SLIP OVER ROUGH AND COATED SURFACES

We study the effect of surface roughness and coatings on fluid flow ov er a solid surface. In the limit of small-amplitude roughness and thin lubricating films we are able to derive asymptotically an effective s lip boundary condition to replace the no-slip condition over the surfa ce. When the film is absent, the result is a Navier slip condition in which the slip coefficient equals the average amplitude of the roughne ss. When a layer of a second fluid covers the surface and acts as a lu bricating film, the slip coefficient contains a term which is proporti onal to the viscosity ratio of the two fluids and which depends on the dynamic interaction between the film and the fluid. Limiting cases ar e identified in which the film dynamics can be decoupled from the oute r flow.