Three-Sphere Low Reynolds Number Swimmer with a Cargo Container

TL;DR

This paper analyzes a low Reynolds number swimmer composed of three spheres, with one large cargo sphere, deriving its swimming velocity and showing it scales inversely with the cube of the sphere's radius.

Contribution

It provides an analytical study of a three-sphere swimmer with a cargo sphere using Stokes flow and Green's functions, revealing the velocity scaling law.

Findings

Swimming velocity scales as 1/R^3 with the cargo sphere radius.

Analytical expressions for the flow and motion are derived.

The model extends understanding of cargo transport at low Reynolds numbers.

Abstract

A recently introduced model for an autonomous swimmer at low Reynolds number that is comprised of three spheres connected by two arms is considered when one of the spheres has a large radius. The Stokes hydrodynamic flow associated with the swimming strokes and net motion of this system can be studied analytically using the Stokes Green's function of a point force in front of a sphere of arbitrary radius $R$ provided by Oseen. The swimming velocity is calculated, and shown to scale as $1/R^3$ with the radius of the sphere.