Dynamics and stability of Purcell's three-link microswimmer near a wall.

The motion of swimming microorganisms is strongly influenced by the presence of boundaries. Attraction of bacteria and sperm cells to surfaces is a well-known phenomenon which has been observed in experiments and confirmed by numerical simulations. This effect is studied in this work from a viewpoint of dynamical systems theory by analyzing a swimmer model which is a variant of the classical Purcell's three-link swimmer near an infinite plane wall. The underlying geometric structure of the swimmer's dynamics and its relation to stability are elucidated. It is found that a swimmer which breaks its fore-aft symmetry has a preferred swimming direction in which its motion is passively stable and converges to a fixed separation distance from the wall.