Coupled self-organized hydrodynamics and Stokes models for suspensions of active particles

Pierre Degond Department of Mathematics, Imperial College London, London, SW7 2AZ, UK Sara Merino-Aceituno Department of Mathematics, Imperial College London, London, SW7 2AZ, UK; Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria; Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9RH, UK Fabien Vergnet Laboratoire de mathématiques d’Orsay (LMO), Université Paris-Sud, CNRS, Universit Paris-Saclay, 15 rue Georges Clémenceau, 91405, Orsay Cedex, France Hui Yu Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, 52062, Aachen, Germany; Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing, 100084, China

Fluid Dynamics and Shock Waves mathscidoc:2205.14015

Journal of Mathematical Fluid Mechanics, 21, (6), 2019.1
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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@inproceedings{pierre2019coupled,
  title={Coupled self-organized hydrodynamics and Stokes models for suspensions of active particles},
  author={Pierre Degond, Sara Merino-Aceituno, Fabien Vergnet, and Hui Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520145356904080306},
  booktitle={Journal of Mathematical Fluid Mechanics},
  volume={21},
  number={6},
  year={2019},
}
Pierre Degond, Sara Merino-Aceituno, Fabien Vergnet, and Hui Yu. Coupled self-organized hydrodynamics and Stokes models for suspensions of active particles. 2019. Vol. 21. In Journal of Mathematical Fluid Mechanics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520145356904080306.
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