Journal
PHYSICAL REVIEW LETTERS
Volume 122, Issue 9, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.122.098002
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Funding
- National Science Foundation [DMR-0820341, DMS-1463962, DMS-1620331, DMR 767-1121288, DMS-1661900]
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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.
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