Competing effect of disorder on phase separation in active systems

We investigate the impact of random pinned disorder on a collection of self-propelled particles. To achieve this, we construct a continuum model by formulating the coupled hydrodynamic equations for slow variables: local density and momentum density of particles. The disorder in the system acts as pinning sites, effectively immobilizing the particles that come into contact with them. Our numerical results reveal that weak disorder leads to phase separation in the system at density and activity lower than the typical values for motility-induced phase separation. We construct a phase diagram using numerical simulations as well as linearized approximation in the plane of activity and packing fraction of particles at weak disorder densities. On increasing disorder density, the system shows the microphase separation, while at large disorder densities the system becomes heterogeneous and eventually undergoes kinetic arrest. The structure factor tail deviates from Porod's law, indicating increased roughness at domain interfaces under strong disorder. Furthermore, we analyze the fractal dimension of the interface as a function of disorder density, highlighting the increasing irregularity of phase-separated domains. We also find that disorder significantly suppresses number fluctuations in the system.