Current density distribution and limiting current density in ion-exchange membrane electrodialysis

The limiting current density equation of an ion-exchange membrane electrodialyzer contains the current density nonuniformity coefficient φ. In order to clarify the characteristics of φ, current density distribution theory is developed as follows: Electrodes are conductors and their electrical resistance and ohmic loss are negligibly small compared to the values between the electrodes. Accordingly, the voltage difference between the electrodes at the entrance of desalting cells Vin are regarded as nearly equal to the value at the exit Vout, and at the position p distant from the inlets of desalting cells Vp; Vin=Vout (1) and Vin=Vp (2). p is the dimensionless distance from the inlet of a desalting cell at which current density is equal to the average current density of an electrodialyzer. Current density distribution is expressed by the quadratic equation: i=a1+a2(x/l)+a3(x/l)2 (3), l flow length of a desalting cell; x the distance from the inlet of a desalting cell. Developing , φ, p, a1, a2 and a3 are obtained. The theory agrees with the experimental results.