Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. I. Axisymmetric motion

TL;DR

This paper analyzes how a small solid particle moves near a spherical elastic membrane, revealing how membrane curvature affects mobility and demonstrating the importance of shearing resistance, validated by boundary integral simulations.

Contribution

It provides an analytical expression for particle mobility near a spherical elastic membrane, highlighting the effects of curvature and membrane properties, with validation through simulations.

Findings

Membrane curvature introduces an additional peak in mobility.

Shearing resistance is crucial for particle mobility near the membrane.

Analytical results agree well with boundary integral simulations.

Abstract

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a non-vanishing resistance towards shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.