Swimming in circles of a Janus particle by diffusion of insoluble surfactant on its active face

An exact solution is obtained for the Stokes flow around an active circular two-dimensional Janus swimmer whose active face is a free surface and its inert face is a no-slip surface, a conceptual design motivated by recent work on superhydrophobic surfaces. Locomotion is driven by Marangoni stresses associated with the diffusion of insoluble surfactant from one edge of the active face to the other. The dynamical system governing the motion of the swimmer is derived explicitly in terms of the swimmer geometry. It is shown that this Marangoni-driven actuation mechanism results in a translational-rotational coupling causing the Janus particle to swim in circles while spinning about its center. While idealized, the model swimmer exemplifies a set of minimal ingredients needed to set up such translational-rotational coupling.