Rough geometries with viscoelastic Boger fluids: Predicting the apparent wall slip with a porous medium approach

Multiphase fluids and highly non-Newtonian fluids often show wall slip. The typical approach to reduce wall slip in experiments is to use roughened geometries, which are thin porous layers. However, the presence of the roughness introduces in itself an apparent wall slip due to the flow within the porous layer. To account for wall slip typically, measurements must be run at several gaps in a plate-plate device. With Newtonian fluids, the apparent wall slip can be conveniently accounted for in the measurements at a single gap since it can be accurately predicted using models describing the flow of Newtonian fluids through and over porous media. Here, we extend this approach to viscoelastic fluids by using Minale's model [Phys. Fluids 28, 023102 and 023103 (2016)] for the flow of second order fluids (SOFs) through and over a porous medium. In this work, we first validate the theoretical predictions and then propose an experimental protocol to measure a SOF with rough geometries by executing the experiments at a single chosen gap. Two Boger fluids are used as model SOFs, and three different rough geometries are considered: Two commercial crosshatched plates and a homemade pillared one. The apparent wall slip is shown to be reduced for the viscoelastic fluids, with respect to the Newtonian case, and agreement with the theoretical predictions is excellent.