Enhancement of concentration polarization due to gel accumulated at membrane surface

Model for concentration polarization enhanced by gel accumulated at membrane surface has been proposed. The model can be applied for laminar regime in thin channel RO elements. It provides distribution of concentration in the liquid phase and within the gel layer. Model allows analyzing the influence of thickness of fouling layer on the CP degree, surface concentration, osmotic pressure and membrane permeability. The model is based on the following assumptions: (1) the fluid is assumed to be incompressible, continuous and isothermal with uniform density field under the steady-state conditions; (2) within selected control area all the characteristics are assumed to be position independent; (3) process is accompanied by accumulation of gel layer at membrane surface along with concentration polarization; (4) diffusion layer and deposited gel contains different components and these layers are characterized by different values of diffusivity coefficients; (5) correlation for effective hindered back diffusion coefficient within deposited layer is adopted from Boudreau [B.P. Boudreau, The diffusive tortuosity of fine-grained unlithified sediments, Geochim. Cosmochim. Acta, 60 (16) (1996) 3139-3142]; (6) 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) in the presence of gel layer the membrane surface concentration, C,M, is enhanced due to hindered back diffusion of salt ions that, in turn, result in growth of osmotic pressure at the membrane surface. The elevated surface concentration, C,M, also result in elevated salt concentration in permeate and decrease of the net driving force; (B) analysis of calculated data indicates high sensitivity of CP degree to coefficient of hindered back diffusion, in particular 35% decrease of coefficient of hindered back diffusion within the gel can result in 54% growth of degree of concentration polarization. Proposed model can be incorporated into algorithm for calculation of longitudinal distribution of CP degree, resistance and trans-membrane flux. Calculated data and projections are attached. (c) 2006 Elsevier B.V. All rights reserved.