Skip to main content
SpringerLink
Log in

Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition

  • Published:
Russian Journal of Electrochemistry Aims and scope Submit manuscript

Abstract

A relatively simple mathematical model based on the Poisson equation is considered. The model is intended for modeling transport through multilayered ion-exchange membranes operating at overlimiting currents. The boundary-value problem is solved by a numerical method of parallel shooting and by an approximate method based on the assumption that the charge density is distributed quasi-uniformly. Concentration profiles in diffusion layers and membranes, current–voltage curves, and dependences of effective transport numbers on the current density are examined.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Rubinstein, I. and Shtilman, L., J. Chem. Soc., Faraday Trans. 2, 1979, vol. 75, p. 231.

    Google Scholar 

  2. Zabolotskii, V.I. and Nikonenko, V.V., Perenos ionov v membranakh (The Ion Transport in Membranes), Moscow: Nauka, 1996.

    Google Scholar 

  3. Rubinstein, I., Zaltzman, B., and Kedem, O., J. Membr. Sci., 1997, vol. 125, p. 17.

    Google Scholar 

  4. Kharkats, Yu.I., Elektrokhimiya, 1985, vol. 21, p. 974.

    Google Scholar 

  5. Budnikov, E.Yu., Maksimychev, A.V., Kolyubin, A.V., et al., Zh. Fiz. Khim., 1999, vol. 73, p. 198.

    Google Scholar 

  6. Urtenov, M.Kh., Kraevye zadachi dlya sistemy uravnenii Nernsta-Planka-Puassona (Boundary-Value Problems for a Set of Nernst-Planck-Poisson Equations), Krasnodar: Kubanskii Gos. Univ., 1998.

    Google Scholar 

  7. Grafov, B.M. and Chernenko, A.A., Dokl. Akad. Nauk SSSR, 1962, vol. 146, p. 241.

    Google Scholar 

  8. Nikonenko, V.V., Zabolotskii, V.I., and Gnusin, N.P., Elektrokhimiya, 1989, vol. 25, p. 301.

    Google Scholar 

  9. Listovnichii, A.V., Elektrokhimiya, 1989, vol. 25, p. 1651.

    Google Scholar 

  10. Urtenov, M.E. and Nikonenko, V.V., Elektrokhimiya, 1993, vol. 29, p. 239.

    Google Scholar 

  11. Nikonenko, V.V. and Urtenov, M.Kh., Elektrokhimiya, 1996, vol. 32, p. 207.

    Google Scholar 

  12. Nikonenko, V.V. and Urtenov, M.Kh., Elektrokhimiya, 1996, vol. 32, p. 215.

    Google Scholar 

  13. Manzanares, J.A., Murphy, W.D., Mafe, S., and Reiss, H., J. Phys. Chem., 1993, vol. 97, p. 8524.

    Google Scholar 

  14. Manzanares, J.A., Mafe, S., Hernandez, M.J., and Pellicer, J., Abstracts of Papers, Int. Congress on Membranes and Membrane Processes, Heidelberg, Germany, 1993.

  15. Lebedev, K.A. and Kovalev, I.V., Elektrokhimiya, 1999, vol. 35, p. 1224.

    Google Scholar 

  16. Nikonenko, V.V., Zabolotskii, V.I., Gnusin, N.P., and Lebedev, K.A., Elektrokhimiya, 1985, vol. 21, p. 784.

    Google Scholar 

  17. Lebedev, K.A., Nikonenko, V.V., and Zabolotskii, V.I., Elektrokhimiya, 1987, vol. 23, p. 555.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kuban State University, ul. Stavropol'skaya 149, Krasnodar, 350040, Russia

    V. I. Zabolotskii, V. V. Nikonenko & K. A. Lebedev

  2. University of Valencia, Valencia, Spain

    J. A. Manzanares & S. Mafe

Authors
  1. V. I. Zabolotskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. A. Manzanares
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Mafe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. V. Nikonenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. A. Lebedev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zabolotskii, V.I., Manzanares, J.A., Mafe, S. et al. Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition. Russian Journal of Electrochemistry 38, 819–827 (2002). https://doi.org/10.1023/A:1016801425856

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1016801425856

Keywords

Search

Navigation