Skip to main content
SpringerLink
Log in

The Nernst-Planck Equation in Thermodynamic Transport Theories

  • Chapter
Mass Transfer and Kinetics of Ion Exchange

Part of the book series: NATO ASI Series ((NSSE,volume 71))

Abstract

The first investigations of Boyd (1) concerning the kinetics of ion exchange are based on a solution of the second Fick’s law. Thereby the boundary conditions were taken into account by the well known method developed by Fourier in his famous book “Theorie Analytique De La Chaleur” (1822) (2).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyd, G.E., Adamson, A.W., and Myers, L.S., Jr., J.Amer.Chem. Soc. 67, 2836 (1947)

    Article  Google Scholar 

  2. See “The Analytical Theory of Heat by Joseph Fourier. Translated, with notes, by Alexander Freeman, Dover Publications, Inc., New York (1955).

    Google Scholar 

  3. Helfferich, F. and Plesset M.S., J.Chem.Phys. 28, 418(1958)

    Article  CAS  Google Scholar 

  4. I. Gyarmati, Non-equilibrium Thermodynamics, Springer Verlag Berlin-Heidelberg-New York (1970)

    Google Scholar 

  5. G. Dickel and G. Backhaus, J.Chem.Soc.Faraday Trans. 2, 74, 115, 124 (1978)

    Google Scholar 

  6. G. Dickel, Electro-Mechanical Equilibrium in Membranes, Topics in Bioelectrochemistry and Bioenergetics Vol.4. (1981). John Wiley and Sons Ltd.

    Google Scholar 

  7. K.S. Spiegler, Trans.Faraday Soc. 54, 1408 (1958)

    Article  CAS  Google Scholar 

  8. P. Meares, D.G. Dawson, A.H. Sutton and J.F. Thain, Ber. Bunsenges. Phys. Chem. 71, 765 (1967)

    CAS  Google Scholar 

  9. L. Onsager, Phys.Rev. 37, 405 (1931); 38, 2265 (1931)

    Article  CAS  Google Scholar 

  10. O. Bolza, Lectures on the Calculus of Variations, Chelsea Publ. Co., New York

    Google Scholar 

  11. D. Hilbert, Ges.Werke Bd.3.S.32. Springer Verlag Berlin- Heidelberg-New York (1970)

    Google Scholar 

  12. G. Dickel and B. Pitesa, J.Chem.Soc., Faraday Trans, II, 77, 441 (1981)

    Article  CAS  Google Scholar 

  13. I. Prigogine, Etude thermodynamique des Phénomènes Irréversibles(Thesis) Dunod, Paris and Desoer, Liege (1947)

    Google Scholar 

  14. G. Schmid, Z. Elektrochem., 54, 424 (1950); 55, 229, 295, 684 (1951); 56, 35, 181 (1952) Ber.Bunsenges., Phys.Chem, 71, 778 (1967)

    CAS  Google Scholar 

  15. P. Meares, J.F. Thain and D.G. Dawson, Membranes Vol.1, Chapter 2, edited by G. Eisenman, Marcel Dekker, Inc., New York(1972)

    Google Scholar 

  16. R. Schloegl, Stofftransport durch Membranen, Steinkopf-Verlag Darmstadt, (1969)

    Google Scholar 

  17. G. Dickel and H. Hoenig, Z.Phys.Chem. (Frankfurt/Main) 90, 198, (1974)

    Article  CAS  Google Scholar 

  18. H.S. Harned, B.B. Owen, Physical Chemistry of Electrolytic Solutions, Reinhold, Pub, Co., New York (1950)

    Google Scholar 

  19. G. Dickel, G. Backhaus and E. Hauerwaas, Z.Phys.Chem., 258, (1978)

    Google Scholar 

  20. R. Kretner, H. Hoenig and G. Dickel, Z.Phys.Chem. (Frankfurt/Main) 106, 330 (1977)

    Article  CAS  Google Scholar 

  21. G. Dickel and R. Kretner, Z. Phys.Chem. (Frankfurt/Main) 118, 161 (1979)

    Article  CAS  Google Scholar 

  22. A.L. Hodgkin and B. Katz. J. Physiolog. London 108, 37(1949)

    CAS  Google Scholar 

  23. F. Helfferich, J.Phys. Chem. 66, 39 (1962)

    Article  CAS  Google Scholar 

  24. G. Dickel and R. Kretner, J.Chem. Soc., Faraday Trans.2 74, 2225 (1978)

    Article  CAS  Google Scholar 

  25. W. Guggenheim, J. Phys.Chem. 33, 842 (1929); 34, 1540(1930)

    Article  CAS  Google Scholar 

  26. G. Dickel, to be published

    Google Scholar 

  27. R. S. De Groot, Thermodynamics of Irreversible Processes, North Holland Publ. Co., Amsterdam (1958)

    Google Scholar 

  28. D. Enskog, Physik. Z. 12, 56, 553(1911). Ann.Physik 38, 731 (1912)

    Google Scholar 

  29. I.W.R. Hamilton, Irish Transactions 15–17 (1828–30)

    Google Scholar 

  30. G. Dickel, to be published

    Google Scholar 

  31. P. Fries, Dissertation München, (1951)

    Google Scholar 

  32. G. Dickel and A. Meyer, Z.Electrochem.Ber.der Bunsenges. 57, 901(1953)

    Google Scholar 

  33. G.E. Boyd, F. Vaslow and S. Lindenbaum, J.Phys.Chem.68, 590(1964)

    Article  CAS  Google Scholar 

  34. G. Dickel u.W. Franke, Z.Phys.Chem. (Frankfurt/Main)80, 190(1972)

    Article  CAS  Google Scholar 

  35. D. Fiederer, Dissertation München (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physical Chemistry, University of Munich, Germany

    G. Dickel

Authors
  1. G. Dickel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Bari, Italy

    Lorenzo Liberti (Senior Researcher at the Water Research Institute of the National Research Council of Italy Associate Professor of Industrial Chemistry at the Faculty of Engineering) (Senior Researcher at the Water Research Institute of the National Research Council of Italy Associate Professor of Industrial Chemistry at the Faculty of Engineering)

  2. Pennsylvania State University, University Park, PA, 16802, USA

    Friedrich G. Helfferich (Professor of Chemical Engineering) (Professor of Chemical Engineering)

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Martinus Nijhoff Publishers, The Hague

About this chapter

Cite this chapter

Dickel, G. (1983). The Nernst-Planck Equation in Thermodynamic Transport Theories. In: Liberti, L., Helfferich, F.G. (eds) Mass Transfer and Kinetics of Ion Exchange. NATO ASI Series, vol 71. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6899-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-6899-8_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6901-8

  • Online ISBN: 978-94-009-6899-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation