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Primary instability of a visco-plastic film down an inclined plane: experimental study

Published online by Cambridge University Press:  07 July 2021

D. Mounkaila Noma ,
S. Dagois-Bohy Open the ORCID record for S. Dagois-Bohy [Opens in a new window] ,
S. Millet Open the ORCID record for S. Millet [Opens in a new window] ,
V. Botton ,
D. Henry  and
H. Ben Hadid
D. Mounkaila Noma*
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon/CNRS, École Centrale de Lyon/Université Claude Bernard Lyon 1/INSA Lyon, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
S. Dagois-Bohy
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon/CNRS, École Centrale de Lyon/Université Claude Bernard Lyon 1/INSA Lyon, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
S. Millet
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon/CNRS, École Centrale de Lyon/Université Claude Bernard Lyon 1/INSA Lyon, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
V. Botton
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon/CNRS, École Centrale de Lyon/Université Claude Bernard Lyon 1/INSA Lyon, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
D. Henry
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon/CNRS, École Centrale de Lyon/Université Claude Bernard Lyon 1/INSA Lyon, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
H. Ben Hadid
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon/CNRS, École Centrale de Lyon/Université Claude Bernard Lyon 1/INSA Lyon, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

We study experimentally the primary instability of a visco-plastic film flow down an inclined plane. The experimental set-up is a channel with a varying slope angle, in which a permanent flow of a Herschel–Bulkley fluid (carbopol or kaolin) is established. Controlled perturbations are imposed at the entrance of the channel to generate surface waves, and their downstream evolution is observed with a laser sensor system measuring the local fluid thickness. Growth rates and cutoff frequencies are obtained after processing the thickness signal, and experimental critical Reynolds and Bingham numbers are deduced. We find that the experimental stability map obtained is well described by the pseudo-plug model of Balmforth & Liu (J. Fluid Mech., vol, 519, 2004, pp. 33–54), a model obtained after neglecting the film thickness compared with its length. This is not the case for dispersion effects (growth rates, cutoff frequencies, phase speeds), for which a more accurate model is needed.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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