Collinear swimmer propelling a cargo sphere at low Reynolds number

TL;DR

This paper investigates how a linear chain of small spheres can propel a larger cargo sphere at low Reynolds numbers, analyzing swimming velocity and energy dissipation through hydrodynamic interactions.

Contribution

It introduces a model of a collinear swimmer with a cargo sphere, utilizing fundamental solutions of Stokes' equations to analyze propulsion at low Reynolds numbers.

Findings

Derived expressions for swimming velocity and dissipation rate.

Quantified the influence of hydrodynamic interactions on propulsion efficiency.

Provided a framework for understanding cargo transport by microswimmers.

Abstract

The swimming velocity and rate of dissipation of a linear chain consisting of two or three little spheres and a big sphere is studied on the basis of low Reynolds number hydrodynamics. The big sphere is treated as a passive cargo, driven by the tail of little spheres via hydrodynamic and direct elastic interaction. The fundamental solution of Stokes' equations in the presence of a sphere with no-slip boundary condition, as derived by Oseen, is used to model the hydrodynamic interactions between the big sphere and the little spheres.