Stokesian swimming of a sphere by radial helical surface wave

TL;DR

This paper analyzes how a sphere can swim using radial helical surface waves based on Stokes equations, providing explicit formulas for swimming velocities and energy dissipation.

Contribution

It derives explicit expressions for the mean translational and rotational velocities and dissipation rates of a sphere swimming via radial helical surface waves.

Findings

Explicit formulas for swimming velocities

Quantitative analysis of energy dissipation

Theoretical framework for radial helical wave swimming

Abstract

The swimming of a sphere by means of radial helical surface waves is studied on the basis of the Stokes equations. Explicit expressions are derived for the matrices characterizing the mean translational and rotational swimming velocities and the mean rate of dissipation to second order in the wave amplitude.