Active Microemulsions: Coupling Phase Separation and Polar Order

A mixture of oil, water, and polar surfactant molecules in equilibrium is known to form microemulsions and to exhibit a variety of modulated phases, including lamellar, hexagonal, and cubic structures. Inspired by this complex phase equilibrium and experiments in mixtures of polar cytoskeletal filaments and motor proteins, we develop an out-of-equilibrium analogue by coupling the Cahn-Hilliard model to the Toner-Tu equation. The resulting phase-separating system couples the polarization of ``active surfactants'' to density gradients, aligning the polarization vector normal to the interface or to the gradient of local curvature. A numerical investigation of the model in two dimensions, accompanied by linear stability analysis, reveals transitions between various dynamical steady states upon varying the distance from the critical point for phase separation and the strength of density–polarization coupling, including mixed-isotropic, demixed-isotropic, and demixed-polarized phases. Preliminary results also suggest the emergence of networks of polar interfaces separating disordered domains, similar to structures observed in mixtures of microtubules and Kinesin-4 motor proteins.