Modelling fluid flow over solid surfaces

Models of fluid flow over solid surfaces are proposed. The models utilise a varying viscosity that is constant away from a solid surface and that becomes infinite as the solid surface is approached. The varying viscosity introduces an inner boundary layer. Consequently, we are able to explain, qualitatively, the discrepancy between theoretical predictions of the conventional theory of fluid flow with experimental data of flow over a flat plate with distributed roughness. Our model also explains the discrepancy between an increased amount of drag observed in some experiments and a theoretical predicted drag from Newtonian fluids with a constant viscosity. Couette flow over a rough surface is utilised to demonstrate the underlining nature of the modelling. Arguments for the consistency of our models are provided.