Abstract:A mathematical model was developed to monitor the facilitated transport of germanium(IV) from oxalic acid solutions through a flat sheet supported liquid membrane (FSSLM) containing four trialkylphosphine oxides (Cyanex 923). The FSSLM modeling was based on the extraction constant (K_ext) calculated from the liquid-liquid extraction (LLX) modeling. The LLX model presented a reliable calculation of the extraction constant (K_ex= 2.057×10³ L/mol⁴). The FSSLM model was solved using Matlab^？ software according to extraction constant, Fick’s law, and diffusional principles. The model predicts the overall mass transfer coefficient (K_org) to be 3.84 cm/s. Using this value, diffusion coefficients (D_m) for various Cyanex 923 concentrations of 0.126, 0.252, 0.378, 0.505, 0.631 and 0.757 mol/L are found to be 8.50×10^-4, 4.30×10^-4, 1.87×10^-4, 5.87×10^-5, 2.57×10^-5, 2.09×10^-5 cm²/s, respectively. The results show that the diffusion rate of the current study is approximately more than that of similar FSSLM systems containing Cyanex 923 used to transport various metals. The modeling values are in good agreement with the experimental data, showing the good reliability of the mathematical model.

Key words: supported liquid membrane; Cyanex 923; germanium; transport; mathematical modeling