Activity induced phase separation

We consider a mixture of passive (i.e., Brownian) and active (e.g., bacterial or colloidal swimmers) particles, and analyze the stability conditions of either uniformly mixed or phase segregated steady states consisting of phases enriched with different types of particles. We show that in sufficiently dilute mixtures the system behaves as if it were exposed to two separate heat baths of uneven temperatures. It can be described within a second virial approximation neglecting three body and higher order collisions. In this approximation, we define non-equilibrium "chemical potentials" whose gradients govern diffusion fluxes and a non-equilibrium "osmotic pressure", which governs the mechanical stability of the interface.