Geometric control of active collective motion

TL;DR

This paper investigates how confinement geometries influence the collective motion of active suspensions, revealing distinct dynamic states and transitions, and providing a theoretical framework for controlling active matter in microfluidic systems.

Contribution

It introduces a mean-field kinetic theory to analyze active suspension dynamics in confined geometries, explaining experimental observations and predicting new transition behaviors.

Findings

Identified three states in circular domains: equilibrium, vortex, chaos.

Observed transitions in racetrack geometries: equilibrium, pumping, waves, chaos.

Theoretical predictions match experimental results.

Abstract

Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and the emergence of unidirectional pumping motions in periodic racetrack geometries. Motivated by these findings, we analyze the two-dimensional dynamics in confined suspensions of active self-propelled swimmers using a mean-field kinetic theory where conservation equations for the particle configurations are coupled to the forced Navier-Stokes equations for the self-generated fluid flow. In circular domains, a systematic exploration of the parameter space casts light on three distinct states: equilibrium with no flow, stable vortex, and chaotic motion, and the transitions between these are explained and predicted quantitatively using a linearized theory. In periodic racetracks, similar transitions from equilibrium to net pumping to traveling waves to chaos are observed in agreement with experimental observations and are also explained theoretically. Our results underscore the subtle effects of geometry on the morphology and dynamics of emerging patterns in active suspensions and pave the way for the control of active collective motion in microfluidic devices.