Impact of Ionic Strength and Charge Density on Donnan Potential in the NaCl-Cation Exchange Membrane System

Abstract

This work aims to theoretically investigate the effect of both the fixed charge density of ion exchange membranes and the ionic strength of the treated aqueous NaCl solution on the generated Donnan potential at thermodynamic equilibrium conditions. The direct objective of our work is to calculate the equilibrium concentration of the Cl− co-ion inside a swelled cation-exchange membrane equilibrated with a water/NaCl system. Two activity coefficient models are employed, i.e., the Debye–Huckel (DH) model (as a reference model) and the Meissner model, which is known for its applicability in treating concentrated solutions. Experimental data available in the literature for Donnan potential are used to verify model predictions. Our study confirms that a high fixed charge density is required to counterbalance the deterioration in membrane selectivity encountered in high-salinity systems. The DH model can be safely used to predict the Donnan potential for feed compositions up to 0.1 M. At higher compositions, the DH model significantly overestimates the predicted (absolute) Donnan potential compared to the Meissner model. The osmotic pressure resulting from the difference in ionic concentration between the membrane phase and the feed phase is found to have insignificant effects on the Donnan potential. The equilibrium computations and methodology are presented in a general way that enables handling multivalent electrolyte systems such as CaCl2.