JP Journal of Heat and Mass Transfer
Volume 13, Issue 3, Pages 303 - 323
(August 2016) http://dx.doi.org/10.17654/MT013030303 |
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A GENERAL ANALYTIC EXPRESSION BASED ON THE LOCAL ELECTRICAL NEUTRALITY DESCRIBING ION TRANSPORT THROUGH AN ION-EXCHANGE MEMBRANE
Kenji Tado, Yoshihiko Sano, Xiaohui Bai and Akira Nakayama
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Abstract: The local electrical neutrality has been assumed to investigate the transverse ion transport through an ion-exchange membrane with a fixed charge density. General analytical expressions satisfying the Poisson-Nernst-Planck equations were sought to reveal ion concentration and electric potential profiles within the membrane. The Donnan equations were exploited to link the concentration in the solution and the concentration in the membrane at the interface. The osmotic pressure driven convection was also taken into account for full consideration, in addition to molecular diffusion and electrophoresis. The resulting set of the analytical expressions are found to agree well with the numerical results based on the full Poisson-Nernst-Planck equations without assuming the local electrical neutrality. The validation of the present analytic expressions was followed by a series of computations to investigate the characteristics of various parameters associated with the ion transport through an ion-exchange membrane with a fixed charge density. |
Keywords and phrases: electrodialysis, ion transport, mathematical model, desalination. |
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