Investigating nanofiltration of multi-ionic solutions using the steric, electric and dielectric exclusion model

The aim of this work was to test the ability of the steric, electric and dielectric exclusion (SEDE) model to describe the separation of multi-ionic solutions (3 and 4 ions) by nanofiltration. To this end, mixed solutions of Pb(NO3)2Pb(NO3)2 and Co(NO3)2·6H2OCo(NO3)2·6H2O at various pH were filtered through a nanofiltration polyamide membrane. The structural features of the membrane active layer were inferred from glucose rejection rates and water permeability. The charge state of the membrane active layer was evaluated for the various solutions from coupled tangential streaming potential (TSP) and electric conductance measurements. Calculations were carried out using different approaches. Modelling results show that the experimental rejection rates are not well described incorporating the two types of dielectric exclusion mechanisms, i.e. Born dielectric effect and image forces contribution, in the steric/electric model. However, the description is found to be satisfactory considering (i) steric, electric and Born dielectric exclusion mechanisms, with two fitted parameters: the effective volume charge density, X  , and the dielectric constant of the solution inside the pores, εpεp, or (ii) steric, electric exclusion mechanisms and image forces, with two fitted parameters, X   and the dielectric constant of the active layer material, εmεm. εpεp and εmεm were assessed in the range of 56.3–74.6 and 7–10, respectively. The values of 7–10 for εmεm are different from the commonly used value for dry polyamide (i.e. εm=3εm=3). It might be due to the wetting of the polymer. In both approaches, the fitted values of X were found to be smaller than X values inferred from TSP measurements, which is in agreement with the charge regulation phenomenon.