Stresslet asymptotics for a treadmilling swimmer near a two-dimensional corner: hydrodynamic bound states

The dynamics of a circular treadmilling low Reynolds number swimmer near a right-angled corner is studied in the asymptotic limit in which the radius of the treadmiller is small. The governing dynamical equations are found explicitly, correct to third order in the swimmer radius, by means of Mellin transform techniques. The existence of arc-like periodic orbits, or ‘hydrodynamic bound states’, in the corner region is identified, and these orbits are found to be attractors in the dynamics for a large range of initial swimmer locations and orientations. The analytical approach may be extended to wedge regions of other fractional angles.