Permeation mechanism and interplay between ions in nanofiltration

Nanofiltration (NF) is widely used today for water purification, however, governing physical mechanisms are still largely unclear and predictive modeling remains a challenge, especially, for mixed ionic solutions. The current study systematically investigates NF of binary mixtures of NaCl and CaCl₂ with the purpose to understand the mechanisms and interplay between different ions in the membrane. Using extensive filtration data and the Nernst-Planck relations, the paper concludes that (a) the standard mean-field models based on an average Donnan potential are unsuitable for describing ion permeation in NF; (b) the observed ranking of ion permeabilities (Na⁺ > Cl^- > Ca²⁺) points to the solvation (Born) energy rather than interaction with fixed charges as the main factor controlling ion permeation; (c) the fixed charges are largely neutralized by pairing with counter-ions, which reduces their role in ion permeation; (d) saturation of Ca²⁺ uptake and its competition with Na⁺ for pairing with fixed charges may explain the unusual decrease of Ca²⁺ permeability with Ca²⁺ concentration and its strong effect on Na⁺ permeability. These conclusions, inconsistent with the commonly used mean-field picture, strongly suggest the need to revise the current approach to NF modeling.