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Primary instability of a shear-thinning film flow down an incline: experimental study

Published online by Cambridge University Press:  24 May 2017

M. H. Allouche ,
V. Botton ,
S. Millet ,
D. Henry ,
S. Dagois-Bohy Open the ORCID record for S. Dagois-Bohy [Opens in a new window] ,
B. Güzel  and
H. Ben Hadid
M. H. Allouche
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France INSA Euro-Méditerranée, Université Euro-Méditerranéenne de Fès, Route de Meknès, BP51, Fez, Morocco
V. Botton
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France INSA Euro-Méditerranée, Université Euro-Méditerranéenne de Fès, Route de Meknès, BP51, Fez, Morocco
S. Millet
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
D. Henry
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
S. Dagois-Bohy*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
B. Güzel
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France Yildiz Technical University, Department of Naval Architecture and Marine Engineering, Marine Machinery, 34349 Yildiz, Istanbul, Turkey
H. Ben Hadid
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
*
†Email address for correspondence: simon.dagois-bohy@univ-lyon1.fr
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Abstract

The main objective of this work is to study experimentally the primary instability of non-Newtonian film flows down an inclined plane. We focus on low-concentration shear-thinning aqueous solutions obeying the Carreau law. The experimental study essentially consists of measuring wavelengths in marginal conditions, which yields the primary stability threshold for a given slope. The experimental results for neutral curves presented in the $(Re,f_{c})$ and $(Re,k)$ planes (where $f_{c}$ is the driving frequency, $k$ is the wavenumber and $Re$ is the Reynolds number) are in good agreement with the numerical results obtained by a resolution of the generalized Orr–Sommerfeld equation. The long-wave asymptotic extension of our results is consistent with former theoretical predictions of the critical Reynolds number. This is the first experimental evidence of the destabilizing effect of the shear-thinning behaviour in comparison with the Newtonian case: the critical Reynolds number is smaller, and the ratio between the critical wave celerity and the flow velocity at the free surface is larger.

JFM classification

Instability: Instability Non-Newtonian Flows: Non-Newtonian Flows Interfacial Flows (free surface): Thin films
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , R1
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Copyright
© 2017 Cambridge University Press 

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