Active Turbulence leads to Microphase Separation

Phase-separating active-passive mixtures are a new class of non-equilibrium binary fluids. Recent experiments have demonstrated a number of unconventional properties of these systems, including propagating interfacial waves and stable microphase separated states. We use a continuum model of active nematics coupled to a scalar phase field to study these phenomena. As with previous models of scalar active matter coupled to flow, we find that activity can arrest the transition to bulk phase separation. The active flows lead to a steady state composed of splitting and merging extensile droplets – an active emulsion. We find that there is a steady droplet size distribution with a mean radius controlled by the activity. To capture the evolution to this dynamical steady state and its properties, we describe the emulsion using coagulation-fragmentation equations for the droplet sizes. Using this model, we derive the coarsening exponents. We finally compare our results to experiments in a mixture of a passive fluid and an active microtubule suspension.