(280c) Instabilities, Pattern Formation, and Mixing In Suspensions of Swimming Particles

We use kinetic theory to study the linear stability and the non-linear pattern formation in suspensions of swimming particles. The evolution of a suspension is modeled using a continuity equation for the particle configurations, coupled to a mean-field description of the flow arising from the stress exerted by the particles on the fluid. Based on this model, we first investigate the stability of both aligned and isotropic suspensions. In aligned suspensions, an instability is shown to always occur at finite wavelengths, a result that extends previous theoretical predictions. In isotropic suspensions, we demonstrate the existence of an instability for the active particle stress, in which shear stresses are eigenmodes and grow exponentially at long scales. Non-linear effects are also investigated using numerical simulations in two dimensions. These simulations confirm the results of the stability analysis, and the long-time non-linear behavior is shown to be characterized by the formation of strong density fluctuations, which merge and break up in time in a quasi-periodic fashion. These complex motions result in efficient fluid mixing, which we quantify by means of a multiscale mixing norm.