The European Physical Journal Special Topics

, Volume 192, Issue 1, pp 101–108 | Cite as

Convective instabilities in films of binary mixtures

Regular Article

Abstract.

We present a model for the evolution of films of isothermal binary liquid mixtures with a free evolving surface. The model is based on model-H supplemented by appropriate boundary conditions at the free surface and the solid substrate. The equations account for the coupled transport of the concentration of a component (convective Cahn-Hilliard equation) and the momentum (Korteweg-Navier-Stokes equation). The inclusion of convective motion makes surface deflections possible, i.e., the model allows to study couplings between the decomposition of the mixture and the evolving surface corrugations. We present selected steady layered film states for representative polymer mixtures, and show that convective motion favors their destabilization and qualitatively changes the linear instability modes in experimentally accessible ranges of parameters.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Reiter, A. Sharma, Phys. Rev. Lett. 87, 166103 (2001)CrossRefADSGoogle Scholar
  2. 2.
    L. Rockford, Y. Liu, P. Mansky, T.P. Russell, M. Yoon, S.G.J. Mochrie, Phys. Rev. Lett. 82, 2602 (1999)CrossRefADSGoogle Scholar
  3. 3.
    M. Geoghegan, G. Krausch, Prog. Polym. Sci. 28, 261 (2003)CrossRefGoogle Scholar
  4. 4.
    K.R. Thomas, N. Clarke, R. Poetes, M. Morariu, U. Steiner, Soft Matter 6, 3517 (2010)CrossRefADSGoogle Scholar
  5. 5.
    A. Sharma, R. Khanna, Phys. Rev. Lett. 81, 3463 (1998)CrossRefADSGoogle Scholar
  6. 6.
    S. Kalliadasis, U. Thiele (eds.), Thin Films of Soft Matter (Springer, Wien, 2007)Google Scholar
  7. 7.
    U. Thiele, J. Phys.: Condens. Matter 22, 084019 (2010)CrossRefADSGoogle Scholar
  8. 8.
    D. Bonn, J. Eggers, J. Indekeu, J. Meunier, E. Rolley, Rev. Mod. Phys. 81, 739 (2009)CrossRefADSGoogle Scholar
  9. 9.
    R. Yerushalmi-Rozen, T. Kerle, J. Klein, Science 285, 1254 (1999)CrossRefGoogle Scholar
  10. 10.
    D.M. Anderson, G.B. McFadden, A.A. Wheeler, Ann. Rev. Fluid Mech. 30, 139 (1998)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)CrossRefADSGoogle Scholar
  12. 12.
    U. Thiele, S. Madruga, L. Frastia, Phys. Fluids 19, 122106 (2007)CrossRefADSGoogle Scholar
  13. 13.
    S. Madruga, U. Thiele, Phys. Fluids 21, 062104 (2009)CrossRefADSGoogle Scholar
  14. 14.
    E.J. Doedel, R.C. Paffenroth, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B.E. Oldeman, B. Sandstede, X.J. Wang, AUTO2000: Continuation and bifurcation software for ordinary differential equations (Concordia University, Montreal, 1997)Google Scholar
  15. 15.
    H.P. Fischer, P. Maass, W. Dieterich, Europhys. Lett., 42, 49 (1998)CrossRefADSGoogle Scholar
  16. 16.
    O.A. Frolovskaya, A.A. Nepomnyashchy, A. Oron, A.A. Golovin, Phys. Fluids 20, 112105 (2008)CrossRefADSGoogle Scholar
  17. 17.
    L. Frastia, U. Thiele, L.M. Pismen, Mathematical Modelling of Natural Phenomena (2010) (in press)Google Scholar

Copyright information

© EDP Sciences and Springer 2011

Authors and Affiliations

  1. 1.Universidad Politécnica de Madrid, ETSI AeronáuticosMadridSpain
  2. 2.Instituto Pluridisciplinar, Universidad ComplutenseMadridSpain
  3. 3.Department of Mathematical SciencesLoughborough UniversityLoughborough, LeicestershireUK

Personalised recommendations