Flow-Induced Phase Separation for Active Brownian Particles in Four-Roll-Mill Flow

We investigate the collective dynamics of active Brownian particles (ABPs) subjected to a steady two-dimensional four-roll-mill flow using numerical simulations. By varying the packing fraction ($\phi$), we uncover a novel flow-induced phase separation (FIPS) that emerges beyond a critical density ($\phi \geq 0.6$). The mean-square displacement (MSD) exhibits an intermediate bump between ballistic and diffusive regimes, indicating transient trapping and flow-guided clustering. The effective diffusivity decreases quadratically with $\phi$, while the drift velocity remains nearly constant, demonstrating that large-scale transport is primarily dictated by the background flow. Number fluctuations show a crossover from normal to giant scaling, signaling the onset of long-range density inhomogeneities in the FIPS regime. Our findings provide new insights into the coupling between activity, crowding, and flow, offering a unified framework for understanding phase behavior in driven active matter systems.