Mathematical modeling on non-dispersive extraction of germanium from aqueous solutions using Aliquat 336

In this work, the mathematical modeling of the facilitated transport of germanium (non-dispersive extraction) through a flat sheet membrane with an Aliquat 336 carrier was described. The flat sheet supported liquid membrane (FSSLM) experiments were performed under conditions germanium ≈ 100 mg/L, tartaric acid concentration of 2.76 mmol/L, and carrier concentrations of 2.5-10%v/v. The extraction equilibrium, mass transfer, and diffusion equations based on Fick's law were the principles of modeling. Modeling was carried out by programming in Matlab mathematical software to obtain the extraction (K_ex) and mass transfer constants (K_m) as the objective parameters. According to the model resolution, K_ex and K_m were found to be 0.178 and 9.25 × 10^-2 cm/s, respectively. The correlation coefficients between model and experimental data relating to the Aliquat 336 concentrations of 2.5, 5, 7.5, and 10%v/v were found as 0.96, 0.98, 0.99, and 0.92. The parameters of root mean square error, bias, and scatter index showed the model accuracy. In addition, diffusion coefficients relating to Aliquat 336 concentrations of 2.5, 5, 7.5, and 10%v/v were calculated using mass transfer coefficients to be 2.4 × 10^-4, 2.23 × 10^-4, 1.91 × 10^-4, and 1.79 × 10^-4 cm²/s, respectively.