Three-body correlations and conditional forces in suspensions of active hard disks

TL;DR

This paper develops an approximate analytical theory for three-body correlations and forces in active Brownian disks, validated by simulations, to better understand the collective behavior and structure in active suspensions related to MIPS.

Contribution

It introduces a novel analytical framework for three-body correlations in active Brownian particles, linking forces, propulsion speed, and collective phenomena like MIPS.

Findings

Good agreement between theory and simulations for pair-distribution functions.

Identification of preferred force directions related to propulsion and surrounding particles.

The theory provides insights into the collective behavior and structure of active suspensions.

Abstract

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, sheds new light onto the collective behavior, and makes a step towards an emerging liquid state theory.