Mixing-demixing phase diagram for simple liquids in nonuniform electric fields

Abstract

We deduce the mixing-demixing phase diagram for binary liquid mixtures in an electric field for various electrode geometries and arbitrary constitutive relation for the dielectric constant. By focusing on the behavior of the liquid-liquid interface, we produce simple analytic expressions for the dependence of the interface location on experimental parameters. We also show that the phase diagram contains regions where liquid separation cannot occur under any applied field. The analytic expression for the boundary "electrostatic binodal" line reveals that the regions' size and shape depend strongly on the dielectric relation between the liquids. Moreover, we predict the existence of an "electrostatic spinodal" line that identifies conditions where the liquids are in a metastable state. We finally construct the phase diagram for closed systems by mapping solutions onto those of an open system via an effective liquid composition. For closed systems at a fixed temperature and mixture composition, liquid separation occurs in a finite "window" of surface potential (or charge density). Higher potentials or charge densities counterintuitively destroy the interface, leading to liquid mixing. These results give valuable guides for experiments by providing easily testable predictions for how liquids behave in nonuniform electric fields.

Interface initiation and propagation in liquid demixing with electric fields

“…Figure 1(b) details the relation of mathematically analogous structures between the non-uniform electric field and nofield phase diagrams. 11,12 Given these analogies, we borrow ideas from critical behavior 25 and plott L versus a rescaled concentration φ * 0 , where φ * 0 = (φ 0 − φ s )/φ s below and φ * 0 = (φ 0 − φ i )/φ i above the emergence line, Fig 1(b). Figure 5(b) shows how the lag time from a wide range of data in the φ 0 − T plane, Fig.…”

“…For liquid-liquid demixing under non-uniform electric fields, the constraint of material conservation in closed systems produces different equilibrium (long-time) concentration profiles φ(r) in comparison to open systems with the same parameters (φ 0 , T, M). 10,11 These differences, however, can be explained by considering an alternative "effective bulk" concentration acting on the closed system. 11 In contrast, recent investigations 12 demonstrate that the dynamics of the non-equilibrium interface are equivalent for open and closed systems for the same parameters (φ 0 < φ c , T, M) during early times.…”

“…10,11 These differences, however, can be explained by considering an alternative "effective bulk" concentration acting on the closed system. 11 In contrast, recent investigations 12 demonstrate that the dynamics of the non-equilibrium interface are equivalent for open and closed systems for the same parameters (φ 0 < φ c , T, M) during early times. Therefore, at some "intermediate" time, the presence of a second boundary at R 2 influences the behavior of the inter- face in a closed system such that the dynamics diverge from that of an open system.…”

“…4 The spatial gradients created by these fields induce large changes to the phase diagram in comparison to uniform electric fields; moreover, new behaviors have been uncovered, such as location-dependent interface properties and unusual kinetic regimes. [9][10][11][12] And as non-uniform fields always occur on small scales and are actively used in many devices, [13][14][15] the potential for further technological development is immense.…”

Phase separation dynamics of simple liquids in non-uniform electric fields

“…We recently overcame this challenge by implementing local markers to successfully construct the phase diagram. 19 In this manuscript, we extend this formalism to phase separation kinetics. Unlike standard nucleation processes and spinodal decomposition, the properties of the interface in time depend on its location in space.…”