Phase separation in active systems: field theoretical description

Active particles extract energy from the environment and dissipate it to self-propel. One of their notable self-organizing phenomenologies is phase separation into dense (liquid) and dilute (vapor) regions, which happens even for purely repulsive units. This phenomena, although generically happening far-from-equilibrium, was first described via an approximate mapping onto equilibrium liquid-vapor phase separation.

Recently it has become clear, however, that phase separation in active systems generically displays strongly non-equilibrium features. In experiments, phase separation is often arrested to a finite length-scale (micro-phase separation). Active systems can undergo bubbly phase separation, where a seemingly boiling liquid coexists with a vapour region, and even more complex forms of phase separation have been observed experimentally. 

I will describe our recent efforts to describe phase separation in active matter and, more generally, in systems where detailed balance is broken locally. These results will be investigated via field-theoretical analysis, extending Model B to include the leading-order terms that break detailed balance (Active Model B+). This allowed to rationalize microphase separation, of either liquid droplets or vapour bubbles, and bubbly phase separation via a generic mechanism: the fact that at high activity Ostwald ripening can go into reverse. We further discover that activity can cause an instability of the liquid-vapor interface, giving rise to another form of active phase separation resembling to active foam states. Simulations of particle models further strengthen the figure.