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

Abstract

We provide an experimental framework to measure the flow rate--pressure drop relation for Newtonian and shear-thinning fluids in two common deformable configurations: (\textit{i}) a rectangular channel and (\textit{ii}) an axisymmetric tube. Using the Carreau model to describe the shear-dependent viscosity, we identify the key dimensionless rheological number, $Cu$, 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 taking into account the two-way-coupled fluid-structure interaction between the flow and its compliant confining boundaries. We thus identify the second key dimensionless number, $\alpha$, 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 $Cu$ on the flow rate-pressure drop relation. Finally, we delineate four distinct physical regimes of flow and deformation by mapping our experimental flow rate-pressure drop data for Newtonian and shear-thinning fluids into a $Cu-\alpha$ plane.

10 pages, 4 figures; v2 accepted for publication in Physical Review Fluids

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Cited by in corpus (3)

• Experimental investigation of the flow rate--pressure drop relation of a viscoelastic Boger fluid in a deformable channel
• Oscillatory flows in three-dimensional deformable microchannels
• Pressure drop reduction due to coupling between shear-thinning fluid flow and a weakly deformable channel wall: A reciprocal theorem approach