Mathematical modelling of unsteady-state transport of metal ions through supported liquid membrane

In this study, a mathematical model for unsteady-state transport of metal ions from aqueous solution through supported liquid membrane containing carrier is presented. For a transport process using supported liquid membrane, the three resistances to consider are the membrane resistance and the aqueous boundary layer resistances at the side of feed and stripping phases. The transport of species in the feed, the membrane and the stripping phases is modelled by Fickʹs second law. Time-dependent boundary conditions for the feed, the membrane and the stripping phases are obtained by means of kinetics of chemical reaction in the feed–membrane and the membrane–stripping interface. Partial differential equations obtained for the feed, the membrane and the stripping phases are analytically solved by using Duhamelʹs Theorem. Concentration distribution within the aqueous film layers and membrane as a function of position and time was derived from models obtained. The obtained model is checked against experimental data corresponding to the transport of copper ions from aqueous solution through supported liquid membrane by LIX 984.