Confinement-Induced Motion of Ciliates

The time dynamics of flagellar and ciliary beating is often neglected in theories of microswimmers, with the most common models prescribing a time-constant actuation of the surrounding fluid. By explicitly introducing a metachronal wave, coarse-grained to a sinusoidal surface slip velocity, we show that a spatial resonance between the metachronal wave and the corrugation of a confining cylindrical channel enables a ciliate to swim even when it cannot move forward in a bulk fluid. Using lubrication theory, we reduce the problem to the Adler equation that reveals an oscillatory and steady swimming regime. Interestingly, a ciliate can even reverse its swimming direction in a corrugated channel compared to the bulk fluid.