Dynamics of cruising swimming by a deformable sphere for two simple models

TL;DR

This paper investigates the periodic swimming dynamics of deformable spheres using two models, deriving exact solutions to Navier-Stokes equations to understand fluid forces and velocity behavior.

Contribution

It provides exact second-order solutions for the fluid dynamics of deformable spheres in swimming models, advancing theoretical understanding.

Findings

Exact solutions to Navier-Stokes equations for the models

Calculation of oscillating fluid forces

Determination of time-dependent swimming velocity

Abstract

The dynamics of periodic swimming is studied for two models of a deformable sphere, the dipole-quadrupole model and the quadrupole-octupole model. For the two models the solution of the Navier-Stokes equations can be found exactly to second order in the amplitude of stroke. Hence the oscillating force exerted by the fluid on the body is calculated. This allows calculation of the periodic time-dependent center of mass velocity.