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==In membrane science and technology==
In [[Membrane technology|membrane science and technology]], concentration polarization refers to the emergence of concentration gradients at a membrane/solution interface resulted from selective transfer of some species through the membrane under the effect of transmembrane driving forces.<ref>E.M.V. Hoek, M. Guiver, V. Nikonenko, V.V. Tarabara, A.L. Zydney, Membrane Terminology, in: E.M.V. Hoek, V.V. Tarabara (Eds.), Encyclopedia of Membrane Science and Technology, Wiley, Hoboken, NJ, 2013, Vol. 3, pp. 2219–2228.</ref>
Generally, the cause of concentration polarization is the ability of a membrane to transport some species more readily than the other(s) (which is the [[membrane permselectivity]]): the retained species are concentrated at the upstream membrane surface while the concentration of transported species decreases. Thus, concentration polarization phenomenon is inherent to all types of membrane separation processes. In the cases of [[gas separation]]s, [[pervaporation]], [[membrane distillation]], [[reverse osmosis]], [[nanofiltration]], [[ultrafiltration]], and [[microfiltration]] separations, the concentration profile has a higher level of solute nearest to the upstream membrane surface compared with the more or less well mixed bulk fluid far from the membrane surface. In the case of [[Kidney dialysis|dialysis]] and [[electrodialysis]], the concentrations of selectively transported dissolved species are reduced at the upstream membrane surface compared to the bulk solution.
The emergence of concentration gradients is illustrated in Figs. 1a and 1b. Fig. 1a shows the concentration profile near and within a membrane when an external driving force is just applied to an initially equilibrium system. Concentration gradients have not yet formed. If the membrane is selectively permeable to species 1, its flux (<math>J_1^m</math>) within the membrane is higher than that in the solution (<math>J_1^s</math>). Higher flux in the membrane causes a decrease in the concentration at the upstream membrane surface (<math>c_1'</math>) and an increase at the downstream surface (<math>c_1''</math>), Fig. 1b. Thus, the upstream solution becomes depleted and the downstream solution becomes enriched in regard to species 1. The concentration gradients cause additional diffusion fluxes, which contribute to an increase of the total flux in the solutions and to a decrease of the flux in the membrane. As a result, the system reaches a steady state where <math>J_1^s=J_1^m</math>. The greater the external force applied, the lower <math>c_1^\prime</math>. In electrodialysis, when <math>c_1'</math> becomes much lower than the bulk concentration, the resistance of the depleted solution becomes quite elevated. The current density related to this state is known as the [[limiting current density]].<ref>H. Strathmann, Ion-Exchange Membrane Separation Processes, Elsevier, Amsterdam, 2004 p. 166</ref>
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