A closed-form solution for a mathematical model of emulsion liquid membrane

This paper presents the first ever closed-form solution for a mathematical model of emulsion liquid membrane (ELM). The model combines the following features: mass transfer of solute across the film between the external phase and the membrane phase, chemical equilibrium of the extraction reaction at the external phase–membrane interface, simultaneous diffusion of the solute–carrier complex inside the globule membrane phase and stripping of the complex at the membrane–internal phase interface, chemical equilibrium of the stripping reaction at the membrane–internal phase interface. By solving the resulting simultaneous partial differential equations using the Laplace transform method, we obtain formulas for (1) the concentration of solute in the external phase versus time, (2) concentration profile inside the membrane globule, and (3) interfacial concentration at the external–membrane phase interface versus time. The model predictions agree very well with the experimental data obtained from the removal of arsenic by emulsion liquid membranes.