Kinetic theory of motility induced phase separation for active Brownian particles

When two active Brownian particles collide, they slide along each other until they can continue their free motion. For persistence lengths much larger than the particle diameter, the directors do not change, but the collision can be modeled as producing a net displacement on the particles compared to their free motion in the absence of the encounter. With these elements, a Boltzmann--Enskog-like kinetic theory is built. A linear stability analysis of the homogeneous state predicts a density instability resulting from the effective velocity reduction of tagged particles predicted by the theory.