Hydrodynamic equations for active Brownian particles in the high-persistence regime

In the high persistence regime of noninertial active Brownian particles (ABPs), polarization becomes a relevant dynamical field. Based on a recently proposed kinetic description for ABPs, 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 for an additional regularizing pressure term to saturate the system at high densities. With the inclusion of this term, the solutions illustrate the clustering dynamics in detail, 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.