Dependence of phase behavior and surface tension on particle stiffness for active Brownian particles

TL;DR

This paper develops a microscopic and continuum theoretical framework to predict phase behavior, pressure, and surface tension in active Brownian particles, validated by simulations, revealing intrinsic interface properties and the importance of pressure formulation.

Contribution

It introduces a novel analytical method for predicting dense phase structure and a continuum model that accurately captures pressure and surface tension in active particle systems.

Findings

Predicted dense phase structure matches Brownian dynamics simulations.

Formulating pressure as interparticle pressure yields consistent continuum predictions.

Surface tension and interface width are intrinsic system properties, independent of activity and stiffness.

Abstract

We study quasi two-dimensional, monodisperse systems of active Brownian particles (ABPs) for a range of activities, stiffnesses, and densities. We develop a microscopic, analytical method for predicting the dense phase structure formed after motility-induced phase separation (MIPS) has occurred, including the dense cluster's area fraction, interparticle pressure, and radius. Our predictions are in good agreement with our Brownian dynamics simulations. We, then, derive a continuum model to investigate the relationship between the predicted interparticle pressure, the swim pressure, and the macroscopic pressure in the momentum equation. We find that formulating the point-wise macroscopic pressure as the interparticle pressure and modeling the particle activity through a spatially variant body force -- as opposed to a volume-averaged swim pressure -- results in consistent predictions of pressure in both the continuum model and the microscopic theory. This formulation of pressure also results in nearly zero surface tension for the phase separated domains, irrespective of activity, stiffness, and area fraction. Furthermore, using Brownian dynamics simulations and our continuum model, we showed that both the interface width and surface tension, are intrinsic characteristics of the system. On the other hand, if we were to exclude the body force induced by activity, we find that the resulting surface tension values are linearly dependent on the size of the simulation, in contrast to the statistical mechanical definition of surface tension.