Statistical Mechanics of Transport Processes in Active Fluids II: Equations of Hydrodynamics for Active Brownian Particles

TL;DR

This paper develops a continuum-level hydrodynamic model for active Brownian particles, incorporating active forces, director fields, and swim pressure, advancing the understanding of active fluid dynamics.

Contribution

It derives a comprehensive continuum description including balance laws and the evolution of the director field, highlighting the role of aligning interactions and active pressure in active matter.

Findings

Active force appears as a body force proportional to a director field.

Bulk currents require inter-particle aligning interactions.

Derived expression for active or swim pressure in equilibrium.

Abstract

We perform a coarse-graining analysis of the paradigmatic active matter model, Active Brownian Particles, yielding a continuum description in terms of balance laws for mass, linear and angular momentum, and energy. The derivation of the balance of linear momentum reveals that the active force manifests itself directly as a continuum-level body force proportional to an order parameter-like director field, which therefore requires its own evolution equation to complete the continuum description of the system. We derive this equation, demonstrating in the process that bulk currents may be sustained in homogeneous systems only in the presence of inter-particle aligning interactions. Further, we perform a second coarse-graining of the balance of linear momentum and derive the expression for active or swim pressure in the case of mechanical equilibrium.