Scattering of low-Reynolds-number swimmers

We describe the consequences of time-reversal invariance of the Stokes equations for the hydrodynamic scattering of two low-Reynolds-number swimmers. For swimmers that are related to each other by a time-reversal transformation, this leads to the striking result that the angle between the two swimmers is preserved by the scattering. The result is illustrated for the particular case of a linked-sphere model swimmer. For more general pairs of swimmers, not related to each other by time reversal, we find that hydrodynamic scattering can alter the angle between their trajectories by several tens of degrees. For two identical contractile swimmers, this can lead to the formation of a bound state.