Influence of Wall Deformation on a Slip Length

Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 37)


This paper presents the effect of a wall deformation on the boundaries conditions of a shear flow of the viscous fluid over a deformable wall which has a periodic deformation and small amplitude. The Reynolds number for the flow over a wall is low and the creeping flow equations apply. The no-slip boundary condition on the deformable wall applies. By using an asymptotic expansion, the analytic expression is obtained for the slip length.


Creeping flow Shear flow Deformable wall Slip length Amplitude 


  1. 1.
    Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  2. 2.
    Beebe, D.J., Mensing, G.A., Walker, G.M.: Physics and applications of microfluidics in biology. Ann. Rev. Biomed. Eng. 4(1), 261–286 (2002)CrossRefGoogle Scholar
  3. 3.
    Hocking, L.: A moving fluid interface on a rough surface. J. Fluid Mech. 76(4), 801–817 (1976)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Jansons, K.M.: Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough surface with a perfect slip microscopic boundary condition. Phys. Fluids 31(1), 15–17 (1988)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lamb, H.: Hydro Dynamics. 6th ed. 738. Dover, New York (1932)Google Scholar
  6. 6.
    Priezjev, N.V.: Effect of surface roughness on rate-dependent slip in simple fluids. J. Chem. Phys. 127(14), 144708 (2007)CrossRefGoogle Scholar
  7. 7.
    Priezjev, N.V., Darhuber, A.A., Troian, S.M.: Slip behavior in liquid films on surfaces of patterned wettability: comparison between continuum and molecular dynamics simulations. Phys. Rev. E 71(4), 041608 (2005)CrossRefGoogle Scholar
  8. 8.
    Squires, T.M., Quake, S.R.: Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77(3), 977 (2005)CrossRefGoogle Scholar
  9. 9.
    Tuck, E., Kouzoubov, A.: A laminar roughness boundary condition. J. Fluid Mech. 300, 59–70 (1995)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Vinogradova, O.I., Yakubov, G.E.: Surface roughness and hydrodynamic boundary conditions. Phys. Rev. E 73(4), 045302 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Faculty of ScienceMoulay Ismail UniversityMeknesMorocco

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