Mobility of an axisymmetric particle near an elastic interface

TL;DR

This paper develops an analytical framework to compute how an axisymmetric particle's mobility near an elastic membrane is affected by membrane properties, applicable to particles of arbitrary shape with validation against simulations.

Contribution

It provides general frequency-dependent mobility correction formulas for axisymmetric particles near elastic membranes, applicable to arbitrary shapes and validated through simulations.

Findings

Bending dominates translation-rotation coupling corrections.

Shearing significantly influences rotational mobility.

Analytical results agree well with boundary integral simulations.

Abstract

Using a fully analytical theory, we compute the leading order corrections to the translational, rotational and translation-rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle's shape-dependent bulk mobility and the shape-independent parameters such as the membrane-particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle's eccentricity. We find that the corrections to the translation-rotation coupling mobility are primarily determined by bending, whereas shearing manifests itself in a more pronounced way in the rotational mobility. We demonstrate the validity of the analytical approximations by a detailed comparison with boundary integral simulations of a truly extended spheroidal particle. They are found to be in a good agreement over the whole range of applied frequencies.