Effect of the background flow on 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, <i>τ</i>, and a scaled speed, <i>V</i>, characterizing the ratio of ABP to fluid time and speed scales, respectively. The parameter space defined by <i>τ</i> and <i>V</i> reveals three distinct ABP distribution regimes. At low speeds, <i>V</i> ≪ 1, flow dominates, leading to a homogeneous mixture. Conversely, at high speeds, <i>V</i> ≫ 1, motility prevails, resulting in MIPS. In the intermediate regime (<i>V</i> ∼ 1), the system's behavior depends on <i>τ</i>. For <i>τ</i> < 1, a moderately mixed homogeneous phase emerges, while for <i>τ</i> > 1, a novel phenomenon, 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.