Transport of salt mixtures through nanofiltration membranes: Numerical identification of electric and dielectric contributions

In this paper, a knowledge model is used to describe the rejection of ionic components in various proportions obtained by mixing two salts (NaCl and Na2SO4 or NaCl and MgCl2). This model is based on a description of the transport within the pores via the extended Nernst–Planck equation and the steric, electric and dielectric exclusion phenomena at the membrane/solution interfaces. Electric and dielectric contributions on the separation selectivity are investigated from experimental results by estimating, respectively, the membrane charge density Xd and the solvation energy through the dielectric constant within the pores ɛp. A new way of numerical identification is presented in this paper, which consists in identifying simultaneously this couple of parameters (ɛp, Xd) from mixture experiments. This method appears to be particularly convenient, as it does not require additional assumption to decouple their influences on rejection. The obtained values are discussed with respect to the mixture type and its composition. It was found that the values of both ɛp and Xd are physically consistent and show monotonous behaviors with the proportions of ions. In particular, ɛp decreases linearly when the proportion of divalent ions increases.