Flow rate–pressure drop relations for shear-thinning fluids in deformable configurations: Theory and experiments

The flow rate--pressure drop relations for laminar flow of Newtonian fluids in common geometries are well understood. However, a complete understanding of how the interplay between shear-thinning rheology and wall compliance sets the flow rate--pressure drop relation for a deformable configuration is still lacking. Here, we provide detailed quantitative comparisons between theory and experiments for the flow rate--pressure drop relation for Newtonian and shear-thinning fluids in two common deformable configurations: a rectangular channel and an axisymmetric tube. Such a comparison is of fundamental importance since it provides insight into the adequacy of the constitutive model used.