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Modelling falling film flow: an adjustable formulation

Published online by Cambridge University Press:  29 November 2022

Sanghasri Mukhopadhyay Open the ORCID record for Sanghasri Mukhopadhyay [Opens in a new window] ,
Christian Ruyer-Quil Open the ORCID record for Christian Ruyer-Quil [Opens in a new window]  and
R. Usha Open the ORCID record for R. Usha [Opens in a new window]
Sanghasri Mukhopadhyay
Affiliation:
Department of Mathematics, School of Advanced Science, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
Christian Ruyer-Quil*
Affiliation:
Université Savoie Mont Blanc, CNRS, LOCIE, 73000 Chambéry, France
R. Usha
Affiliation:
Department of Mathematics, IIT Madras, Chennai 600036, Tamil Nadu, India
*
†Email address for correspondence: Christian.Ruyer-Quil@univ-smb.fr
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Abstract

A new two-equation model for gravity-driven liquid film flow based on the long-wave expansion has been derived. The novelty of the model consists in using a base velocity profile combining parabolic (Ruyer-Quil & Manneville, Eur. Phys. J. B, vol. 15, issue 2, 2000, pp. 357–369) and ellipse (Usha et al., Phys. Fluids, vol. 32, issue 1, 2020, 013603) profile functions in the wall-normal coordinate. The dependence on a free parameter $A$ related to the eccentricity of an ellipse serves as an adjustable parameter. The resulting models are consistent at $O(\varepsilon )$ for inertia terms and at $O(\varepsilon ^2)$ for viscous diffusion effects, and predict accurately the primary instability. Appropriate tuning of the adjustable parameter helps to recover accurate predictions for the asymptotic wave celerity of nonlinear solitary waves. Further, the model is shown to capture the closed separation vortices that can form underneath the troughs of precursory capillary ripples.

JFM classification

Interfacial Flows (free surface): Thin films Nonlinear Dynamical Systems: Low-dimensional models Waves/Free-surface Flows: Solitary waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , R3
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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