Kinetics of cluster formation in active suspension: Coarsening regime

The active suspension has an amazing property to undergo a phase transition into dense and dilute gas phases, even in the absence of the interparticle forces of attraction. In this work, the phase transition in active suspension is considered within a minimal model, in which self-propelled particles are moving with a constant speed, while their direction of propagation is governed by mutual collisions. The final stage of cluster formation in active suspension is studied when the larger clusters grow by consuming the smaller ones. The analysis of kinetic equation for the evolution of the number of particles in a cluster and conservation of particles law in active suspension shows that the number of clusters decreases with time according to a power of minus three fifths and the average number of particles in a cluster depends on their speed and time in the power of three fifths. The size distribution function of clusters is obtained, which is found to be asymmetric with respect to the average number of particles in clusters.