Microscopic theory for the phase separation of self-propelled repulsive disks

TL;DR

This paper develops a microscopic mean-field theory to explain phase separation in self-propelled repulsive disks, revealing a force imbalance mechanism and phase diagram features including reentrant fluid behavior.

Contribution

It introduces a novel closure scheme for deriving hydrodynamic equations from the microscopic model of self-propelled particles without alignment.

Findings

Identifies force imbalance as the cause of phase separation.

Derives a phase diagram with a minimal drive threshold.

Shows reentrant fluid phase at high propulsion speeds.

Abstract

Motivated by recent experiments on colloidal suspensions, we study analytically and numerically a microscopic model for self-propelled particles lacking alignment interactions. In this model, even for purely repulsive interactions, a dynamical instability leading to phase separation has been reported. Starting from the many-body Smoluchowski equation, we develop a mean-field description based on a novel closure scheme and derive the effective hydrodynamic equations. We demonstrate that the microscopic origin of the instability is a force imbalance due to an anisotropic pair distribution leading to self-trapping. The phase diagram can be understood in terms of two quantities: a minimal drive and the force imbalance. At sufficiently high propulsion speeds there is a reentrance into the disordered fluid.