Influence of wall roughness on the slip behavior of viscous fluids

Recent developments in microfluidic and nanofluidic technologies have renewed interest in the influence of surface roughness on the slip behavior of viscous fluids (see the survey by PRIEZJEV and TROIAN [20] and the references cited therein). As a matter of fact, this issue have been subjected to discussion for over two centuries by many distinguished scientists who developed the foundations of fluid mechanics, including Bernoulli, Coulomb, Navier, Couette, Poisson, Stokes, to name only a few. Consider a viscous fluid confined to a domain Ω in the Euclidean physical space R, the boundary of which represents a solid wall. Assuming impermeability of the wall we have u · n = 0 on ∂Ω, (1.1)