The European Physical Journal E

, Volume 31, Issue 3, pp 253–262 | Cite as

Droplets sliding on fibres

Regular Article

Abstract

We present the results of a combined experimental and theoretical investigation of oil droplets sliding on fibres. First, both the axisymmetric shape and the motion of a droplet on a vertical fibre are described. The motion is shown to result from a balance between the droplet weight and the viscous stresses. On a long-term range, the droplet loses some mass through coating the fibre, which decreases its velocity. In a second time, we rationalize the behaviour of a droplet that encounters a junction between vertical and horizontal fibres. Depending on its size, the droplet may cross the junction or remain blocked. The transition is well described by an ordinary differential equation equivalent to a damped harmonic oscillator truncated to the neighbourhood of the horizontal fibre. This simple system is the basic element for more complex fiber networks that would be useful in microfluidic applications involving droplets.

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References

  1. 1.
    S.N. Reznik, W. Salalha, A.L. Yarin, E. Zussman, J. Fluid Mech. 574, 179 (2007)MATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    P. Contal, J. Simao, D. Thomas, T. Frising, S. Callé, J.C. Appert-Collin, D. Bémer, Aerosol Sci. 35, 263 (2004)CrossRefGoogle Scholar
  3. 3.
    A.L. Yarin, G.G. Chase, W. Liu, S.V.Doiphode, D.H. Reneker, AIChE J. 52, 217 (2006)CrossRefGoogle Scholar
  4. 4.
    J. Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires (Gauthier-Villars, Paris, 1873)Google Scholar
  5. 5.
    I.L. Kliakhandler, S.H. Davis, S.G. Bankoff, J. Fluid Mech. 429, 381 (2001)MATHCrossRefADSGoogle Scholar
  6. 6.
    R.V. Craster, O.K. Matar, J. Fluid Mech. 553, 85 (2006)MATHCrossRefMathSciNetADSGoogle Scholar
  7. 7.
    C. Duprat, C. Ruyer-Quil, S. Kalliadasis, F. Giorgiutti-Dauphiné, Phys. Rev. Lett. 98, 244502 (2007)CrossRefADSGoogle Scholar
  8. 8.
    Lord Rayleigh, Proc. R. Soc. London 29, 71 (1879)CrossRefGoogle Scholar
  9. 9.
    A.L. Yarin, A. Oron, Ph. Rosenau, Phys. Fluids A 5, 91 (1993)MATHCrossRefADSGoogle Scholar
  10. 10.
    B.J. Carroll, J. Colloid Interface Sci. 57, 488 (1976)CrossRefGoogle Scholar
  11. 11.
    G. McHale, M.I. Newton, Colloids Surf. A: Physicochem. Eng. Aspects 206, 79 (2002)CrossRefGoogle Scholar
  12. 12.
    A. Kumar, S. Hartland, J. Colloid Interface Sci. 124, 67 (1988)CrossRefGoogle Scholar
  13. 13.
    A.L. Yarin, W. Liu, D.H. Reneker, J. Appl. Phys. 91, 4751 (2002)CrossRefADSGoogle Scholar
  14. 14.
    S. Dawar, H. Li, J. Dobson, G.G. Chase, Drying Technol. 24, 1283 (2006)CrossRefGoogle Scholar
  15. 15.
    E. Lorenceau, D. Quéré, J. Fluid Mech. 510, 29 (2004)MATHCrossRefADSGoogle Scholar
  16. 16.
    N. LeGrand, A. Daerr, L. Limat, J. Fluid Mech. 541, 293 (2005)CrossRefADSGoogle Scholar
  17. 17.
    S.N. Reznik, A.L. Yarin, Phys. Fluids 14, 118 (2002)CrossRefMathSciNetADSGoogle Scholar
  18. 18.
    J. Bico, D. Quéré, J. Fluid Mech. 467, 101 (2002)MATHCrossRefADSGoogle Scholar
  19. 19.
    E. Lorenceau, C. Clanet, D. Quéré, J. Colloid Interface Sci. 279, 192 (2004)CrossRefGoogle Scholar
  20. 20.
    P.G. de Gennes, Rev. Mod. Phys. 57, 827 (1985)CrossRefADSGoogle Scholar
  21. 21.
    T. Gilet, D. Terwagne, N. Vandewalle, Appl. Phys. Lett. 95, 014106 (2009)CrossRefADSGoogle Scholar
  22. 22.
    L.D. Landau, B. Levich, Acta Physicochim. USSR 17, 42 (1942)Google Scholar
  23. 23.
    D. Quéré, Annu. Rev. Fluid Mech. 31, 347 (1999)CrossRefADSGoogle Scholar
  24. 24.
    P. Aussillous, D. Quéré, Phys. Fluids 12, 2367 (2000)CrossRefADSGoogle Scholar
  25. 25.
    D.R. Link, S.L. Anna, D.A. Weitz, H.A. Stone, Phys. Rev. Lett. 92, 054503 (2004)CrossRefADSGoogle Scholar
  26. 26.
    H.A. Stone, A.D. Stroock, A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004)CrossRefADSGoogle Scholar
  27. 27.
    T. Squires, S.R. Quake, Rev. Mod. Phys. 77, 977 (2005)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.GRASPUniversity of LiegeLiegeBelgium

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