Active phase separation: new phenomenology from non-equilibrium physics

In active systems, whose constituents have non-equilibrium dynamics at local level, fluid-fluid phase separation is widely observed. Examples include the formation of membraneless organelles within cells; the clustering of self-propelled colloidal particles in the absence of attractive forces, and some types of ecological segregation. A schematic understanding of such active phase separation was initially borrowed from what is known for the equilibrium case, in which detailed balance holds at microscopic level. However it has recently become clear that in active systems the absence of detailed balance, although it leave phase separation qualitatively unchanged in some regimes (for example domain growth driven by interfacial tension via Ostwald ripening), can in other regimes radically alter its phenomenology at mechanistic level. For example, microphase separation can be caused by reverse Ostwald ripening, a process that is hard to imagine from an equilibrium perspective. This and other new phenomena arise because, instead of having a single, positive interfacial tension like their equilibrium counterparts, the fluid-fluid interfaces created by active phase separation can have several distinct interfacial tensions governing different properties, some of which can be negative. These phenomena can be broadly understood by studying continuum field theories for a single conserved scalar order parameter (the fluid density), supplemented with a velocity field in cases where momentum conservation is also present. More complex regimes arise in systems described by multiple scalar order parameters (especially with nonreciprocal interactions between these); or when an order parameter undergoes both conserved and non-conserved dynamics (such that the combination breaks detailed balance); or in systems that support orientational long-range order in one or more of the coexisting phases. In this Review, we survey recent progress in understanding the specific role of activity in phase separation, drawing attention to many open questions. We focus primarily on continuum theories, especially those with a single scalar order parameter, reviewing both analytical and numerical work. We compare their predictions with particle-based models, which have mostly been studied numerically although a few have been explicitly coarse-grained to continuum level. We also compare, where possible, with experimental results. In the latter case, qualitative comparisons are broadly encouraging whereas quantitative ones are hindered by the dynamical complexity of most experimental systems relative that of simplified (particle-level or continuum) models of active matter.