Scattering of low Reynolds number swimmers

TL;DR

This paper explores how time reversal symmetry in Stokes' flow affects the scattering behavior of low Reynolds number swimmers, revealing preserved angles for symmetric pairs and significant reorientation for others, including bound state formation.

Contribution

It demonstrates the impact of time reversal invariance on swimmer scattering and introduces a linked-sphere model to illustrate these effects.

Findings

Time reversal symmetry preserves the angle between symmetric swimmers.

Hydrodynamic scattering can significantly change the angle between non-symmetric swimmers.

Identical contractile swimmers can form bound states due to hydrodynamic interactions.

Abstract

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 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.