Limits of the Hydrodynamic No-Slip Boundary Condition

A controversial point in fluid dynamics is to distinguish the relative importance of surface roughness and fluid-surface intermolecular interactions in determining the boundary condition. Here hydrodynamic forces were compared for flow of Newtonian fluids past surfaces of variable roughness but similar, poorly wetted, surface chemistry. The critical shear stress and shear rate to observe deviations from predictions using the no-slip boundary condition increased nearly exponentially with increasing roughness and diverged at $\approx 6$ nm rms roughness. We conclude that local intermolecular interactions dominated when the surface was very smooth, but roughness dominated otherwise. This quantifies the limits of both ideas.