Effect of fluid inertia on the motion of a collinear swimmer

TL;DR

This paper investigates how fluid inertia influences the swimming behavior of simple multi-sphere systems in viscous fluids, revealing that non-identical spheres can swim and chains of identical spheres are more efficient.

Contribution

It introduces a simplified model incorporating both Stokes friction and added mass effects to analyze swimmer motion in inertial fluids.

Findings

Non-identical two-sphere systems can swim due to inertia.

Three-sphere chains exhibit higher swimming efficiency.

Explicit formulas for swimming velocity and energy dissipation are provided.

Abstract

The swimming of a two-sphere system and of a three-sphere chain in an incompressible viscous fluid is studied on the basis of simplified equations of motion which take account of both Stokes friction and added mass effects. The analysis is based on an explicit expression for the asymptotic periodic swimming velocity and a corresponding evaluation of the mean rate of dissipation. The mean swimming velocity of the two-sphere system is found to be non-vanishing provided that the two spheres are not identical. The swimming of a comparable chain of three identical spheres is much more efficient.