Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles

TL;DR

This paper develops a macroscopic coupled model for active particles in a fluid, integrating self-propelled particle dynamics with fluid interactions, and analyzes stability and extensions of the model.

Contribution

It introduces a coupled Self-Organized Hydrodynamics-Stokes system derived from microscopic models, including stability analysis and extensions for realistic conditions.

Findings

Both pullers and pushers exhibit unstable modes.

The coupled system captures fluid-particle interactions at high densities.

Extensions include repulsion, inertia, and finite Reynolds number effects.

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 (SOH)-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.