Slow rotation of a spherical particle inside an elastic tube

TL;DR

This paper analytically investigates how a spherical particle's rotation near an elastic cylindrical tube is affected by membrane properties, revealing specific dependencies on shearing and bending, and validating results with simulations.

Contribution

It provides the first analytical calculation of rotational mobility functions of a particle inside an elastic tube considering both shearing and bending effects.

Findings

Rotational mobility correction depends on shearing for axis rotation.

Bending influences mobility about perpendicular axes.

Good agreement between analytical results and boundary integral simulations.

Abstract

In this paper, we present an analytical calculation of the rotational mobility functions of a particle rotating on the centerline of an elastic cylindrical tube whose membrane exhibits resistance towards shearing and bending. We find that the correction to the particle rotational mobility about the cylinder axis depends solely on membrane shearing properties while both shearing and bending manifest themselves for the rotational mobility about an axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing frequency, the particle rotational mobility nearby a no-slip rigid cylinder is recovered only if the membrane possesses a non-vanishing resistance towards shearing. We further show that for the asymmetric rotation along the cylinder radial axis, a coupling between shearing and bending exists. Our analytical predictions are compared and validated with corresponding boundary integral simulations where a very good agreement is obtained.