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Axisymmetric instability of elastic tubes conveying power-law fluids

Published online by Cambridge University Press:  10 May 2022

Anastasia Podoprosvetova Open the ORCID record for Anastasia Podoprosvetova [Opens in a new window]  and
Vasily Vedeneev Open the ORCID record for Vasily Vedeneev [Opens in a new window]
Anastasia Podoprosvetova
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
Vasily Vedeneev*
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
*
†Email address for correspondence: [email protected]
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Abstract

Instability of collapsible tubes is studied theoretically and experimentally in many papers in the context of biological applications. Up to the present day, only Newtonian fluid flows in elastic tubes have been studied. However, there are circumstances when blood, bile and other biological fluids show essentially non-Newtonian behaviour. In this paper, we re-investigate theoretically axisymmetric stability of elastic tubes conveying power-law fluids. It is shown that for the power-law index $n=1$, i.e. for the Newtonian case, axisymmetric disturbances in infinite-length tubes are damped, which is in accordance with experimental and theoretical observations, where the oscillations always involve non-axisymmetric motion of the tube walls. However, for $n<0.611$, the axisymmetric disturbances can be growing, which predicts a new type of instability of elastic tubes conveying pseudoplastic (shear-thinning) fluids. For $n<1/3$, local instability of axisymmetric perturbations becomes absolute in infinite tubes, while finite-length tubes become globally unstable. The effects of the axial tension, elastic tube length and, if present, lengths of inlet and outlet rigid tubes on the stability of finite-length tubes are analysed.

JFM classification

Biological Fluid Dynamics: Flow-vessel interactions Non-Newtonian Flows: Rheology Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A61
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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