Derivation of the Navier slip and slip length for viscous flows over a rough boundary

In this paper, we derive the Navier slip boundary condition for flows over a rough surface, by combining homogenization methods and boundary layer techniques. The Navier slip condition is derived as the effective boundary condition, in the limit as the roughness becomes small; it is the first order...

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Bibliographic Details
Published in:Physics of fluids (1994) 2017-05, Vol.29 (5)
Main Authors: Jiménez Bolaños, Silvia, Vernescu, Bogdan
Format: Article
Language:English
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Summary:In this paper, we derive the Navier slip boundary condition for flows over a rough surface, by combining homogenization methods and boundary layer techniques. The Navier slip condition is derived as the effective boundary condition, in the limit as the roughness becomes small; it is the first order corrector to the no-slip condition on the limiting smooth surface. Using this method, we are simultaneously able to provide a formula for computing the slip length for various geometries. The paper provides a theoretical justification for the observed slip in micro- or nanofluidics, as well as a computational tool. Computations done using FreeFem++ agree with experimental data.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4982899