The Stokes equations with Fourier boundary conditions on a wall with asperities (Q2725350)

The authors study the effect of wall rugosity on the solution of the Stokes system with Fourier boundary conditions, which include the stress tensor and a friction coefficient. For small periodic asperities, the authors prove that the velocity field, pressure and drag, respectively, converge to the velocity field, pressure and drag of a homogenized Stokes problem with smooth walls, where a homogenized friction coefficient appears. This shows that, contrary to Dirichlet boundary conditions, rugosity is dominant for Fourier boundary conditions. In the particular case of a plate, the limit drag is larger than the drag of smooth wall.