Motility-Induced Phase Separation

TLDR

Self‑propelled particles, such as synthetic colloids and microorganisms, consume energy to move, violating equilibrium thermodynamics and tending to accumulate where they move more slowly, which can create a positive feedback that drives motility‑induced phase separation. The authors provide a selective overview of the rapidly developing field of motility‑induced phase separation, concentrating on theory and simulation while briefly speculating on experimental implications. At leading order in gradients, a mapping relates variable‑speed self‑propelled particles to passive particles with attractions, and the review discusses this theoretical framework and its simulation studies. Simulations confirm that the leading‑order mapping reproduces equilibrium‑like phase separation, but higher‑order gradient effects break this correspondence and generate new non‑equilibrium phenomena.

Abstract

Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: the steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density, for either biochemical or steric reasons. This creates positive feedback which can lead to motility-induced phase separation (MIPS) between dense and dilute fluid phases. At leading order in gradients, a mapping relates variable-speed, self-propelled particles to passive particles with attractions. This deep link to equilibrium phase separation is confirmed by simulations, but generally breaks down at higher order in gradients: new effects, with no equilibrium counterpart, then emerge. We give a selective overview of the fast-developing field of MIPS, focusing on theory and simulation but including a brief speculative survey of its experimental implications.