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A General Solution of the Nernst-Planck Equations for Ion Exchange with Rate Control by Liquid-Phase Mass Transfer

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Ion Exchange Advances

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Abstract

A general analytical solution for the Nernst-Planck equations in a Nernst film is presented. The solution reduces to all known analytical solutions in the literature for special cases, e.g., binary or equal-valence ion exchange. In addition, it provides an approximation in the general case of any number of counterions and co-ions with different valences. The approximation is in good agreement with the computationally much more cumbersome numerical solution. The solution presented delivers only the momentary fluxes. To obtain the concentrations and loadings as a function of time, numerical integration is still required.

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Author information

Authors and Affiliations

  1. Water Technology Division, Institute for Radiochemistry, P.O.Box 3640, D-7500, Karlsruhe, Germany

    W. H. Höll & H. Sontheimer

Authors
  1. M. Franzreb
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  2. W. H. Höll
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  3. H. Sontheimer
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, University of Bradford, UK

    M. J. Slater

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© 1992 United Kingdom Atomic Energy Authority

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Franzreb, M., Höll, W.H., Sontheimer, H. (1992). A General Solution of the Nernst-Planck Equations for Ion Exchange with Rate Control by Liquid-Phase Mass Transfer. In: Slater, M.J. (eds) Ion Exchange Advances. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2864-3_22

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  • DOI: https://doi.org/10.1007/978-94-011-2864-3_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-882-3

  • Online ISBN: 978-94-011-2864-3

  • eBook Packages: Springer Book Archive

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