Effect of the background flow on the motility induced phase separation

We simulate active Brownian particles (ABPs) with soft-repulsive interactions subjected to a four-roll-mill flow. In the absence of flow, this system exhibits motility-induced phase separation (MIPS). To investigate the interplay between MIPS and flow-induced mixing, we introduce dimensionless parameters: a scaled time, $\tau$, and a scaled velocity, $\mathrm{v}$, characterizing the ratio of ABP to fluid time and velocity scales, respectively. The parameter space defined by $\tau$ and $\mathrm{v}$ reveals three distinct ABP distribution regimes. At low velocities $\mathrm{v}\ll 1$, flow dominates, leading to a homogeneous mixture. Conversely, at high velocities $\mathrm{v}\gg 1$, motility prevails, resulting in MIPS. In the intermediate regime ($\mathrm{v}\sim 1$), the system’s behavior depends on $\tau$. For $\tau <1$, a moderately mixed homogeneous phase emerges, while for $\tau >1$, a novel phase, termed flow-induced phase separation (FIPS), arises due to the combined effects of flow topology and ABP motility and size. To characterize these phases, we analyze drift velocity, diffusivity, mean-squared displacement, giant number fluctuations, radial distribution function, and cluster-size distribution.