Title: 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.