The European Physical Journal Special Topics

, Volume 192, Issue 1, pp 135–143 | Cite as

Large-scale Marangoni convection in a liquid layer with insoluble surfactant of low concentration

  • A. Mikishev
  • A. Nepomnyashchy
Regular Article
  • 57 Downloads

Abstract.

We derive a system of amplitude equations describing the evolution of a large-scale Marangoni patterns in a liquid layer with poorly conducting boundaries in the presence of a small amount of an insoluble surfactant on the free flat interface. The presence of quadratic nonlinear terms in the amplitude equation leads to the selection of hexagonal patterns. The type of hexagons bifurcating into the subcritical region, depends on the parameters of the system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S.H. Davis, Annu. Rev. Fluid Mech. 19, 403 (1987)CrossRefMATHADSGoogle Scholar
  2. 2.
    P. Colinet, J.C. Legros, M.G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, Berlin, 2001)Google Scholar
  3. 3.
    A.A. Nepomnyashchy, M.G. Velarde, P. Colinet, Interfacial Phenomena and Convection (Chapman and Hall/CRC Press, Boca Raton, 2002)Google Scholar
  4. 4.
    J.R. Pearson, J. Fluid Mech. 4, 489 (1958)CrossRefMATHADSGoogle Scholar
  5. 5.
    G.I. Sivashinsky, Physica D 4, 227 (1982)CrossRefMATHADSMathSciNetGoogle Scholar
  6. 6.
    E. Knobloch, Physica D 41, 450 (1990)CrossRefMATHADSMathSciNetGoogle Scholar
  7. 7.
    L. Shtilman, G. Sivashinsky, Physica D 52, 477 (1991)CrossRefMATHADSMathSciNetGoogle Scholar
  8. 8.
    A.A. Golovin, A.A. Nepomnyashchy, L.M. Pismen, Physica D 81, 117 (1995)CrossRefMATHGoogle Scholar
  9. 9.
    J.C. Berg, A.A. Acrivos, Chem. Eng. Sci. 20, 737 (1965)CrossRefGoogle Scholar
  10. 10.
    H.J. Palmer, J.C. Berg, J. Fluid Mech. 51, 385 (1972)CrossRefMATHADSGoogle Scholar
  11. 11.
    A.A. Nepomnyashchy, I.B. Simanovskii, Fluid Dyn. 21, 469 (1986)Google Scholar
  12. 12.
    E.A. Ryabitskii, Fluid Dyn. 28, 3 (1993)CrossRefADSGoogle Scholar
  13. 13.
    A. Mikishev, A. Nepomnyashchy, Microgravity Sci. Technol. (2010) (to be published)Google Scholar
  14. 14.
    V.G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, N.J., 1962)Google Scholar
  15. 15.
    A. Oron, A. Nepomnyashchy, Phys. Rev. E 69, 016313 (2004)CrossRefADSGoogle Scholar
  16. 16.
    F.H. Busse, J. Fluid Mech. 30, 625 (1967)CrossRefMATHADSGoogle Scholar
  17. 17.
    C.D. Eggleton, Y.P. Pawar and K.J. Stebe, J. Fluid Mech. 385, 79 (1999)CrossRefMATHADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2011

Authors and Affiliations

  • A. Mikishev
    • 1
  • A. Nepomnyashchy
    • 1
  1. 1.Department of MathematicsTechnion – Israel Institute of TechnologyHaifaIsrael

Personalised recommendations