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 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 behavior. In contrast, for quadrupolar swimmers, details of the internal dynamics are important in determining the bulk behavior. In the broken symmetry phases, fluctuations of hydrodynamic variables destabilize order. Interestingly, this instability is not generic and depends on the length scale.