The effect of solution leakage in an ion-exchange membrane electrodialyzer on mass transport across a membrane pair

In a practical-scale ion-exchange membrane electrodialyzer, the dimensions of all parts of the unit are not always consistent with the values in the specifications. Small pinholes can open because the strength of ion-exchange membranes is relatively low. Gaps may occur between the components of the unit in the assembly of the electrodialyzer. If a pressure difference exists between desalting cells and concentrating cells in these circumstances, solutions leak across the membranes during the operation of the unit. Solution leakage includes those moving from desalting cells to concentrating cells and those moving from concentrating cells to desalting cells. Applying the overall mass transport equation to the ion-exchange membrane electrodialysis of seawater, solution leakage in a practical-scale electrodialyzer was estimated. The effects of solution leakage on the transport of electrolytes in a solution across a membrane pair, electrolyte concentrations in a desalting cell and a concentrating cell, current efficiency and the desalting ratio of a desalted solution were evaluated. Further, the effect of solution leakage on the perm-selectivity coefficient of K+ ions, Mg2+ ions and Ca2+ ions against Na+ ions and the perm-selectivity coefficient of SO42− ions against Cl− ions were also evaluated. The overall mass transport equation includes the membrane pair characteristics such as the overall transport number λ, the overall permeability coefficient μ, the overall electro-osmotic coefficient φ and the overall concentration-osmotic coefficient ρ. λ, μ and φ were expressed by the function of ρ. Relationship between the overall mass transport equation and the non-equilibrium thermodynamics was discussed.