Irreversible thermodynamics and overall mass transport in ion-exchange membrane electrodialysis

Abstract

An ion-exchange membrane electrodialysis phenomenon was presented by using phenomenological equation based on the irreversible thermodynamics. The overall mass transport equation was introduced based on the electrodialysis of seawater. The overall mass transport equation was joined to the phenomenological equation by setting both equations are equivalent each other. As the result of this process, the overall membrane characteristics appeared in the overall mass transport equation (overall transport number λ, overall solute permeability μ, overall electro-osmotic permeability ϕ and overall hydraulic conductivity ρ) were expressed by the function of the irreversible membrane pair characteristics appeared in the phenomenological equation (transport number t, solute permeability ω, electro-osmotic permeability β and hydraulic conductivity L P). λ, μ, ϕ, r (electric resistance) and W (water content) were expressed by the empirical function of ρ. Reflection coefficient was discussed by defining the pressure reflection coefficient σ and concentration reflection coefficient σ′. From the pressure dialysis of a KCl solution, σ of an ion-membrane was generally assumed to be 1. σ′ corresponded with the permselectivity between ions and water molecules across an ion-exchange membrane at just after electric current interruption (electric current switching off concept), and was expressed by the function of μ, ρ and logarithmic mean concentration C *. t, ω, β, L P, L PD (osmotic volume flow coefficient), L DP (ultrafiltration coefficient) and L D (exchange flow parameter) included in the phenomenological equation were computed by applying the overall mass transport equation to electrodialysis experiments. The influence of concentration polarization upon the overall membrane characteristics measurement was negligibly small.