Collective dynamics of micro-swimmers in Brinkman flows

Micro-swimmers live and have evolved in multiplex environments containing inert particles, obstacles, and impurities which affect their motion. Understanding the swimmers' locomotion and interactions in such inhomogenous environments viscous fluids is crucial to understanding their emerging dynamics.

We derive a model for rigid active particles immersed in viscous Brinkman flows -- which approximate with a linear resistance term the presence of much smaller inert impurities or stationary obstacles. We show that resistance alters the disturbance flow generated as each active particle swims, and as such alters the hydrodynamical interactions between swimmers and ultimately modifies their coupled dynamics. Simulations implemented using the Immersed Boundary Method show that resistance inhibits correlated collective dynamics in micro-swimmer suspensions because resistance hinders each individual's motion and its interactions with others. We analyze the resulting dynamics for varying resistance strengths, and show that a high resistance, in accordance with results from analysis of the related continuum model, can fully suppress the emergence of macroscopic collective motion.