Three-sphere low-Reynolds-number swimmer with a cargo container

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/R3 with the radius of the sphere.