Slip over rough and coated surfaces

Abstract

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