Microscopic theory for the phase separation of self-propelled repulsive disks

Motivated by recent experiments on colloidal suspensions, we study analytically and numerically a microscopic model for self-propelled particles lacking alignment interactions. In this model, even for purely repulsive interactions, a dynamical instability leading to phase separation has been reported. Starting from the many-body Smoluchowski equation, we develop a mean-field description based on a novel closure scheme and derive the effective hydrodynamic equations. We demonstrate that the microscopic origin of the instability is a force imbalance due to an anisotropic pair distribution leading to self-trapping. The phase diagram can be understood in terms of two quantities: a minimal drive and the force imbalance. At sufficiently high propulsion speeds there is a reentrance into the disordered fluid.