normal migration occurs at a specific oscillation period.

Deformation scales linearly with membrane elasticity up to a plateau.

Maximum deformation scales with wall distance to the power 1/3.

Abstract

The motion of an initially spherical capsule in a wall-bounded oscillating shear flow is investigated via an accelerated boundary integral implementation. The neo-Hookean model is used as the constitutive law of the capsule membrane. The maximum wall-normal migration is observed when the oscillation period of the imposed shear is of the order of the relaxation time of the elastic membrane; hence, the optimal capillary number scales with the inverse of the oscillation frequency and the ratio agrees well with the theoretical prediction in the limit of high-frequency oscillation. The migration velocity decreases monotonically with the frequency of the applied shear and the capsule-wall distance. We report a significant correlation between the capsule lateral migration and the normal stress difference induced in the flow. The periodic variation of the capsule deformation is roughly in phase with that of the migration velocity and normal stress difference, with twice the frequency of the imposed shear. The maximum deformation increases linearly with the membrane elasticity before reaching a plateau at higher capillary numbers when the deformation is limited by the time over which shear is applied in the same direction and not by the membrane deformability. The maximum membrane deformation scales as the distance to the wall to the power 1/3 as observed for capsules and droplets in near-wall steady shear flows.