Boundary Layer for a Non-Newtonian Flow Over a Rough Surface

Abstract

We analyze how small irregularities of a solid wall affect the steady flow of a non-Newtonian fluid. We consider the generalized Stokes system for power-law type fluids, with no-slip boundary conditions. Irregularities are modeled by small periodic variations of the boundary surface, described by a small parameter. We derive an effective boundary condition---a wall law---on a smoothed boundary, with the smallest possible approximation error (in terms of the parameter). The keypoint of the mathematical analysis is the study of the boundary layer generated by the irregularities. We stress that our results apply both to shear thickening and shear thinning fluids.