Chemotactic aggregation dynamics of micro-swimmers in Brinkman flows

Abstract: We study through analysis and simulations of a continuum model the collective chemotactic dynamics of micro-swimmers immersed in viscous Brinkman flows. The Brinkman viscous flow approximates with a resistance or friction term the presence of inert impurities or stationary obstacles immersed in the fluid, an environment that can be regarded as a wet porous medium. Analysis of the linearized system reveals that resistance primarily affects the development of collective swimming instabilities and barely affects chemotactic instabilities. We present a parameter phase space for the distinct types of dynamics we can expect in the case of auto-chemotactic bacteria-like pusher swimmers for varying medium resistance, chemotactic response strength, and hydrodynamic coupling strength values. Simulations of the full nonlinear system show that resistance impacts the collective dynamics for each of these states because it inhibits the hydrodynamic interactions and the emergence of the collective swimmer. Surprisingly, and not expected from the linear analysis predictions, we find that resistance also hampers the chemotactic aggregation of the swimmers because it impedes their ability to navigate efficiently and collectively towards chemical cues and assemble into clusters. We show simulations of the complex system for parameters sets from each of the phase-space regions and quantify the observed behavior. Lastly, we discuss the experimental values of the parameters and discuss possible future experimental realizations of this system.