Clockwise-directional circle swimmer moves counter-clockwise in Petri dish- and ring-like confinements

Abstract

A self-propelled rod which is driven by a constant internal force and torque performs circular motion in two spatial dimensions with an “internal” radius governed by the torque-to-force ratio and is referred to as a circle swimmer. Using analytical methods and computer simulations, we study the Brownian dynamics of a circle swimmer in a confining Petri dish- or ring-shaped geometry and compute the mean of the swimmer's position, its steady-state properties and its orientational motion. For small torque-to-force ratios, the confinement inverts the orientational sense of the motion: a clockwise-directional circle swimmer moves counter-clockwise in the confinement. Our results are verifiable for self-propelled colloidal rods, for vibrated granular rods and for motile bacteria in cylindrical confinements.