Two-field theory for phase coexistence of active Brownian particles

Active Brownian particles (ABPs) serve as a minimal model of active matter systems. When ABPs are sufficiently persistent, they undergo a liquid-gas phase separation and, in the presence of obstacles, accumulate around them, forming a wetting layer. Here, we perform simulations of ABPs in a quasi-one-dimensional domain in the presence of a wall, studying the dynamics of the polarization field. Over the course of time, we observe a transition from a homogeneous (where all particles are aligned) to a heterogeneous (where particles align only at the interface) polarization regime. We propose coarse-grained equations for the density and polarization fields based on microscopic and phenomenological arguments that correctly account for the observed phenomena.