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Influence of Wall Deformation on a Slip Length

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Innovations in Smart Cities and Applications (SCAMS 2017)

Abstract

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.

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References

  1. Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  3. Hocking, L.: A moving fluid interface on a rough surface. J. Fluid Mech. 76(4), 801–817 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  5. Lamb, H.: Hydro Dynamics. 6th ed. 738. Dover, New York (1932)

    Google Scholar 

  6. Priezjev, N.V.: Effect of surface roughness on rate-dependent slip in simple fluids. J. Chem. Phys. 127(14), 144708 (2007)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. Squires, T.M., Quake, S.R.: Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77(3), 977 (2005)

    Article  Google Scholar 

  9. Tuck, E., Kouzoubov, A.: A laminar roughness boundary condition. J. Fluid Mech. 300, 59–70 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Vinogradova, O.I., Yakubov, G.E.: Surface roughness and hydrodynamic boundary conditions. Phys. Rev. E 73(4), 045302 (2006)

    Article  Google Scholar 

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Correspondence to Redouane Assoudi .

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Assoudi, R., Lamzoud, K., Chaoui, M. (2018). Influence of Wall Deformation on a Slip Length. In: Ben Ahmed, M., Boudhir, A. (eds) Innovations in Smart Cities and Applications. SCAMS 2017. Lecture Notes in Networks and Systems, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-74500-8_83

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  • DOI: https://doi.org/10.1007/978-3-319-74500-8_83

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74499-5

  • Online ISBN: 978-3-319-74500-8

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