Hydrodynamic interactions significantly influence phase-ordering kinetics in complex fluids. While passive fluid phase separation is well studied, the impact of active components remains relatively unexplored. We examine pure- and quasi-two-dimensional mixtures of attractive colloids and self-rotating particles in a solvent. Varying rotor rotational speed and area fraction yield diverse dynamic patterns such as percolated networks and round droplets composed of passive colloids alone. At intermediate rotation speeds, inertial chiral flows, accompanied by the inverse energy cascade, lead to self-similar power-law coarsening with a growth exponent of 1/2. The flows spontaneously organize within fluid domains, exhibiting turbulent and chiral characteristics. Surprisingly, these turbulent flows can sustain hexatic order hydrodynamically stabilized by the Magnus force under certain conditions. Conversely, at higher speeds, nonlinear hydrodynamic interactions impede phase separation. Our findings illuminate the intriguing dynamic interplay between phase separation and chiral turbulence, effectively bridging the realms of phase ordering and turbulent physics. Published by the American Physical Society 2024
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