Solvent mixing and ion partitioning effects in spontaneous charging and electrokinetic flow of immiscible liquid-liquid interface

Electrokinetic transport occurs at the two-liquid interfaces due to its inevitably spontaneous charging induced by imbalanced partition and/or specific adsorption. The diffuse feature of the liquid-liquid interface is essential in interpretation of its electrokinetic behavior and the interplay of the two charging mechanisms is strongly dependent on the interfacial physicochemical properties, which are often ignored in previous studies and may lead to the impractical electrokinetic predictions. We propose a diffuse interface framework which includes a modified Boltzmann formulation, to incorporate the solvent mixing effect and unify the description of both possible charging mechanisms. The permittivity- and viscosity-related solvent mixing effects are stressed when imbalanced ion partition dominates and the viscosity ratio is large. The effects of permittivity-dependent ion partition and organic impurity ions are exhaustively discussed for nonpolar and polar organic liquids. For polar organic liquid with moderate permittivity, the water velocity presents a nonmonotonic dependency on the impurity concentration under different pHs, resulting from the competitive effect of the two charging mechanisms. A semiempirical correction formula for the sharp interface model is proposed to eliminate the modeling deviations, while the viscosity interpolation model is demonstrated to have a great impact on the interpretation of the electroosmotic velocity profile. Our work sheds light on the further studies of the complex electrokinetic multiphase flows with complex geometry, large deformation, contact line dynamics, and weak nonequilibrium transport.