Parallel transport by surface and pore diffusion in a porous membrane

Abstract

To investigate parallel transport by surface and pore diffusion within a porous material, we measured uptake curves and concentration profiles for adsorption of a direct dye on a cellulose membrane. A surface diffusion model, a pore diffusion model, and a homogeneous model each predicted well the uptake curves but not the concentration profiles, although the surface diffusion model gave a better agreement than the pore diffusion model. The surface diffusivities determined by assuming surface diffusion control, pore diffusivities assuming pore diffusion control, and the effective diffusivities for the homogeneous model (Deff) obtained from the uptake curves varied with the concentration of the dye and the stimulator (NaCl). The experimental concentration profiles were predicted well by the parallel surface and pore diffusion model. The surface diffusivities for the parallel diffusion model (Ds) were determined from the values of the intercepts of the plots of Deff[1 + (εpCo/qo)] vs εpCo/qo. The pore diffusivities (Dp) were obtained by matching the theoretical concentration profiles for the parallel diffusion model with the experimental data. The values of Ds and Dp were independent of the concentrations of the dye and the stimulator (NaCl), although the stimulator significantly increased the extent of adsorption. When qo/εpCo ⪢ 260, surface diffusion was the rate-controlling step. For lower qo/εpCo, the adsorption rate increased concomitantly because of the contribution of pore diffusion.