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Nonlinear evolution of viscoplastic film flows down an inclined plane

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Abstract

In this article, we experimentally investigate the nonlinear behaviour of a viscoplastic film flow down an inclined plane. We focus on the nonlinear instabilities that appear as roll waves. Roll waves are generated by perturbing a permanent flow of Herschel–Bulkley fluid (Carbopol 980) at low frequencies. To determine the local thickness of the film, we used a laser sensor and a camera to globally capture the transverse shape of the waves. For a regular forcing, the results show the existence of different regimes. First, we observe primary instabilities below the cut-off frequency at the entrance of the channel. After the exponential growth of the wave in the linear regime, we recognise the nonlinear dynamics with the existence of finite amplitude waves. This finite amplitude depends on the frequency, the Reynolds number and the inclination angle. The results show that this instability is supercritical. At moderate Reynolds numbers, the finite 2-D waves become sensitive to transverse perturbations, due to a secondary instability, and become 3-D waves. The experimental results illustrate a phenomenology of viscoplastic film flows similar to Newtonian fluids, except for the capillary waves.

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Data availability statement

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We thank S. Martinez and G. Geniquet for their assistance building the experimental set-up.

Funding

No funding was received for conducting this study.

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Authors and Affiliations

  1. LMFA, UMR 5509, Univ Lyon, CNRS, Université Claude Bernard Lyon 1, École Centrale Lyon, INSA Lyon, 69134, Ecully, France

    Djibrilla Mounkaila Noma, Simon Dagois-Bohy, Séverine Millet, Hamda Ben Hadid, Valéry Botton & Daniel Henry

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  1. Djibrilla Mounkaila Noma
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  2. Simon Dagois-Bohy
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  3. Séverine Millet
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Contributions

The authors confirm contribution to the paper as follows: conceptualisation, methodology and data collection: DMN and SDB; analysis, interpretation of results and writing: DMN, SDB and SM; and supervision, discussion and critical review: HBH, DH and VB.

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Correspondence to Djibrilla Mounkaila Noma or Simon Dagois-Bohy.

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Mounkaila Noma, D., Dagois-Bohy, S., Millet, S. et al. Nonlinear evolution of viscoplastic film flows down an inclined plane. Eur. Phys. J. E 46, 68 (2023). https://doi.org/10.1140/epje/s10189-023-00316-4

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