Comparison between theory and experiments for the flow rate-pressure drop relation for shear-thinning fluids in deformable configuration

We provide an experimental framework to measure the flow rate-pressure drop relation for Newtonian and shear-thinning fluids in two common deformable configurations: (i) a rectangular channel and (ii) an axisymmetric tube. Using the Carreau model to describe the shear-dependent viscosity, we identify the key dimensionless rheological number, which characterizes shear thinning, and we show that our experiments lie within the power-law regime of shear rates. To rationalize the experimental data, we derive the flow rate-pressure drop relation accounting for the two-way-coupled fluid-structure interaction between the flow and its compliant confining boundaries. We thus identify the second key dimensionless number, which characterizes the compliance of the conduit. We then compare the theoretical flow rate-pressure drop relation to our experimental measurements, finding excellent agreement between the two. We further contrast our results for shear-thinning and Newtonian fluids to highlight the influence of rheology on the flow rate-pressure drop relation.