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

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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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Degond, P., Merino-Aceituno, S., Vergnet, F., & Yu, H. (2019). Coupled Self-Organized Hydrodynamics and Stokes Models for Suspensions of Active Particles. Journal of Mathematical Fluid Mechanics, 21(1). https://doi.org/10.1007/s00021-019-0406-9

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