Hydrodynamics of Thin Viscous Films

  • Ralf BlosseyEmail author
Part of the Theoretical and Mathematical Physics book series (TMP)


Chapter 4 mirrors Chap.  2 of Part I: while the latter developed the concepts from statistical mechanics, the present chapter introduces the concepts from hydrodynamics of thin films. While the key theoretical tool for the statistical mechanics aspects is the effective interface potential, a similar key rôle in the hydrodynamics of thin films is played by the lubrication approximation. Chapter 4 explains how thin film equations can be derived for different regimes of surface slip. Mathematical properties of the thin film equation and its numerics are discussed, as well as their application to experiments of dewetting polymer films.


Contact Line Capillary Number Slip Length Disjoin Pressure Lubrication Approximation 
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.


  1. Bäumchen, O., Fetzer, R., Jacobs, K.: Reduced interfacial entanglement density affects the boundary conditions of polymer flow. Phys. Rev. Lett. 103, 247801 (2009) ADSCrossRefGoogle Scholar
  2. Bäumchen, O., Jacobs, K.: Slip effects in polymer thin films. J. Phys., Condens. Matter 22, 033102 (2010) ADSCrossRefGoogle Scholar
  3. Becker, J., Grün, G., Seemann, R., Mantz, H., Jacobs, K., Mecke, K.R., Blossey, R.: Complex dewetting scenarios captured by thin-film models. Nat. Mater. 2, 59–63 (2003) ADSCrossRefGoogle Scholar
  4. Becker, J., Grün, G.: The thin-film equation: recent advances and some new perspectives. J. Phys., Condens. Matter 17, S291–S307 (2005) ADSCrossRefGoogle Scholar
  5. Brochard-Wyart, F., Redon, C.: Dynamics of liquid rim instabilities. Langmuir 8, 2324–2329 (1992) CrossRefGoogle Scholar
  6. Brochard-Wyart, F., de Gennes, P.G., Hervert, H., Redon, C.: Wetting and slippage of polymer melts on semi-ideal surfaces. Langmuir 10, 1566–1572 (1994a) CrossRefGoogle Scholar
  7. Dal Passo, R., Garcke, H., Grün, G.: On a fourth-order degenerate parabolic equation: global entropy estimates and qualitative behaviour of solutions. SIAM J. Math. Anal. 29, 321–342 (1998) MathSciNetzbMATHCrossRefGoogle Scholar
  8. Eggers, J.: Dynamics of liquid nanojets. Phys. Rev. Lett. 89, 084502 (2002) ADSCrossRefGoogle Scholar
  9. Fetzer, R., Jacobs, K., Münch, A., Wagner, B., Witelski, T.P.: New slip regimes and the shape of dewetting thin liquid films. Phys. Rev. Lett. 95, 127801 (2005) ADSCrossRefGoogle Scholar
  10. Fetzer, R., Rauscher, M., Münch, A., Wagner, B.A., Jacobs, K.: Slip-controlled thin-film dynamics. Europhys. Lett. 75, 638–644 (2006) ADSCrossRefGoogle Scholar
  11. Fetzer, R., Rauscher, M., Seemann, R., Jacobs, K., Mecke, K.: Thermal noise influences fluid flow in thin films during spinodal dewetting. Phys. Rev. Lett. 99, 114503 (2007a) ADSCrossRefGoogle Scholar
  12. Fetzer, R., Münch, A., Wagner, B., Rauscher, M., Jacobs, K.: Quantifying hydrodynamic slip: a comprehensive analysis of dewetting profiles. Langmuir 23, 10559–10566 (2007b) CrossRefGoogle Scholar
