Instabilities and Pattern Formation in Active Particle Suspensions: Kinetic Theory and Continuum Simulations

We use kinetic theory and nonlinear continuum simulations to study the collective dynamics in suspensions of self-propelled particles. The stability of aligned suspensions is first analyzed, and we demonstrate that such suspensions are always unstable to fluctuations, a result that generalizes previous predictions by Simha and Ramaswamy. Isotropic suspensions are also considered, and it is shown that an instability for the particle stress occurs in that case. Using simulations, nonlinear effects are investigated, and the long-time behavior of the suspensions is observed to be characterized by the formation of strong density fluctuations, resulting in efficient fluid mixing.