Phase separation dynamics of simple liquids in non-uniform electric fields
Spatially non-uniform electric fields can phase separate initially homogeneous mixtures of liquids. Here, we investigate the dynamics of phase separation using a modified Cahn-Hilliard equation and find three kinetically distinct regimes in the phase diagram: (1) discontinuous and (2) continuous interface formation kinetics and (3) a metastable state. By considering all possible solutions of the free energy density, we are able to map the time behavior in the vicinity of the interface as a series of equilibrium interfaces "moving" in the parameter space of the equilibrium phase diagram. The kinetic phase diagram, consequently, contains an "emergence line" that delineates the experimental conditions where a non-equilibrium interface can be forbidden from forming close to a charged surface. When the interface can form on the charged surface, an abrupt transition occurs that produces electrical signatures which distinguish the discontinuous from the continuous transition region. The third kinetic regime describes non-spontaneous phase separation and potential metastable states, and is bounded by the "electrostatic spinodal" line. The equivalent kinetic regimes exist in closed systems and can be found by considering an effective concentration in an open system.