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.
Keywords
Cite
@article{arxiv.1803.05543,
title = {Active matter invasion of a viscous fluid: unstable sheets and a no-flow theorem},
author = {Christopher J. Miles and Arthur A. Evans and Michael J. Shelley and Saverio E. Spagnolie},
journal= {arXiv preprint arXiv:1803.05543},
year = {2019}
}