The European Physical Journal Special Topics

, Volume 226, Issue 6, pp 1219–1228

Numerical simulation and stability analysis of solutocapillary effect in ultrathin films

Regular Article
Part of the following topical collections:
  1. IMA8 - Interfacial Fluid Dynamics and Processes

Abstract

Polar fluids, like water or polydimethylsiloxane, are widely used in technical and medical applications. Capillary effects arising from surface tension gradients can be significant in thin liquid films. The present paper is dedicated to investigation of capillary flow due to a surfactant added to a polar liquid under conditions when intermolecular forces and disjoining pressure play an important role. Evolution equations are formulated for a film profile and the surfactant concentration. Stability analysis shows that the Marangoni effect destabilizes the film, and oscillatory modes appear at slow evaporation rates. We find that the film has four stability modes of at slow evaporation: monotonic stable, monotonic unstable, oscillatory stable, and oscillatory unstable, depending on the wave number of disturbances.

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References

  1. 1.
    O.V. Voinov, Fluid Dyn. 11, 714 (1976)ADSCrossRefGoogle Scholar
  2. 2.
    O.V. Voinov, J. Appl. Mech. Tech. Phys. 18, 216 (1977)ADSCrossRefGoogle Scholar
  3. 3.
    B.V. Derjagin, Colloid J USSR 17, 191 (1955)Google Scholar
  4. 4.
    G.F. Teletzke, H.T. Davis, L.E. Scriven, Revue. Phys. Appl. 23, 989 (1988)CrossRefGoogle Scholar
  5. 5.
    P.G. de Gennes, Rev. Mod. Phys. 57, 827 (1985)ADSCrossRefGoogle Scholar
  6. 6.
    W.B. Hardy, The London, Edinburgh, and Dublin Philos. Mag. J. Sci. 38, 49 (1919)CrossRefGoogle Scholar
  7. 7.
    D. Beaglehole, J. Phys. Chem. 93, 893 (1989)CrossRefGoogle Scholar
  8. 8.
    L. Leger, M. Erman, A.M. Guinet-Picard, D. Ausserre, C. Strazielle, Phys. Rev. Lett. 60, 2390 (1988)ADSCrossRefGoogle Scholar
  9. 9.
    L. Leger, M. Erman, A.M. Guinet-Picard, D. Ausserre, C. Strazielle, J.J. Benattar, F. Rieutord, J. Daillant, L. Bosio, Rev. Phys. Appl. 23, 1047 (1988)CrossRefGoogle Scholar
  10. 10.
    J. Daillant, J.J. Benattar, L. Bosio, L. Leger, Eurohys. Lett. 6, 431 (1988)ADSCrossRefGoogle Scholar
  11. 11.
    F. Heslot, N. Fraysse, A.M. Cazabat, Nature 338, 640 (1989)ADSCrossRefGoogle Scholar
  12. 12.
    M. Voue, M.P. Valignat, G. Oshanin, A.M. Cazabat, J. De Conick, Langmuir 14, 5951 (1998)CrossRefGoogle Scholar
  13. 13.
    B.V. Deryagin, N.V. Churaev, Langmuir 3.5, 607 (1987)CrossRefGoogle Scholar
  14. 14.
    A.V. Lyushnin, A.A. Golovin, L.M. Pismen, Phys. Rev. E 65, 021602 (2002)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    I. Leizerson, S.G. Lipson, A.V. Lyushnin, Phys. Rev. E 68, 051601 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    I. Leizerson, S.G. Lipson, A.V. Lyushnin, Nature 422, 395 (2003)ADSCrossRefGoogle Scholar
  17. 17.
    U. Thiele, M. Mertig, W. Pompe, Phys. Rev. Lett. 80, 2869 (1998)ADSCrossRefGoogle Scholar
  18. 18.
    I. Leizerson, S.G. Lipson, A.V. Lyushnin, Langmuir 20, 291 (2004)CrossRefGoogle Scholar
  19. 19.
    A. Sharma, Langmuir 9, 861 (1993)CrossRefGoogle Scholar
  20. 20.
    R.V. Craster, O.K. Matar, Rev. Mod. Phys. 81, 1131 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    E. Sultan, A. Boudaoud, M. Ben Amar, J. Fluid Mech. 543, 183 (2005)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    V.Yu. Gordeeva, A.V. Lyushnin, Eur. Phys. J. Special Topics 219, 45 (2013)ADSCrossRefGoogle Scholar
  23. 23.
    D.P. Gaver, J.B. Grotberg, J. Fluid Mech. 213, 127 (1990)ADSCrossRefGoogle Scholar
  24. 24.
    S. Rafai, D. Sarker, V. Bergeron, J. Meunier, D. Bonn, Langmuir 18, 10486 (2002)CrossRefGoogle Scholar
  25. 25.
    G. Karapetsas, R.V. Craster, O.K. Matar, J. Fluid. Mech. 670, 5 (2011)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    V.Yu. Gordeeva, A.V. Lyushnin, Tech. Phys. 59, 656 (2014)CrossRefGoogle Scholar
  27. 27.
    N. Kumar, A. Couzis, C. Maldarelli, J. Colloid Interface Sci. 267, 272 (2003)CrossRefGoogle Scholar
  28. 28.
    M.A. Clay, M.J. Miksis, Phys. Fluids 16, 3070 (2004)ADSCrossRefGoogle Scholar
  29. 29.
    L.V. Scriven, C.V. Sternling, Nature (London) 187, 186 (1960)ADSCrossRefGoogle Scholar
  30. 30.
    O.E. Jensen, J.B. Grotberg, Phys. Fluids A 5, 58 (1993)ADSCrossRefGoogle Scholar
  31. 31.
    S.G. Yiantsios, B.G. Higgins, Phys. Fluids 154, 022102 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    S.K. Serpetsi, S.G. Yiantsios, Phys. Fluids 24, 122104 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    T. Kollner, K. Schwarzenberger, K. Eckert, T. Boeck, Phys. Fluids 25, 092109 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    S.G. Yiantsios, S.K. Serpetsi, F. Doumenc, B. Guerrier, Int. J. Heat Mass Transfer 89, 1083 (2015)CrossRefGoogle Scholar
  35. 35.
    A.V. Lyushnin, L. Pismen, Tech. Phys. 60, 782 (2015)CrossRefGoogle Scholar
  36. 36.
    V.Yu. Gordeeva, A.V. Lyushnin, Adv. Mater. Res. 1105, 105 (2015)CrossRefGoogle Scholar
  37. 37.
    D.A. Edwards, H. Brenner, D.T. Wasan, Interfacial Transport Processes and Rheology (Butterworth-Heinemann, Boston, 1991)Google Scholar
  38. 38.
    N. Samid-Merzel, S.G. Lipson, D.S. Tannhauser, Phys. Rev. E 57, 2906 (1998)ADSCrossRefGoogle Scholar
  39. 39.
    A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys. 69, 931 (1997)ADSCrossRefGoogle Scholar
  40. 40.
    G.Z.E. Gershuni, E.M. Zhukhovitskii, Convective Stability of Incompressible Fluids (1976)Google Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Perm National Research Polytechnic University, Lysva branchPermskii kraiRussia
  2. 2.Perm State Pedagogical UniversityPermRussia

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