Phase separation of active Brownian particles in two dimensions: Anything for a quiet life

TL;DR

This paper presents a detailed theoretical framework for motility-induced phase separation in active Brownian particles, incorporating superadiabatic forces and spatial-orientational dependencies, aligning well with simulation results.

Contribution

It introduces a comprehensive power functional theory that accounts for superadiabatic forces and detailed spatial-orientational dynamics in active particle phase separation.

Findings

Quantitative agreement with Brownian dynamics simulations

Detailed analytical resolution of density and current distributions

Identification of superadiabatic forces driving phase separation

Abstract

Active Brownian particles display self-propelled movement, which can be modelled as arising from a one-body force. Although their interparticle interactions are purely repulsive, for strong self propulsion the swimmers phase separate into dilute and dense phases. We describe in detail a recent theory (Phys. Rev. E 100, 052604 (2019); Phys. Rev. Lett. 128, 26802 (2019)) for such motility induced phase-separation. Starting from the continuity equation and the force density balance, the description is based on four superadiabatic contributions to the internal force density. Here the superadiabatic forces are due to the flow in the system and they act on top of the adiabatic forces that arise from the equilibrium free energy. Phase coexistence is described by bulk state functions and agrees quantitatively with Brownian dynamics simulation results from the literature. We describe in detail all analytical steps to fully resolve the spatial and orientational dependence of the one-body density and current. The decomposition into angular Fourier series leads to coupling of total density, polarization and all higher modes. We describe the power functional approach, including the kinematic dependence of the superadiabatic force fields and the quiet life effect that pushes particles from fast to slow regions, and hence induces the phase separation.