Abstract
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.
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