Modelling of selective ion partitioning between ion-exchange membranes and highly concentrated multi-ionic brines

In recent years, the growing interest in the use of Ion-exchange membranes, in the treatment of highly concentrated multi-ionic brines for the selective recovery of critical elements, has prompted the research of fundamental models capable of predicting the IEMs selectivity towards like-charged species. Prior studies have proposed ion partitioning models limited to single-salt solutions that were validated only up to moderate salt concentrations. In this work, we developed a novel multi-ionic extension of the Manning counter-ion condensation model, aiming to predict the sorption selectivity of like-charged counter-ions. Furthermore, the peNRTL model was coupled with the extended Manning to broaden its applicability range, encompassing membrane equilibrated with very highly concentrated solutions. Novel experimental ion sorption tests with single-salt and binary solutions including NaCl, KCl, MgCl2, and CaCl2 at high concentrations were performed with the commercial cation-exchange membrane Fumasep FKE-50, provided by Fumatech. To the best of Authors' knowledge, the proposed model for the first time successfully provided quantitative predictions of multi-ionic ion partitioning for all the systems investigated up to extremely high external salt concentrations. The outcomes of this work suggest a strong influence of the local non-electrostatic interactions on the activity coefficients in the membrane phase at high external concentration and highlight the key role of counter-ions hydration state in the condensation phenomenon.