Swimming of a deformable slab in a viscous incompressible fluid with inertia

TL;DR

This paper investigates how a deformable slab swims in a viscous incompressible fluid, optimizing efficiency based on fluid properties and stroke polarization, using Navier-Stokes equations.

Contribution

It introduces a continuum of wave displacements for the slab and analyzes optimal swimming efficiency considering inertia and viscosity effects.

Findings

Optimal efficiency depends on fluid viscosity and density ratio.

High viscosity yields more efficient strokes than classical solutions.

Efficiency is maximized with nearly irrotational flow at low viscosity.

Abstract

The swimming of a deformable planar slab in a viscous incompressible fluid is studied on the basis of the Navier-Stokes equations. A continuum of plane wave displacements, symmetric on both sides of the slab and characterized by a polarization angle, allows optimization of the swimming efficiency with respect to polarization. The mean swimming velocity and mean rate of dissipation are calculated to second order in the amplitude of the stroke. The optimum efficiency depends on the ratio of viscosity and mass density of the fluid. For high viscosity a stroke is found with significantly higher efficiency than Taylor's solution for a swimming sheet. For low viscosity the efficiency is optimal for a nearly irrotational flow pattern.