Modelling the salt rejection of nanofiltration membranes for ternary ion mixtures and for single salts at different pH values

Zeta potential measurements were performed to gain more insight in the rejection mechanisms of nanofiltration membranes. The zeta potential as well as the calculated surface charge increased at pH 7 with increasing salt concentration in the bulk. The isoelectric point of both membranes investigated (PVD1, Desal 5DK) is at a pH of about 4. The membranes are positively charged below this pH-value and are negative at higher pH-values. Rejection measurements were performed for both membranes. The rejection of single salt solutions at different concentrations, the rejection of ternary ion mixtures as well as the rejection at different pH-values were determined experimentally. For the modelling of the rejection by nanofiltration membranes, the zeta potential measurements were used to calculate the surface charge of the membrane. An empirical approach was proposed to incorporate the change of the dielectric constant between bulk and pore solution to calculate the ion distribution between bulk and pore solution. The decrease of the NaCl rejection as well as the increase of the CaCl2 rejection was well described by the model. The rejection of ternary ion mixtures of NaCl/Na2SO4 and NaCl/CaCl2 were determined experimentally and were predicted by the model except for the NaCl/CaCl2 mixture in the case of the Desal 5DK membrane, where the negative rejections of Na+ were not predicted. The rejections at different pH-values exhibit a minimum, which coincides in the case of the PVDI with the isoelectric point of the membrane surface. The pH of the rejection minimum for the Desal 5DK is one pH unit higher than the isoelectric point.