Swimmers in thin films: from swarming to hydrodynamic instabilities

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.

4 pages, 2 figures, references added, typos corrected, new introduction

References in corpus (4)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• Analytic results for the three-sphere swimmer at low Reynolds number
• A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms

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