The charge-regulation concept is combined with the theory of irreversible processes to predict multi-component electrolyte transport in nanofiltration membranes. Charging of the membrane surface is described using a 1-pK site-binding model with a triple-layer electrostatic description. Mass transport is described using Maxwell-Stefan relations, based on the uniform potential approach.
A predictive model is resented, which requires no adjustable parameters. Input data is obtained from independent measurements, e.g., electrophoretic mobility data. Model predictions for retention and flux are discussed for an asymmetric โฅ-alumina nanofiltration membrane for NaCl and a mixture of NaCl with CaCl 2 . Double layer overlap in the pores, leading to charge regulation, appears to have a marked influence on the potential across the pore ( ฯ = 59-88% for 4 nm pores), and thus on separation. Furthermore, the membrane surface charge and potential vary significantly over the pore length, rendering the assumption of a constant charge and potential generally applied in literature questionable. Additionally, the model predicts typical nanofiltration behaviour, including non-equal cation and anion retention at extreme pH values, dependencies of retention and flux on the permeability and thickness of the top-layer and the support, and the influence of an additional external mass transport resistance. A sensitivity analysis suggests that for an accurate quantitative prediction of the separation behaviour of inorganic NF membranes it is not possible to use more simple descriptions for ion adsorption and mass transport than the 1-pK triple-layer model and the Maxwell-Stefan relations.