Swimming of an assembly of rigid spheres at low Reynolds number

TL;DR

This paper develops a matrix-based method to calculate swimming speed and power for assemblies of rigid spheres in viscous fluids at low Reynolds numbers, accounting for arbitrary sizes and elastic interactions.

Contribution

It introduces a novel matrix formulation and eigenvalue approach for optimizing swimming performance of sphere assemblies in viscous fluids.

Findings

Matrix formulation for swimming speed and power calculation

Eigenvalue problem for small amplitude swimming optimization

Straightforward method for assessing swimming performance

Abstract

A matrix formulation is derived for the calculation of the swimming speed and the power required for swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent. The spheres may have arbitrary radii and may interact with elastic forces. The analysis is based on the Stokes mobility matrix of the set of spheres, defined in low Reynolds number hydrodynamics. For small amplitude swimming optimization of the swimming speed at given power leads to an eigenvalue problem. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres.