Analytical approximate solution of competitive facilitated transport of acid gases through liquid membranes

An analytical approximate solution for the competitive facilitation factor of components A and E across a liquid membrane is developed in the case of instantaneous reactions inside the liquid membranes. This analytical solution solves the dimensionless, nonlinear diffusion-reaction transport problem governing the competitive facilitated transport of two gaseous components through liquid membranes. Prediction of the facilitation factors has been obtained for the equilibrium chemical reaction regime, considering the unequal complexes diffusivities and cases of zero and nonzero permeate side solute concentrations. This mathematical solution leads to analytical expressions for the concentration profiles of the species across the liquid membrane. In comparison with the present numerical solution and also numerical calculations and experimental data from the open literature, the difference between the analytical predictions and those obtained from the numerical solution were found to be in well agreement.