Active matter invasion of a viscous fluid: unstable sheets and a no-flow theorem

Abstract

We investigate the dynamics of a dilute suspension of hydrodynamically interacting motile or immotile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities, governed at small times by an equation which also describes the Saffman-Taylor instability in a Hele-Shaw cell, or Rayleigh-Taylor instability in two-dimensional flow through a porous medium. Thin sheets of aligned pusher particles are always unstable, while sheets of aligned puller particles can either be stable (immotile particles), or unstable (motile particles) with a growth rate which is non-monotonic in the force dipole strength. We also prove a surprising "no-flow theorem": a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow everywhere and for all time.

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Cited by in corpus (8)

• Swimming in Complex Fluids
• Chemotactic smoothing of collective migration
• Fingering Instability of Active Nematic Droplets
• Asymmetric fluctuations and self-folding of active interfaces
• Trapping of swimmers in a vortex lattice
• Hele-Shaw flow for parity odd three-dimensional fluids
• The $\mathbf{Q}$-tensor Model with Uniaxial Constraint
• Anisotropy of the hydrostatic stress for Hall droplets with in-plane magnetic field