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Concentration Polarization pp. 87-121 $100.00
Authors:  Yoshinobu Tanaka (IEM Research, Ibaraki, Japan)
Under an applied electric current, a boundary layer is formed on the desalting surface of an ion exchange membrane and the salt concentration in the layer is depleted. This phenomenon is termed concentration polarization. Depletion of the salt at the membrane surface means that an increasing fraction of the voltage drop is dissipated in transporting ions across the boundary layer rather than through the membrane. A point can be reached at which the ion concentration at the membrane surface is zero. The current through the membrane at this point is called the limiting current density. At over limiting current density the extra power is dissipated by the side reaction such as water dissociation. Concentration polarization is extremely important phenomenon in ion exchange membrane electrodialysis because it influences the performance of an electrodialyzer.
We assume here that a cation exchange membrane is immersed for example in a NaCl solution and an electric current density i is applied across the membrane. In a desalting side of the membrane, Na+ ion transport numbers in the solution tNa is 0.4, while that in the membrane t_Na is 0.95. In this situation, Na+ ion flux in the solution; JNa = tNa(i/F) = 0.4(i/F) is less than Na+ ion flux in the membrane; J_Na = t_Na(i/F) = 0.95(i/F). In order to maintain the material balance, NaCl concentration is decreased and the concentration gradient dc/dx is generated in the boundary layer. The above is the simplified explanation of the concentration polarization in ion exchange membrane electrodialysis. The material balance in the boundary layer is consequently given as: FitdxdCDFitNaNa_ (5.1)
in which F is the Faraday constant dC/dx is concentration gradient and D is the diffusion constant of NaCl in this situation.
Eq. (5.1) is equivalent to the following Nernst-Planck equation, which is applied some times to express the ionic transport in a solution. 

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Concentration Polarization pp. 87-121