Gibbsian surface thermodynamic analysis of emulsion liquid membranes

The emulsion liquid membrane is a promising technique for separating pollutants such as metals, weak acids and bases, mineral species, hydrocarbons, and biological substances. The popularity of the membrane process is due to its high mass transfer efficiency, process simplicity, and low energy consumption. Despite significant advancements in the field of emulsion liquid membranes, the effect of the interfacial curvature on component distribution remains largely uninvestigated. In the present study, considering the emulsion liquid membrane where no reaction takes place, the thermodynamic equilibrium relationships are calculated while considering the effect of interfacial curvature between the phases. The Gibbsian surface thermodynamic method is employed to derive the equations at equilibrium for the composite system of emulsion liquid membrane. With the obtained equations, the mole fraction and percentage extraction of the desired substance can be calculated under various conditions, such as different surfactant concentration, and droplet size, as well as assuming ideal or non-ideal condition for the solution. The results indicate that by reducing the size of internal droplets to the nanoscale, the effect of interfacial curvature becomes significant, and the extraction percentage gets higher.