Self-Diffusion Through Ion Exchange Membranes

When an ion exchange membrane divides solutions of the same concentration and composition, the flux of solute and solvent is zero. However, ion, solute and solvent do transport across the membrane, a process known as self-diffusion. The self-diffusion flux is proportional to the self-diffusion coefficient and the concentration of species in the membrane and inversely proportional to the membrane thickness. The self-diffusion coefficient is evaluated by diffusion of a radiotracer (isotopic or tracer diffusion).16 

Because the flux through the membrane (of thickness d) is equal to that through the diffusion boundary layer (of thickness 5) at steady state, 

When equilibrium is attained at each membrane-solution interface, namely, CA jC = CA /C, CA /C = CA /C, the flux of self-diffusion is,16,17 

The rate of self-diffusion is controlled by diffusion either across the membrane or across the diffusion boundary layer. In the first case, the rate of diffusion is completely controlled by diffusion of A in the membrane phase, and in the second 

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