Active model B+ from run-and-tumble particles on a triangular lattice

Abstract

Active model B+ (AMB+) explains how motility-induced phase separation can be arrested by reverse Ostwald ripening, but its coefficients have not been derived from a microscopic lattice model that shows it. We provide an exact hydrodynamic description of a six-polarity lattice gas on a hexagonal geometry and employ a full gradient expansion with angular-harmonic elimination to rigorously derive AMB+ with every coefficient fixed by the Péclet number Pe. Near the critical point (3/4, 4), coarsening is ordinary; further away, field theory predicts reverse Ostwald ripening of vapor bubbles above Pe $> 4 \sqrt{3}$, and simulations show long-lived bubbly states.