Transport in Electrodialysis Membranes

The rate at which the cations approach the membrane by electrolyte transport is t+I/F. It follows that the total flux of sodium ions to the membrane surface (/+) is the sum of these two terms 

Transport through the membrane is also the sum of two terms, one due to the voltage difference, the other due to the diffusion caused by the difference in ion concentrations on each side of the membrane. Thus, the ion flux through the membrane can be written 

For a selective cationic ion exchange membrane for which i,w) 1, Equation (10.15) can be further simplified to 

This important equation has a limiting value when the concentration of the ion at the membrane surface is zero (c(0)+ 0). At this point the current reaches its maximum value the limiting current is given by the equation 

This limiting current, /liin, is the maximum current that can be employed in an electrodialysis process. If the potential required to produce this current is exceeded, the extra current will be carried by other processes, first by transport of anions through the cationic membrane and, at higher potentials, by hydrogen and hydroxyl ions formed by dissociation of water. Both of these undesirable processes consume power without producing any separation. This decreases the current efficiency of the process, that is, the separation achieved per unit of power consumed. A more detailed discussion of the effect of the limiting current density on electrodialysis performance is given by Krol et al. [20], 

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