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

Liquid-liquid interfaces typically exhibit a diffuse nature, with an interface thickness that is comparable with the electric double layer under practical conditions. In two-liquid electrokinetics, effects of solvent mixing become particularly pronounced when imbalanced ion partitioning dominates the interface charging, which is intricately linked to the interfacial physico-chemical properties. Our study presents a holistic framework to incorporate the general charging mechanisms into a diffuse interface description, paving the way for future research in two-liquid physico-chemical hydrodynamics, where the constitutive relationship of two-liquid interface charging is pivotal.