Interface initiation and propagation in liquid demixing with electric fields.

We investigate the dynamics of liquid-liquid phase separation confined in a charged concentric cylindrical geometry. Two main time scales characterize the non-equilibrium interface behavior: (1) the lag time t(L) for forming an interface, and (2) the relaxation time to equilibrium. We find that t(L) increases as parameters (temperature, bulk composition, and surface charge) approach the electrostatic spinodal line in the phase diagram. Close to this line, t(L) is proportional to a renormalized bulk concentration with an exponent of -1.16 ± 0.03. The relaxation of the interface to equilibrium can be divided into three phases: early, intermediate (power-law), and late (exponential). During power-law relaxation, the location of the rescaled interface is proportional to time with an exponent of -0.94 ± 0.04. Exponential relaxation occurs as a consequence of finite-size effects, and the associated time constant decreases with decreasing system size (with a power-law scaling), decreasing concentration, and increasing surface charge. The time constant also decreases with increasing (decreasing) temperature when the concentration is below (above) the critical concentration.