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

SungGyu Chun1,*, Evgeniy Boyko2,*, Ivan C. Christov3,†, and Jie Feng1,4,‡

  • 1Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 2Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
  • 3School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
  • 4Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *These authors contributed equally.
  • †christov@purdue.edu
  • ‡jiefeng@illinois.edu
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Phys. Rev. Fluids 9, 043302 – Published 25 April, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.043302

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: (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 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 α, 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−α plane.

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Phys. Rev. Fluids 9, 043302– Published 25 April, 2024
  • Received 25 October 2023
  • Accepted 29 March 2024
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