Motility-Induced Phase Separation

TL;DR

Self-propelled particles can spontaneously separate into dense and dilute phases due to their speed dependence on local density, a phenomenon called motility-induced phase separation (MIPS), which challenges traditional equilibrium thermodynamics.

Contribution

This paper provides a theoretical and simulation overview of MIPS, highlighting its connection to equilibrium phase separation and exploring effects beyond the leading order in gradients.

Findings

MIPS results from particles slowing down at high density, causing phase separation.

Simulations confirm the link between self-propelled and passive particles with attractions.

Higher-order effects in gradients lead to new phenomena without equilibrium counterparts.

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.