Swimming with a friend at low Reynolds number

TL;DR

This paper explores the hydrodynamic interactions of microorganisms swimming at low Reynolds number, revealing complex behaviors influenced by their interactions and symmetries, with implications for understanding collective motion.

Contribution

It combines analytic and numerical methods to analyze flow fields and interactions between simple model swimmers, highlighting the dominance of live interactions over dead dipolar terms.

Findings

Swimmers behave like pumps at short distances.

Flow fields depend on symmetry of swimming strokes.

Swimmer interactions can be attractive, repulsive, or oscillatory.

Abstract

We investigate the hydrodynamic interactions between microorganisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a swimmer. At short distances the swimmer behaves like a pump. At large distances the velocity field depends on whether the swimming stroke is invariant under a combined time-reversal and parity transformation. We then consider two swimmers and find that the interaction between them consists of two parts; a dead term, independent of the motion of the second swimmer, which takes the expected dipolar form and a live term resulting from the simultaneous swimming action of both swimmers which does not. We argue that, in general, the latter dominates. The swimmer--swimmer interaction is a complicated function of their relative displacement, orientation and phase, leading to motion that can be attractive, repulsive or oscillatory.