Modelling of the concentration polarization of the bivalents salts using a Nanomax50 membrane in nanofiltration process Original Research Article

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 σ and solute permeability Ps which are estimated numerically. The thickness of the boundary layer, δ, solute concentration at the membrane surface, Cm, and concentration profile in the polarization layer have also been estimated.Ji=−Ci·Di,pd(ln⁢γi)d⁢x−Ci·Di,pR·TVidpdx−Di,pdCidx−zi·Ci·Di,pR·T·F·dψdx+Ki,c·Ci·V(Cm−CP)(C0−CP)=eJ⁢v⁢δD1