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

TL;DR

This paper studies how active particles invade viscous fluids, revealing instabilities in particle sheets and proving a no-flow theorem that describes isotropic distributions causing no fluid movement.

Contribution

It introduces a new instability analysis for active particle invasion and proves a surprising no-flow theorem for isotropic distributions in viscous fluids.

Findings

Aligned pusher sheets are always unstable.

Puller sheets can be stable or unstable depending on motility.

Isotropic distributions cause no fluid flow at any time.

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.