Multicomponent ion transport in a mono and bilayer cation-exchange membrane at high current density

This work describes a model for bilayer cation-exchange membranes used in the chlor-alkali process. The ion transport inside the membrane is modeled with the Nernst–Planck equation. A logistic function is used at the boundary between the two layers of the bilayer membrane to describe the change in the properties of each membrane layer. The local convective velocity is calculated inside the membrane using the Schlögl equation and the equation of continuity. The model calculates the ion concentration profiles inside the membrane layers. Modeling results of mono- and bilayer membranes are compared. The changes in membrane voltage drop and sodium selectivity are predicted. The concentration profile of sodium ions in the bilayer membrane is significantly different from the monolayer membrane. Without the applied current, a linear change in the sodium concentration is observed in the monolayer membrane and in each layer of the bilayer membrane. With an increase in current density, the stronger electromotive force in the carboxylate layer causes a decrease in the sodium concentration in the sulfonate layer, down to the fixed ionic group concentration. This significant decrease of sodium ion concentration in the sulfonate layer results in low concentrations of counter ions and as a consequence a higher permselectivity of the bilayer membrane is obtained when compared to the single-layer membrane. As a drawback, the resistance in the bilayer membrane increases.