Swimmers in thin films: from swarming to hydrodynamic instabilities

TL;DR

This paper models the collective behavior of low Reynolds number swimmers confined to thin films, revealing how hydrodynamic interactions can lead to swarming, ordered states, and their destabilization due to fluctuations, with distinctions between dipolar and quadrupolar swimmers.

Contribution

It provides a theoretical framework for understanding how internal swimmer dynamics influence collective states and instabilities in thin film confined suspensions.

Findings

Hydrodynamic interactions induce swarming and ordered phases.

Fluctuations destabilize ordered states depending on length-scale.

Differences in internal dynamics of dipolar and quadrupolar swimmers are crucial.

Abstract

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses (force dipoles or quadrupoles) on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behaviour. In contrast, for quadrupolar swimmers, our analysis shows that detailed features of the internal dynamics play an important role in determining the bulk behaviour. In the broken symmetry phases, we investigate fluctuations of hydrodynamic variables of the system and find that these destabilize order. Interestingly, this instability is not generic and depends on length-scale.