Hydrodynamic Equations for Active Brownian Particles in the High Persistence Regime

TL;DR

This paper derives Navier-Stokes-like equations for active Brownian particles in the high persistence regime, capturing polarization effects and phase separation, with numerical validation and insights into clustering and wave phenomena.

Contribution

It introduces a new continuum model incorporating polarization for ABP in the high persistence regime, with transport coefficients derived from microscopic dynamics.

Findings

The equations predict density instability leading to phase separation.

Numerical solutions show clustering and polarization at interfaces.

Damped density wave modes emerge due to polarization coupling.

Abstract

In the high persistence regime of non-inertial active Brownian particles (ABP), polarization becomes a relevant dynamical field. Based on a recently proposed kinetic description for ABP, we derive Navier-Stokes-like equations for the density and polarization fields in this regime. Using the Chapman-Enskog method, all transport coefficients in the equations are obtained entirely in terms of the microscopic dynamics. A linear stability analysis of the homogeneous and isotropic state shows that the derived equations correctly describe the density instability associated to the motility induced phase separation. Numerical solutions of the equations in one spatial dimension show the need of an additional regularizing pressure term to saturate the system at high densities. With the inclusion of this term, the solutions illustrate in detail the clustering dynamics, with the formation of polarized regions at the interfaces, and the subsequent coarsening of domains, as well as particle accumulation in presence of gravity. Finally, the derived equations imply that, as an effect of the coupling with the polarization, damped density wave modes appear in the system which were verified with numerical simulations.