Predicting the apparent wall slip when using roughened geometries: A porous medium approach

A common approach to prevent or alleviate wall slip in rotational rheometry is to utilize roughened geometries. While this is a helpful strategy, the presence of the surface roughness introduces a fundamentally different boundary condition, as the flow trough the porous structure needs to be accounted for. In the present work we investigate the use of rough surfaces in rheometry, starting with simple Newtonian fluids. Both structured and randomly structured surfaces are used, i.e. a cross-hatched plate and a sandpaper disc, respectively. We show that the fluid flows within the roughened layer and that the flow in the gap of the rheometer can be modelled as a flow over and through a porous medium. Stokes’ equation and Brinkman’s equation can be coupled at the interface through a suitable stress boundary condition recently developed in the literature that takes the momentum transfer to both the fluid and the solid substrate properly into account [Minale M., Phys Fluids 26, 123102 (2014)]. The predictions of this new model are compared with the experimental results on Newtonian reference fluids and show excellent agreement for the case of the cross-hatched geometry, and satisfactory agreement for the geometry with sandpaper. The analysis provides a way to correct the apparent viscosity by dealing with the extra dissipation in the rough layer using an extrapolation length.