Axisymmetric spheroidal squirmers and self-diffusiophoretic particles

TL;DR

This paper provides an exact analytical study of the motion and flow fields of spheroidal squirmers and self-diffusiophoretic particles, revealing how their shape influences their propulsion and flow characteristics.

Contribution

It extends the understanding of microswimmer hydrodynamics from spherical to spheroidal shapes using exact solutions, highlighting shape-dependent effects on propulsion and flow.

Findings

Spheroidal squirmers' modes contribute differently to velocity and stresslet.

The analytical results are applicable to chemically active spheroidal particles.

Shape significantly affects the flow and propulsion mechanisms.

Abstract

We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical squirmer --- for which, e.g., the velocity of the squirmer and the magnitude of the stresslet associated with the flow induced by the squirmer are respectively determined by the amplitudes of the first two slip ("squirming") modes --- for the spheroidal squirmer each squirming mode either contributes to the velocity, or contributes to the stresslet. The results are straightforwardly extended to the self-phoresis of axisymmetric, spheroidal, chemically active particles in the case when the phoretic slip approximation holds.