Phase separation of rotor mixtures without domain coarsening driven by two-dimensional turbulence

Unlike in thermodynamic systems, phase separation can occur without a thermodynamic driving force in active systems. How phase separation of purely hydrodynamic origin proceeds is an intriguing physical question. To this end, we study the phase separation of a binary mixture of oppositely rotating disks in a two-dimensional (2D) viscous fluid at an athermal condition by hydrodynamic simulations, focusing on the inertia effect. At symmetric and off-symmetric compositions, phase separation forms the oppositely flowing bands and a circular rotating droplet in the disordered matrix phase. In both cases, phase separation creates the largest structure directly from a chaotic state without gradual domain coarsening, unlike in the thermodynamic and corresponding dry rotor mixtures. We show that this unusual behaviour results from the nonlinear convective acceleration, i.e., the inverse cascade phenomena characteristic of 2D turbulence. Our finding reveals nontrivial nonlinear hydrodynamic effects on the self-organisation of active/driven particles in a fluid.