  13. Flitton, J., King, J.R.: Surface-tension driven dewetting of Newtonian and power-law fluids. J. Eng. Math. 50, 241–266 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  14. Grün, G., Rumpf, M.: Nonnegativity-preserving convergent schemes for the thin-film equation. Numer. Math. 87, 113–152 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  15. Grün, G., Mecke, K., Rauscher, M.: Thin-film flow influenced by thermal noise. J. Stat. Phys. 122, 1261–1291 (2006) MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. Jacobs, K., Seemann, R., Schatz, G., Herminghaus, S.: Growth of holes in liquid films with partial slippage. Langmuir 14, 4961–4963 (1998b) CrossRefGoogle Scholar
  17. Kargupta, K., Sharma, A., Khanna, R.: Instability, dynamics and morphology of slipping thin films. Langmuir 20, 244–253 (2004) CrossRefGoogle Scholar
  18. King, J.R., Münch, A., Wagner, B.: Linear stability of a ridge. Nonlinearity 19, 2813–2831 (2006) MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. Landau, L.D., Lifshitz, E.M.: Fluid Dynamics. Butterworth/Heinemann, Stoneham/London (1987) Google Scholar
  20. Mecke, K.R., Stoyan, D. (eds.): Statistical Physics and Spatial Statistics—The Art of Analysing and Modelling Spatial Structures and Pattern Formation. Lecture Notes in Physics, vol. 554. Springer, Berlin (2000) Google Scholar
  21. Mecke, K., Rauscher, M.: On thermal fluctuations in thin film flow. J. Phys., Condens. Matter 17, S3515–S3522 (2005) ADSCrossRefGoogle Scholar
  22. Moseler, M., Landmann, U.: Formation, stability, and breakup of nanojets. Science 289, 1165–1169 (2000) ADSCrossRefGoogle Scholar
  23. Münch, A., Wagner, B., Witelski, T.P.: Lubrication models with small to large slip lengths. J. Eng. Math. 53, 359–383 (2005) zbMATHCrossRefGoogle Scholar
  24. Münch, A., Wagner, B.: Contact-line instability of dewetting thin films. Physica D 209, 178–190 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  25. Münch, A., Wagner, B.: Impact of slippage on the morphology and stability of a dewetting rim. J. Phys., Condens. Matter 23, 184101 (2011) ADSCrossRefGoogle Scholar
  26. Neto, C., Jacobs, K., Seemann, R., Blossey, R., Becker, J., Grün, G.: Satellite hole formation during dewetting: experiment and simulation. J. Phys., Condens. Matter 15, 3355–3366 (2003) ADSCrossRefGoogle Scholar
  27. Rauscher, M., Blossey, R., Münch, A., Wagner, B.: Spinodal dewetting of thin films with large interfacial slip: implications from the dispersion relation. Langmuir 24, 12290–12294 (2008) CrossRefGoogle Scholar
  28. Redon, C., Brochard-Wyart, F., Rondelez, F.: Dynamics of dewetting. Phys. Rev. Lett. 66, 715–718 (1991) ADSCrossRefGoogle Scholar
  29. Seemann, R., Herminghaus, S., Jacobs, K.: Shape of a liquid front upon dewetting. Phys. Rev. Lett. 87, 196101 (2001d). Erratum PRL 87, 249902 ADSCrossRefGoogle Scholar
  30. Seemann, R., Herminghaus, S., Neto, C., Schlagowski, S., Podzimek, D., Konrad, R., Mantz, H., Jacobs, K.: Dynamics and structure formation in thin polymer melt films. J. Phys., Condens. Matter 17, S267–S290 (2005) ADSCrossRefGoogle Scholar
  31. Sekimoto, K., Oguma, R., Kawasaki, K.: Morphological stability analysis of partial wetting. Ann. Phys. 176, 359–392 (1987) ADSCrossRefGoogle Scholar
  32. Snoeijer, J.H., Eggers, J.: Asymptotics of the dewetting rim. Phys. Rev. E 82, 056314 (2010) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.CNRS USR 3078Institut de Recherche InterdisciplinaireVilleneuve d’Ascq CedexFrance

Personalised recommendations