Interfacial Instability in Fluid Layers Under Thermal Constraints

  • Manuel G. Velarde
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 28)

Abstract

Although reports on interfacial convection were published before the beginning of our century and their relevance had been discussed by several authors, a systematic study of the phenomenology did not really occur until the experimental work conducted by Henri BENARD /l/. This author posed himself the task of providing a quantitative description of the (steady) flows arising in a horizontal thin liquid layer heated from below and open to the ambient air. There is some evidence that Benard perceived the relevant role of surface tension in his problem but, however, he did not really address himself the question of interest to us here: how and how much the liquid-air interface affected or was affected by the observed convective flows. It took some fifty years until the right experimental (BLOCK /2/, KOSCHMIEDER /3/) and theoretical questions (PEARSON /4/) were asked and, to a first approximation, unambiguously answered (BIRIKH /5/, NIELD /6/, STERNLING and SCRIVEN /7/).Yet, today we do not dispose of a complete theory of the interfacial phenomena involved in Benard convection. However,interfacial convection is so relevant to chemical engineering, materials sciences, crystal growth (LANGER /8/, OSTRACH /9/, SCHWABE and SCHARMANN/10/) that many aspects of the problems have already been elucidated.

Keywords

Convection Ambi 

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References

  1. 1.
    H. Benard. (a) Rév. Gén. Sci. pures appi. 11, 1261–1271(1900). (b) Ann. Chim Phys. 23, 62–144 (1901)Google Scholar
  2. 2.
    M. Block, Nature 178, 650–651 (1956)ADSCrossRefGoogle Scholar
  3. 3.
    E.L. Koschmieder, J. Fluid Mech. 30, 9–15 (1967)ADSCrossRefGoogle Scholar
  4. 4.
    J. R. A. Pearson, J. Fluid Mech. 4, 489–500 (1958)ADSMATHCrossRefGoogle Scholar
  5. 5.
    R.V. Birikh, J. Appi. Mech. Tech. Phys. 3, 43 (1966)Google Scholar
  6. 6.
    D.A. Nield, J. Fluid Mech. 19, 341–352 (1964)MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    C.V. Sternling, L.E. Scriven, AICHE J. 5, 514–523 (1959)CrossRefGoogle Scholar
  8. 8.
    J.S. Langer, Rev. Mod. Phys. 52, 1–28 (1980)ADSCrossRefGoogle Scholar
  9. 9.
    S. Ostrach, In: Physico Chemical Hydrodynamics, Advance Pub., London, 1977Google Scholar
  10. 10.
    D. Schwabe, A. Scharmann, J. Crystal Growth 52, 435–499 (1981)ADSCrossRefGoogle Scholar
  11. 11.
    C. Dauzere, J. Physique 7, 930–934 (1908)Google Scholar
  12. 12.
    V. Volkovisky, Publications Sci. Tech. Ministere de l’Air 151, Paris (1939)Google Scholar
  13. 13.
    Lord Rayleigh, Phil. Mag. 32, 529–546 (1916)Google Scholar
  14. 14.
    A. R. Low, D. Brunt, Nature 115, 299–301 (1925)ADSCrossRefGoogle Scholar
  15. 15.
    M.G. Velarde, Ch. Normand, Sci. American 243, 78–93 (1980)CrossRefGoogle Scholar
  16. 16.
    R. Perez-Cordon, M.G. Velarde, J. Physique 36, 591–601 (1975)ADSCrossRefGoogle Scholar
  17. 17.
    M..G. Velarde, R. Perez-Cordon, J. Physique 37, 171–182 (1976)Google Scholar
  18. 18.
    L.E. Scriven, C.V. Sternling, Nature 187, 186 (I960)Google Scholar
  19. 19.
    L.E. Scriven, C.V. Sternling, J. Fluid Mech. 19, 321–340 (1964)MathSciNetADSMATHCrossRefGoogle Scholar
  20. 20.
    A. Orell, J. W. Westwater, Chem. Eng. Sci. 16, 127 (1961)CrossRefGoogle Scholar
  21. 21.
    A. Orell, J. W. Westwater, AICHE J. 8, 350–356 (1962)Google Scholar
  22. 22.
    C. J. F. Wanngard, Ph.D. Diss., Royal Inst. Techn., Stockholm, 1980Google Scholar
  23. 23.
    J. Pantaloni, B. Bailleux, J. Salan, M.G. Velarde, J. Non-Equilibrium. Therm 4, 201–218 (1979)Google Scholar
  24. 24.
    J. Pantaloni, P. Cerisier, R. Bailleux, C. Gerbaud, J. Physique Lett. 42, L 147–L 150 (1981)Google Scholar
  25. 25.
    A.V. Hershey, Phys. Rev. 56, 204 (1939)ADSMATHCrossRefGoogle Scholar
  26. 26.
    K. C. D. Hickmann, Ind. Eng. Chem. 44, 1892–1902 (1952)Google Scholar
  27. 27.
    H. Jeffreys, Quart. J. Mech. Appl. Math. 4, 283–283 (1951)MATHGoogle Scholar
  28. 28.
    K. A. Smith, J. Fluid Mech. 24, 401–414 (1966)ADSCrossRefGoogle Scholar
  29. 29.
    M. Bentwich, Int. J. Heat Mass Transfer 9, 663–670 (1966)CrossRefGoogle Scholar
  30. 30.
    J.C. Berg, A. Acrivos, Chem. Eng. Sci. 20, 737–745 (1965)CrossRefGoogle Scholar
  31. 31.
    J.C. Berg, A. Acrivos, M. Boudart, Adv. Chem. Eng. 6, 61–123 (1966)CrossRefGoogle Scholar
  32. 32.
    A. Bose, H.J. Palmer, J. Fluid Mech. 126, 491–506 (1983)ADSMATHCrossRefGoogle Scholar
  33. 33.
    S.H. Davis, L. A. Segel, Phys. Fluids 11, 470–476 (1968)ADSMATHCrossRefGoogle Scholar
  34. 34.
    V. Ludviksson, E.N. Lightfoot, AICHE J. 14, 620–626 (1968)CrossRefGoogle Scholar
  35. 35.
    J.W. Scanlon, L. A. Segel, J. Fluid Mech. 30, 149–162 (1967)ADSMATHCrossRefGoogle Scholar
  36. 36.
    S.H. Davis, G. M. Homsy, J. Fluid Mech. 98, 527–553 (1980)MathSciNetADSMATHCrossRefGoogle Scholar
  37. 37.
    J.L. Castillo, M.G. Velarde, J. Fluid Mech. 125, 463–74 (1982)ADSMATHCrossRefGoogle Scholar
  38. 38.
    J.L. Castillo, M.G. Velarde, J. Colloid Interface Sci., submitted forpublication.Google Scholar
  39. 39.
    E. Ferm, D. Wollkind, J. Non-Equilib. Thermodyn. 7, 169–90 (1982).ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Manuel G. Velarde
    • 1
  1. 1.U.N.E.D.-CienciasE-MadridSpain

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