Virial pressure in systems of active Brownian particles

TL;DR

This paper investigates the pressure behavior of active Brownian particles through theory and simulations, revealing an active equation of state, the influence of confinement, and a phase transition at high activity levels.

Contribution

It derives a nonequilibrium equation of state for ABPs, including wall effects and activity contributions, and identifies a phase transition related to activity and concentration.

Findings

Pressure depends on confinement and wall interactions.

Pressure exhibits nonmonotonic behavior with increasing activity.

A phase transition occurs at high activity and concentration.

Abstract

The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABP). We show that for certain geometries, the mechanical pressure as force/area of a confined systems can equally be expressed by bulk properties, which implies the existence of an nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induce pressure (swim pressure), which can be expressed in terms of a product of the bare and a mean effective propulsion velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional APBs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.