Stochastic Kinetic Theory for Collective Behavior of Hydrodynamically Interacting Active Particles

TL;DR

This paper develops a stochastic kinetic theory to analyze the collective behavior of hydrodynamically interacting microswimmers, revealing insights into spatial correlations, stress, and tracer diffusion in 2D and 3D systems.

Contribution

It introduces a stochastic flux approach into the mean field kinetic equation, providing a new method to study stable regimes of microswimmer suspensions.

Findings

Quantifies spatial correlations of orientation and stress.

Shows enhanced diffusion of tracer particles.

Demonstrates superdiffusion in three-dimensional systems.

Abstract

Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as the enhanced diffusion of tracer particles. Our analysis here focuses primarily on two-dimensional systems, though we also show how superdiffusion of tracers in three dimensions can occur by our framework.