Optimal translational swimming of a sphere at low Reynolds number

TL;DR

This paper analyzes the optimal surface distortions of a sphere to maximize swimming efficiency at low Reynolds numbers, considering irrotational and vorticity flows, and introduces a new performance measure based on energy use.

Contribution

It extends previous models by including vorticity in axisymmetric flows, significantly improving the maximum efficiency of sphere swimming at low Reynolds numbers.

Findings

Including vorticity increases maximum efficiency.

Optimal surface distortions depend on flow assumptions.

A new energy-based performance measure is proposed.

Abstract

Swimming velocity and rate of dissipation of a sphere with surface distortions are discussed on the basis of the Stokes equations of low Reynolds number hydrodynamics. At first the surface distortions are assumed to cause an irrotational axisymmetric flow pattern. The efficiency of swimming is optimized within this class of flows. Subsequently more general axisymmetric polar flows with vorticity are considered. This leads to a considerably higher maximum efficiency. An additional measure of swimming performance is proposed based on the energy consumption for given amplitude of stroke.