Permselectivity of Ions with the Same Charge

When diffusion of electrolyte and osmosis of solvent are negligible, the flux of ion i is 

Because the ratio is also proportional to the concentration ratio of ions A and B in the desalting side solution, if the properties of both ions in the solution are the same, the equivalent ratio of fluxes is divided by the equivalent ratio of both ions in the desalting side solution. The permselectivity of ion A to ion B is defined as follows, 

This is a product of the ratio of the mobility of ion A to that of ion B in the membrane phase and the selectivity coefficient of ion A to ion B. In electrodialysis, diffusion boundary layers are formed at membrane surfaces, where the concentration at the membrane surfaces is not the same as that of the bulk solution. To obtain the real PAB of the ion exchange membrane, the diffusion boundary layer should be eliminated by vigorous agitation of the solution, which corresponds to the limiting value at zero current density, 

In practice, because an equivalent is used as the permeated amount of ions in the measurement, the following equation is conventionally used (see Chapter 5), 

A preliminary theoretical explanation of membrane phenomena has been made in this chapter, which is related to Chapters 4, 5 and 6. However, because an explanation of membrane phenomena by non-equilibrium thermodynamics is important, the reader is encouraged to examine any of the excellent books and reviews that are available. 

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