Profile of Chemical Potential in Pressure-Driven Membrane Processes Accompanied by Gel-Enhanced Concentration Polarization
A model for distribution of chemical potential and concentration polarization enhanced by gel accumulated on membrane surface has been proposed. It provides distribution of chemical potential and concentration in the liquid phase and within the gel layer. The model allows analyzing the influence of thickness of fouling gel layer on the CP degree, surface concentration and chemical potential. The model is based on the following assumptions: process is accompanied by accumulation of gel layer at membrane surface along with concentration polarization; diffusion layer and deposited gel consist of different components and these layers are characterized by different values of diffusivity coefficients; correlation for effective hindered back diffusion coefficient within deposited layer is adopted from [Boudreau, Geochim. Cosmochim. Acta, 60, 1996]; transverse transport is based on the following mechanisms: convection due to pressure difference and back diffusion owing to concentration gradient. The following conclusions have been drawn: (A) diffusion resistance within the gel layer is getting dominant and cannot be ignored; (B) In the presence of a gel layer the membrane surface concentration, C1M, is enhanced due to hindered back diffusion of salt ions that in turn, results in growth of osmotic pressure and chemical potential at the membrane surface. It provides elevated salt concentration in permeate and decreases the net driving force; (C) Analysis of calculated data indicates high sensitivity of CP degree to coefficient of hindered back diffusion within gel layer.