Stokesian swimming of a sphere at low Reynolds number

TL;DR

This paper derives explicit formulas for the swimming velocities and energy dissipation of a sphere performing low Reynolds number swimming, and identifies an efficient helical stroke for propulsion.

Contribution

It provides new explicit expressions for swimming velocities and dissipation, and introduces an efficient helical stroke model for a sphere in viscous fluid.

Findings

Explicit formulas for mean translational and rotational velocities.

Identification of an efficient helical stroke.

Calculated properties of the proposed stroke.

Abstract

Explicit expressions are derived for the matrices determining the mean translational and rotational swimming velocities and the mean rate of dissipation for Stokesian swimming at low Reynolds number of a distorting sphere in a viscous incompressible fluid. As an application an efficient helical propeller-type stroke is found and its properties are calculated.