Active matter invasion of a viscous fluid

Unstable sheets and a no-flow theorem

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

Research output: Contribution to journalArticle

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 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
Volume122
Issue number9
DOIs
StatePublished - Mar 4 2019

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viscous fluids
theorems
Taylor instability
two dimensional flow
isotropy
fluid flow
cascades
dipoles
cells

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Active matter invasion of a viscous fluid : Unstable sheets and a no-flow theorem. / Miles, Christopher J.; Evans, Arthur A.; Shelley, Michael; Spagnolie, Saverio E.

In: Physical Review Letters, Vol. 122, No. 9, 098002, 04.03.2019.

Research output: Contribution to journalArticle

Miles, Christopher J. ; Evans, Arthur A. ; Shelley, Michael ; Spagnolie, Saverio E. / Active matter invasion of a viscous fluid : Unstable sheets and a no-flow theorem. In: Physical Review Letters. 2019 ; Vol. 122, No. 9.
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