Motility-induced phase separation and coarsening in active matter

Active systems, or active matter, are self-driven systems that live, or function, far from equilibrium - a paradigmatic example that we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The non-equilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one, which has recently been the subject of intense interest among biological and soft matter physicists, is that of the so-called "motility-induced phase separation", whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions - we will briefly discuss at the end their role, which is not currently fully understood in this context.