Phase separation dynamics and active turbulence in a binary fluid mixture

Active matter, encompassing natural systems, converts surrounding energy to sustain autonomous motion, exhibiting unique non-equilibrium behaviors such as active turbulence and phase separation. In this study, we develop a continuum two-fluid model for a binary mixture of an active nematic and a passive Newtonian fluid, coupling Cahn-Hilliard dynamics for phase separation with Beris-Edwards nematohydrodynamics and two distinct momentum equations connected by viscous drag. A phase field-based lattice Boltzmann method is used to investigate the existence of active turbulence and phase separation in the binary mixture. We find that active stress enhances velocity and vorticity differences between phases, and that increased active concentration promotes stronger inter-fluid coupling. Activity not only amplifies turbulent fluctuations but also arrests domain coarsening, leading to a finite characteristic length scale that decreases with increasing activity. Key parameters, like active parameter, tumbling parameter and Frank elastic constant, affect the characteristic scale of flow. These results highlight the role of relative motion and drag-mediated momentum transfer in active binary mixtures, providing a framework for studying systems such as bacterial suspensions in polymeric fluids or active emulsions.