Coarsening kinetics in active model B+: Macroscale and microscale phase separation

We perform a comprehensive numerical investigation of the coarsening kinetics of active Brownian particles modeled by the Active Model B+ (AMB+). This model was introduced by Tjhung et al. [E. Tjhung et al., Phys. Rev. X 8, 031080 (2018)2160-330810.1103/PhysRevX.8.031080] and is a generalization of Model B for a conserved order parameter, with two additional activity terms. These terms correspond to rotation-free current (of strength λ) and rotational current (of strength ξ). There is a range of (λ,ξ) values for which the system undergoes macroscale phase separation (MPS). In this case, the order parameter current develops a structured pattern consisting of alternating clockwise and anticlockwise loops along domain walls. These pairs are separated by nodal points where the current magnitude is very small. The mass transfer is driven by the overlap of loops on neighboring droplets. Thus, the mass has to undergo circular trajectories while transferring from smaller droplets to larger droplets. This slows down domain growth in comparison to Model B, where the current is transported by the shortest route between droplets. Thus, there is slower coarsening in AMB+, with an asymptotic growth exponent of 1/4. For another range of (λ,ξ) values, the system undergoes microscale phase separation (µPS), i.e., it reaches a steady-state morphology characterized by a crystal of monodisperse droplets, whose size depends on the parameters. We present detailed results for the kinetics of MPS and µPS in AMB+ with a critical composition, where the system undergoes spinodal decomposition.