Flow rate-pressure drop relations for shear-thinning fluids in deformable configurations: theory and experiments
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| Format: | Preprint |
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2024
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| _version_ | 1866911853594017792 |
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| author | Chun, SungGyu Boyko, Evgeniy Christov, Ivan C. Feng, Jie |
| author_facet | Chun, SungGyu Boyko, Evgeniy Christov, Ivan C. Feng, Jie |
| contents | 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, $α$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flow rate-pressure drop relations for shear-thinning fluids in deformable configurations: theory and experiments Chun, SungGyu Boyko, Evgeniy Christov, Ivan C. Feng, Jie Fluid Dynamics Soft Condensed Matter 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, $α$, 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. |
| title | Flow rate-pressure drop relations for shear-thinning fluids in deformable configurations: theory and experiments |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2401.05513 |