Congestion model of active particle phase separation

Self-propelled particles phase separate into coexisting dense and dilute regions above a critical density. The statistical nature of their stochastic rotation lends itself to various theories that predict the onset of phase separation. However, these theories are ill equipped to describe such behavior when noise become negligible. To overcome this limitation, we present a predictive model that relies on two density-dependent timescales: the mean time particles spend between collisions; and the mean lifetime of a collision. We show that only when the former is less than the later, do collisions last long enough to develop a growing cluster and initiate phase separation. Using both analytical calculations and active Brownian particle simulations, we measure these timescales and determine the critical density for phase separation in both 2D and 3D.