A transport model considering charge adsorption inside pores to describe salts rejection by nanofiltration membranes

In the present work, rejection of mineral salts by nanofiltration membranes is modeled by a new knowledge model considering a charge distribution along the membrane pores. The model is classically based upon the coupling between the extended Nernst-Planck equation of transport within the pores with the Donnan, steric and dielectric interfacial exclusion. In literature, this kind of model is currently being used to describe salt rejections and it requires assessment of the membrane charge density and the dielectric constant of the solution inside the pores or the dielectric constant of the membrane material. Experimental estimation of these parameters, especially the membrane charge density, is difficult. For this reason, these parameters are usually adjusted so as to fit experimental rejections. The novelty of the proposed approach lies with the membrane charge density, which is not considered constant along the pores. Indeed, in this work, the membrane charge density was introduced in the model by means of adsorption isotherms, which were determined beforehand from the streaming potential measurements. In this case, only the dielectric constant inside pores had to be adjusted. The good agreement found between experimental and simulated rejection curves with coherent dielectric constants proves that the model theory is consistent. It has also proved that the estimated membrane charge density was, clearly, not overestimated as it was previously reported and made it possible to foresee a fully predictive model. (C) 2011 Elsevier Ltd. All rights reserved.