Concentrated active suspensions: Kinetic theory, linear stability and numerical simulations

We study concentrated suspensions of self-propelled rod-like particles using a kinetic model which accounts for local hydrodynamic and steric interactions. We report a base state transition from an isotropic to a nematic orientation distribution beyond a critical effective volume fraction consistent with the Doi-Edwards theory for passive rod-like particles (Doi and Edwards 1986). We analyze the kinetic model linearized near the isotropic and nematic basestates and show that steric interactions have a destabilizing effect causing both pusher and puller suspensions to be subject to instabilities. These predictions from the linear theory are confirmed using fully nonlinear three-dimensional numerical simulations of the kinetic equations, which also demonstrate large-scale fluctuations of number density and nematic order parameter.