Spatial variations of pH in electrodialysis stacks: Theory

Electrodialysis (ED) is a well-known electrochemical water desalination technology investigated since the 1950s. In an ED stack, desalination is driven by an applied voltage, which results in selective salt ion electromigration through alternating cation and anion exchange membranes. Transport of hydronium and hydroxide ions during water treatment, together with water dissociation, can lead to unfavorable product acidity or alkalinity, compromise the membrane charge, or enhance scaling. Conversely, pH deviations can also be leveraged to tune the speciation of weak acid/base electrolytes to enhance chlorine disinfectant efficiency, or facilitate electrostatic removal of contaminants with pH-dependent properties. Thus, it is important to understand the effect of varying feedwater salinity and other system parameters on spatial pH deviations in the vicinity of the membrane, and on the pH of the product water. In this work, we propose an ED model including pH effects in a repeating unit operated in the underlimiting current regime. We numerically solve the concentration profiles of both the salt and water ions in a full repeating unit comprised of a cation and anion exchange membrane pair. For the first time to our knowledge, our model domain encompasses the entire ED repeating unit without assuming prescribed stagnant layer thickness in which the water dissociation reaction occurs. This model can be utilized to compare to experimental datasets in the future, and provide insight towards designing ED systems for removal of pH-dependent species.