Separation of chromium (VI) using modified ultrafiltration charged carbon membrane and its mathematical modeling

Supported non-interpenetrating modified ultrafiltration carbon membrane has been prepared by gas phase nitration using NOx (mixture of NO and NO2) at 250 °C and subsequently aminated in the second step using hydrazine hydrate at 60 °C. Separation experiments on the chromic acid solution have been carried out using unmodified (giving 96% rejection), nitrated (giving 84% rejection) and aminated (giving 88% rejection) carbon membrane. The water flux of the modified membrane however, has been found to increase by two times compared to that for the unmodified membrane with only 12% loss in rejection. This work presents a transport mathematical model through cylindrical charged capillaries of the membrane based on two-dimensional space charge model consisting of Nernst-Planck equation for ion transport and non-linear Poisson-Boltzmann equation for the radial distribution of potential. The solutions of these non-linear equations are computationally intensive and the difficulty has been overcome by a series solution of the Poisson-Boltzmann equation for the charge distribution. The effective pore size and non-dimensional pore wall potential of the membranes have been determined using this model by fitting the experimental data of the separation. The effective pore radius of the unmodified, nitrated and aminated carbon membranes are found to be 2.0, 2.8 and 3.3 nm respectively, which are less than the average pore size value determined from the molecular weight cut-off experiment and indicates the partial blocking of the pores by chromate ions.