Skip to main content
Log in

Transfer processes in fractal media

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

An irreversible process in fractal media involves coupling relation between the space and the time. The present note displays how the fractional derivation has to be introduced to describe this effect. As a result the law of the chemical diffusion to a fractal is given.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Villermaux,Génie de la réaction chimique. Conception et fonctionnement des réacteurs, Technique et Documentation (Lavoisier, Paris, 1982).

    Google Scholar 

  2. R. Aris,The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts (Clarendon press, Oxford, 1975).

    Google Scholar 

  3. J. J. Carberry,Applied Kinetics and Chemical Reaction Engineering (MacGraw-Hill, New York, 1976).

    Google Scholar 

  4. R. de Levie,Advances in Electrochemistry and Electrochemical Engineering, Vol. 6, P. Delahay and C. W. Tobias, eds. (Interscience, New York, 1967).

    Google Scholar 

  5. J. Newman, bibliography, Material and Molecular Research Division, Lawrence Berkeley Laboratory and Department of Chemical Engineering, University of California, Berkeley, California 94720.

  6. P. Le Goff, Cinétique physique des réactions chimiques hétérogènes, in Techniques de l'ingénieur, Ref. J. 1210, 1967.

  7. J. Newman and W. Tiedemann,Advances in Electrochemistry and Electrochemical Engineering, Vol. 11, H. Gericher and C. W. Tobias, eds. (Interscience, New York, 1977).

    Google Scholar 

  8. B. Mandelbrot,Les objects fractals (Flammarion, Paris, 1975);Fractal, Form, Chance and Dimension (Freeman, San Francisco, 1977);The Fractal Geometry of Nature (Freeman, San Francisco, 1983).

    Google Scholar 

  9. A. Le Mehaute and G. Crepy, in Salon de la Physique, Paris (1981);C. R. Acad. Sci. (Paris) 294:835–838 (1982).

  10. P. Pfeifer and P. Avnir,J. Chem. Phys. 79(7):3558–3571 (1983).

    Google Scholar 

  11. I. Prigogine,Physique, temps et devenir (Masson, Paris, 1980).

    Google Scholar 

  12. R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics (Wiley-Interscience, New York, 1975).

    Google Scholar 

  13. I. Prigogine,Thermodynamique des phénomènes irréversibles (Dunod, Paris, 1947); G. de Groot,Thermodynamics of irreversible processes (Eisevier, New York, 1962).

    Google Scholar 

  14. A. Le Mehaute, A. de Guibert, M. Délaye, and C. Filippi, C.R. Acad, Sci. (Paris) 294:835–839 (1982); A. Le Mehaute and G. Crepy,Solid State Ionics 9/10=:17–30 (1983).

    Google Scholar 

  15. A. Blanc-Lapierre and B. Picinbono,Fonctions aléatoires (Masson, Paris, 1981); J. C. Gille, M. Pellegrin, and P. Decaulne,Théorie et techniques des asservissements (Dunod, Paris, 1956).

    Google Scholar 

  16. L. Schwartz,Théorie des distributions (Hermann, Paris, 1966).

    Google Scholar 

  17. L. Fruchter, “A propos du contenu fractal de la réponse viscoelastique,” D.E.A., Laboratoires de Marcoussis, internai report. Unpublished.

  18. L. Fruchter and A. Le Mehaute, to be published.

  19. J. Liouville,J. École Polytech. 13:71 (1832); J. M. Guelfan and G. E. Chilov,Les distributions (Dunod, Paris, 1962); K. O. Oldham and J. S. Spanier,The Fractional Calculus (Academic Press, New York, 1974); B. Ross.Fractional Calculus and Its Applications A. Ross Dold, A. Exkmann, and B. Exkmann, eds. (Springer-Verlag, Berlin, 1974).

    Google Scholar 

  20. R. Kopelman, P. W. Klymko, J. S. Newhouse and L. W. Anaker,Phys. Rev. 29:3747–3748 (1984).

    Google Scholar 

  21. P. Evesque,J. Phys. (Paris) 44:1217, 1224 (1983).

    Google Scholar 

  22. E. Von Schweilder,Ann. Phys. (Leipzig) 24:711–714 (1907).

    Google Scholar 

  23. A. Le Mehaute and G. Crepy,C. R. Acad. Sci. (Paris) 294:685 (1982); A. Le Mehaute and A. Dugast,J. Power Sources 9:359–364 (1983).

    Google Scholar 

  24. A. Le Mehaute, three experimental notes in preparation.

  25. T. Hamaide, thesis, Lyon, 1983.

  26. K. J. Laidler,Reaction Kinetics (Pergamon Press, New York, 1963).

    Google Scholar 

  27. K. S. Cole and R. H. Cole,J. Chem. Phys. 9:341–347 (1941).

    Google Scholar 

  28. Y. Adda and J. Philibert,La diffusion dans les solides (INSTN/Press Universitaire de France, 1966).

  29. K. B. Oldham and J. Spanier,J. Electroanal. Chem. 26:31–10 (1970); K. B. Oldham,Anal. Chem. 44:196–201 (1972); M. Grenness and K. B. Oldham,Ann. Chem. 44:1121–1129 (1972); K. B. Oldham,Anal. Chem. 45:39–43 (1973).

    Google Scholar 

  30. R. L. Birke,Anal. Chem. 45:2292–2998 (1973).

    Google Scholar 

  31. A. Le Mehaute and G. Crepy, to be published.

  32. A. Le Mehaute and G. Crepy,Solid State Ionics 9/10:17–30 (1983).

    Google Scholar 

  33. A. Le Mehaute, G. Crepy, G. Marcellin, and T. Hamaide, EUCHEM Conference on Solid State Chemistry and Electrochemistry, Oxford, March 1984.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Le Mehaute, A. Transfer processes in fractal media. J Stat Phys 36, 665–676 (1984). https://doi.org/10.1007/BF01012930

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01012930

Key words

Navigation