Modeling of extraction of dyes and their mixtures from aqueous solution using emulsion liquid membrane

Mathematical modeling of a typical batch extraction system employing emulsion liquid membrane for dyes, namely, crystal violet and methylene blue is carried out. An already available mass transfer model using spherical shell approach is used for one component dye extraction. The same model is extended for the binary system. The resultant ordinary differential equations of the model are solved using Laplace transform. The model parameters are obtained by comparing the experimental data with the calculated values of the dye concentration at various time points using an optimization algorithm. Effects of various process parameters, namely, concentration of surfactant, internal reagent, stirring speed, etc., have been analyzed for both single and binary mixtures using the model results.