Advertisement

Diffuse Interfaces

  • P. Clavin
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)

Abstract

Because of the high activation energy involved in the Arrhenius laws, non-linear kinetic effects cannot be neglected even in first approximation in the dynamics of some flame fronts as for example in solid combustion. This is true even for small variations of the flame temperature. The situation is quite different in crystal growth where, the temperature of the interface Tf being always very close to the equilibrium temperature Te, kinetic effects are assumed to be negligible in a first approximation. By using singular methods originally developed in flame theory, this problem is revisited by solving a particular model for the diffuse interface. The results point out the limits of validity of the Gibbs-Thomson boundary condition. New phenomena that can be produced by non-linear kinetic effects even for (Tf-Te)/Te≪l are predicted, as for example the appearance of intermediate phases of a purely kinetic nature.

Keywords

Flame Front Flame Temperature Lewis Number Kinetic Effect Flame Speed 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ya.B. Zeldovich and D.A. Frank-Kamenetskii, Acta Physicochimia URSS, IX-2-341 (1938)Google Scholar
  2. 2.
    G.I. Sivashinsky, Ann. Rev. Fluid Mech. 15: 179 (1983)CrossRefADSGoogle Scholar
  3. P. Clavin, Prog. Energy Combust. Sci. 11: 1 (1985)CrossRefGoogle Scholar
  4. P. Clavin, in “Combustion and Nonlinear Phenomena”. Les Editions de Physique (1986)Google Scholar
  5. 3.
    P. Pelcé and P. Clavin, J. Fluid Mech. 124: 219 (1982)CrossRefzbMATHADSGoogle Scholar
  6. 4.
    J. Quinard, Thèse Université de Provence, Marseille (1984)Google Scholar
  7. J. Quinard, G. Searby and L. Boyer, Lecture Notes in Physics, 210: 331 (1984) AIAA Progress Series 95: 129 (1984)Google Scholar
  8. 5.
    G.I. Sivashinsky, Acta Astronautica, 4: 1177 (1977)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 6.
    P. Clavin and G. Joulin, J. Physique Lettres, 44: L1 (1983)CrossRefGoogle Scholar
  10. P. Clavin and F.A. Williams, J. Fluid Mech. 116: 251 (1982)CrossRefzbMATHADSGoogle Scholar
  11. 7.
    G. Joulin and P. Clavin, Combust. Flame 35: 139 (1979)CrossRefGoogle Scholar
  12. 8.
    P. Clavin in “Interfacial Phenomena” NATO ASI SERIES to appear (1987)Google Scholar
  13. 9.
    J.A. Britten, Ph. D. Thesis, Univ. Colorado (1984)Google Scholar
  14. J.A. Britten, W.B. Krantz, Combust. Flame 60: 125 (1985)CrossRefGoogle Scholar
  15. 10.
    P. Clavin, B. Denet, J. Monteiller and P. Pelcé, J.M.T.A.(J. Theoretical & Applied Mech.) N° spécial: 173 (1986)Google Scholar
  16. 11.
    G. Sivashinsky, SIAM Appl. Math 40: 432 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 12.
    J. Langer, Rev. Mod. Phys. 52: 1 (1980)CrossRefADSGoogle Scholar
  18. 13.
    P. Clavin, P. Lallemand, Y. Pomeau and G. Searby, J. Fluid. Mech. to appear (1987)Google Scholar
  19. 14.
    J.W.Cahn and J.E. Hilliard, J. Chem. Phys. 28: 258 (1958), 31: 688 (1959)CrossRefADSGoogle Scholar
  20. 15.
    J.B. Collins, H. Levine, Phys. Rev. B 31–9: 6119 (1985)Google Scholar
  21. G. Caqinalp and P. Fife, in “Interfacial Phenomena” NATO ASI SERIES to appear (1977).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • P. Clavin
    • 1
  1. 1.Laboratoire de Recherche en CombustionC.N.R.S. et Université de ProvenceMarseille Cedex 13France

Personalised recommendations