Bifurcations and pattern formation in active suspensions

We consider the Saintillan--Shelley [2008] kinetic model of active rodlike particles in Stokes flow, for which the uniform, isotropic suspension of pusher particles is known to be unstable in certain settings. We determine exactly how the isotropic steady state loses stability in different parameter regimes. Through weakly nonlinear analysis accompanied by numerical simulations, we study each of the various types of bifurcations admitted by the system, including both subcritical and supercritical Hopf and pitchfork bifurcations. Elucidating this system's behavior near these bifurcations provides both a means of verifying the predictive power of the model against experimental observations as well as a theoretical means of comparing this model with other systems which transition to turbulence.