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 stri
king 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 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.
We investigate the way in which oscillating dumb-bells, a simple microscopic model of apolar swimmers, move at low Reynolds number. In accordance with Purcells Scallop Theorem a single dumb-bell cannot swim because its stroke is reciprocal in time. H
owever the motion of two or more dumb-bells, with mutual phase differences, is not time reversal invariant, and hence swimming is possible. We use analytical and numerical solutions of the Stokes equations to calculate the hydrodynamic interaction between two dumb-bell swimmers and to discuss their relative motion. The cooperative effect of interactions between swimmers is explored by considering first regular, and then random arrays of dumb-bells. We find that a square array acts as a micropump. The long time behaviour of suspensions of dumb-bells is investigated and compared to that of model polar swimmers.
