Skip to main content
SpringerLink
Log in

Mathematical simulation of atomic hydrogen diffusion transfer through a multilayer metal membrane at finite pressures

  • Published:
Colloid Journal Aims and scope Submit manuscript

Abstract

Diffusion transfer of atomic hydrogen through multilayer metal membranes has been studied within the lattice model of an ideal gas, with the transfer being described by a set of nonlinear algebraic equations. It has been shown that, for multilayer membranes composed of less than four layers, an analytical expression describing a diffusion flux can be derived. Atomic hydrogen transfer through a membrane consisting of a vanadium layer, the surfaces of which are coated with palladium films, has been analyzed in detail. It has been found that the value of the flux may depend on the transfer direction. The effect of diffusion asymmetry arises at finite pressures of hydrogen on the outer membrane surfaces, when its dissolution in metals is described by nonlinear sorption isotherms. The degree of the diffusion asymmetry increases with a rise in hydrogen pressure and depends on the arrangement of the layers composing a membrane.

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. Lemus, R.G. and Martínez Duart, J.M., Int. J. Hydrogen Energy, 2010, vol. 35, p. 3929.

    Article  CAS  Google Scholar 

  2. Alimov, V.N., Hatano, Y., Busnyuk, A.O., Livshits, D.A., Notkin, M.E., and Mishits, A.I., Int. J. Hydrogen Energy, 2011, vol. 36, p. 7737.

    Article  CAS  Google Scholar 

  3. Xiong, L., Liu, S., and Rong, L., Int. J. Hydrogen Energy, 2010, vol. 35, p. 1643.

    Article  CAS  Google Scholar 

  4. Alimov, V.N., Busnyuk, A.O., Notkin, M.E., and Livshits, A.I., J. Membr. Sci., 2014, vol. 457, p. 103.

    Article  CAS  Google Scholar 

  5. Lu, G.Q., Diniz da Costa, J.C., Duke, M., Giessler, S., Socolow, R., Williams, R.H., and Kreutz, T., J. Colloid Interface Sci., 2007, vol. 314, p. 589.

    Article  CAS  Google Scholar 

  6. Smirnov, L.I. and Gol’tsov, V.A., Al’tern. Energ. Ekol., 2014, no. 1, p. 111.

    Google Scholar 

  7. Hydrogen in Metals, Alefeld, G. and Volkl, J., Eds., Heidelberg: Springer, 1978.

  8. Ugrozov, V.V., Colloid J., 2011, vol. 73, p. 581.

    Article  CAS  Google Scholar 

  9. Landau, L.D. and Lifshitz, E.M., Statistical Physics, New York: Pergamon, 1980.

    Google Scholar 

  10. Shulepov, V.Yu. and Aksenenko, E.V., Reshetochnyi gaz. Vvedenie v teoriyu i izbrannye prilozheniya (Lattice Gas: Introduction to Theory and Selected Applications), Kiev: Naukova Dumka, 1981.

    Google Scholar 

  11. Smirnov, A.A., Molekulyarno-kineticheskaya teoriya metallov (Molecular Kinetic Theory of Metals), Moscow: Nauka, 1966.

    Google Scholar 

  12. Korn, G. and Korn, T., Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. Opredeleniya, teoremy, formuly (Handbook of Mathematics for Scientists and Engineers. Definitions, Theorems, Formulae), Moscow: Nauka, 1978.

    Google Scholar 

  13. Wood, B.J. and Wise, H., J. Catal., 1966, vol. 5, p. 135.

    Article  CAS  Google Scholar 

  14. Swansiger, W.A. and Bastasz, R., J. Nucl. Mater., 1979, vol. 85, p. 335.

    Article  Google Scholar 

  15. Roldughin, V.I. and Zhdanov, V.M., Adv. Colloid Interface Sci., 2011, vol. 168, p. 223.

    Article  CAS  Google Scholar 

  16. Filippov, A.N., Starov, V.M., Kononenko, N.A., and Berezina, N.P., Adv. Colloid Interface Sci., 2008, vol. 139, p. 29.

    Article  CAS  Google Scholar 

  17. Zhdanov, V.M., Roldughin, V.I., and Sherysheva, E.E., J. Eng. Phys. Thermophys., 2013, vol. 86, p. 356.

    Article  CAS  Google Scholar 

  18. Kurchatov, I.M., Laguntsov, N.I., Tronin, V.N., and Uvarov, V.I., Al’tern. Energ. Ekol., 2007, no. 5, p. 125.

    Google Scholar 

  19. Kosinska, I.D. and Fulinski, A., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2005, vol. 72, p. 201.

    Article  Google Scholar 

  20. Kolomeisky, A.B., Phys. Rev. Lett., 2007, vol. 98, p. 5.

    Article  Google Scholar 

  21. Ugrozov, V.V. and Filippov, A.N., Colloid J., 2012, vol. 74, p. 739.

    Article  CAS  Google Scholar 

  22. Ugrozov, V.V., Colloid J., 2011, vol. 73, p. 581.

    Article  CAS  Google Scholar 

  23. Volkov, A.V., Tsarkov, S.E., Gilman, A.V., Khotimsky, V.S., Roldughin, V.I., and Volkov, V.V., Adv. Colloid Interface Sci., 2015, vol. 222, p. 716.

    Article  CAS  Google Scholar 

  24. Volkov, V.V., Mchedlishvili, B.V., Roldughin, V.I., Ivanchev, S.S., and Yaroslavtsev, A.B., Nanotechnol. Russ., 2008, vol. 3, nos. 11–12, p. 656.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Financial University under the Government of the Russian Federation, ul. Shcherbakovskaya 38, Moscow, 123995, Russia

    V. V. Ugrozov

Authors
  1. V. V. Ugrozov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Ugrozov.

Additional information

Original Russian Text © V.V. Ugrozov, 2017, published in Kolloidnyi Zhurnal, 2017, Vol. 79, No. 1, pp. 90–95.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ugrozov, V.V. Mathematical simulation of atomic hydrogen diffusion transfer through a multilayer metal membrane at finite pressures. Colloid J 79, 138–143 (2017). https://doi.org/10.1134/S1061933X17010136

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061933X17010136

Search

Navigation