TY - JOUR
T1 - Active matter invasion of a viscous fluid
T2 - Unstable sheets and a no-flow theorem
AU - Miles, Christopher J.
AU - Evans, Arthur A.
AU - Shelley, Michael J.
AU - Spagnolie, Saverio E.
N1 - Funding Information:
This project was initiated at the Woods Hole Oceanographic Institute as part of the Geophysical Fluid Dynamics summer program. Financial support is acknowledged by M.?J.?S. (National Science Foundation Grants No. DMR-0820341 [NYU MRSEC], No. DMS-1463962, and No. DMS-1620331) and S.?E.?S. (Grants No. DMR 767-1121288 [UW MRSEC] and No. DMS-1661900).
Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/3/4
Y1 - 2019/3/4
N2 - 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.
AB - 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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U2 - 10.1103/PhysRevLett.122.098002
DO - 10.1103/PhysRevLett.122.098002
M3 - Article
C2 - 30932541
AN - SCOPUS:85062947518
SN - 0031-9007
VL - 122
JO - Physical Review Letters
JF - Physical Review Letters
IS - 9
M1 - 098002
ER -