Chemotactic aggregation of micro-swimmers in Brinkman flows

We study through analysis and computer simulations of a continuum model the collective dynamics and chemotactic aggregation 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, and such an environment can be regarded as a wet porous medium. Analysis of the linearized system reveals that resistance affects the hydrodynamic interactions between swimmers and their collective swimming. We present a parameter phase space for the distinct types of dynamics we can expect in the case of chemotactic pusher swimmers. Simulations of the full nonlinear system show that resistance impacts the collective dynamics for each of these states because it inhibits the interactions and collective motion of the swimmers. Surprisingly and unpredicted by linear analysis, we find that resistance also hampers the chemotactic aggregation of the swimmers because it impedes their ability to navigate efficiently towards chemotactic cues and assemble into clusters. We show several simulations of the complex system for various parameters sets and quantify the observed behavior through several measured quantities.