Collective motion of microswimmers in impure flow

We investigate through mathematical modeling, analysis and nonlinear simulations, the collective motion of micro-swimmers in fluids with resistance, which approximate a porous wet material. We use a continuum model to describe the collective dynamics of bacteria that each perform a run-and-tumble motion. The swimmer dynamics is coupled to the fluid dynamics that is modeled through a Stokes-Brinkman equation with an added active stress. The linear stability of the uniform isotropic state reveals that the suspension transitions from a long-wave instability to a finite-range one where the collective bacterial chaotic motion is weakened by the resistance. Simulations of the full nonlinear PDE system confirm the analytical results. We discuss the spread of an initial accumulation of bacteria and show that it depends non-trivially on the medium resistance which suppresses the spread. Last, we outline ongoing work on high performance simulations of the coupled motion of thousands of individually-traced swimmers in Brinkman flows.