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Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles

Authors
  • Degond, Pierre1
  • Merino-Aceituno, Sara1, 2, 3
  • Vergnet, Fabien4
  • Yu, Hui5, 6
  • 1 Imperial College London, London, SW7 2AZ, UK , London (United Kingdom)
  • 2 University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria , Vienna (Austria)
  • 3 University of Sussex, Falmer, Brighton, BN1 9RH, UK , Falmer, Brighton (United Kingdom)
  • 4 Universit Paris-Saclay, 15 rue Georges Clémenceau, Orsay Cedex, 91405, France , Orsay Cedex (France)
  • 5 RWTH Aachen University, Aachen, 52062, Germany , Aachen (Germany)
  • 6 Tsinghua University, Haidian District, Beijing, 100084, China , Haidian District (China)
Type
Published Article
Journal
Journal of Mathematical Fluid Mechanics
Publisher
Springer International Publishing
Publication Date
Jan 31, 2019
Volume
21
Issue
1
Identifiers
DOI: 10.1007/s00021-019-0406-9
Source
Springer Nature
Keywords
License
Green

Abstract

We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek–Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery’s equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-graining we obtain a coupled Self-Organised Hydrodynamics–Stokes system. We perform a linear stability analysis for this system which shows that both pullers and pushers have unstable modes. We conclude by providing extensions of the Vicsek–Stokes model including short-distance repulsion, finite particle inertia and finite Reynolds number fluid regime.

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