Squirmer locomotion in a yield stress fluid

TL;DR

This study numerically investigates how a yield stress environment affects the locomotion of a spherical squirmer, revealing that yield stress influences swimming velocity, power usage, and efficiency, with higher modes potentially enhancing propulsion.

Contribution

It introduces a numerical approach to analyze squirmer locomotion in yield stress fluids and uncovers how non-standard swimming strategies can optimize movement in such environments.

Findings

Swimmers in yield stress fluids have reduced velocity and increased power consumption.

Maximum swimming efficiency occurs at a finite yield limit.

Higher stroke modes can enhance propulsion and efficiency in high yield environments.

Abstract

An axisymmetric squirmer in a Bingham viscoplastic fluid is studied numerically to determine the effect of a yield stress environment on locomotion. The nonlinearity of the governing equations necessitates numerical methods, which is accomplished by solving a variable-viscosity Stokes equation with a Finite Element approach. The effects of stroke modes, both pure and combined, are investigated and it is found that for the treadmill or "neutral" mode, the swimmer in a yield stress fluid has a lower swimming velocity and uses more power. However, the efficiency of swimming reaches its maximum at a finite yield limit. In addition, for higher yield limits, higher stroke modes can increase the swimming velocity and hydrodynamic efficiency of the treadmill swimmer. The higher-order odd-numbered squirming modes, particularly the third stroke mode, can generate propulsion by themselves that increases in strength as the viscoplastic nonlinearity increases till a specific limit. These results are closely correlated with the confinement effects induced by the viscoplastic rigid surface surrounding the swimming body, showing that swimmers in viscoplastic environments, both biological and artificial, could potentially employ other non-standard swimming strategies to optimize their locomotion.