Spontaneous locomotion of a symmetric squirmer

TL;DR

This study reveals that symmetric squirmers can spontaneously start swimming above a critical Reynolds number due to inertia effects, with steady propulsion emerging through a supercritical bifurcation.

Contribution

It demonstrates that fore-aft symmetric squirmers can spontaneously self-propel at finite Reynolds numbers, highlighting a new inertial mechanism for symmetry breaking in microswimmers.

Findings

Spontaneous symmetry breaking occurs above Re ≈ 14.3.

Steady swimming emerges via a supercritical pitchfork bifurcation.

Swimming speed increases monotonically with Reynolds number.

Abstract

The squirmer is a popular model to analyse the fluid mechanics of a self-propelled object, such as a micro-organism. We demonstrate that some fore-aft symmetric squirmers can spontaneously self-propel above a critical Reynolds number. Specifically, we numerically study the effects of inertia on spherical squirmers characterised by an axially and fore-aft symmetric `quadrupolar' distribution of surface-slip velocity; under creeping-flow conditions, such squirmers generate a pure stresslet flow, the stresslet sign classifying the squirmer as either a `pusher' or `puller.' Assuming axial symmetry, and over the examined range of the Reynolds number $Re$ (defined based upon the magnitude of the quadrupolar squirming), we find that spontaneous symmetry breaking occurs in the pusher case above $Re \approx 14.3$, with steady swimming emerging from that threshold consistently with a supercritical pitchfork bifurcation and with the swimming speed growing monotonically with $Re$.