화학공학소재연구정보센터
Desalination, Vol.200, No.1-3, 406-408, 2006
Modelling of the concentration polarization of the bivalents salts using a Nanomax50 membrane in nanofiltration process
The aim of the present work is to propose a model for predicting the transfer mechanism of divalent ions through NF membranes by including the concentration polarization phenomenon and to study its influence on salt rejection. The proposed model is a combination of two transport models: the first one is based on the extended Nernst-Planck equation while the second is based on the film theory. This model is characterized by two transfer parameters: reflection coefficient a and solute permeability P, which are estimated numerically. The thickness of the boundary layer, 6, solute concentration at the membrane surface, C, and concentration profile in the polarization layer have also been estimated. The model is applied for predicting cadmium, calcium, copper and zinc salts rejection at a various concentrations and a comparison, between estimated results with and without considering concentration polarization. J(i) = -C-i (.) D-i,D-p d(ln gamma(i))/dx - Ci (.) D-i,D-p/(RT)-T-. V-i dp/dx - D-i,D-p dC(i/dx) - z(i)(.)C(i)(.)D(i,p)/(RT)-T-. .F. d psi/dx + K-i,K-c (.) C-i (.) V and a film theory (C-m - C-p)/(C-0 - C-P) = e(Jv delta/D1) It is characterized by two transfer parameters: solute permeability P-s and reflection coefficient sigma, and permits us to estimate the thickness of the boundary layer, delta. Solute concentration at the membrane surface, C-m, and concentration profiles in the polarization layer are also estimated. The solution is C-m1 = (1- sigma/Exp[(1-sigma)J(v)/P-s])C-p1/1-sigma.