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

Christopher J. Miles, Arthur A. Evans, Michael J. Shelley, Saverio E. Spagnolie

Research output: Contribution to journalArticlepeer-review


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 that also describes the Saffman-Taylor instability in a Hele-Shaw cell, or the Rayleigh-Taylor instability in a 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 that is nonmonotonic 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.

Original languageEnglish (US)
Article number098002
JournalPhysical Review Letters
Issue number9
StatePublished - Mar 4 2019

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'Active matter invasion of a viscous fluid: Unstable sheets and a no-flow theorem'. Together they form a unique fingerprint.

Cite this