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Slip-enhanced Rayleigh–Plateau instability of a liquid film on a fibre

Published online by Cambridge University Press:  09 January 2023

Chengxi Zhao Open the ORCID record for Chengxi Zhao [Opens in a new window] ,
Yixin Zhang Open the ORCID record for Yixin Zhang [Opens in a new window]  and
Ting Si Open the ORCID record for Ting Si [Opens in a new window]
Chengxi Zhao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Yixin Zhang
Affiliation:
Physics of Fluids Group and Max Planck Center Twente for Complex Fluid Dynamics, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Ting Si*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: tsi@ustc.edu.cn
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Abstract

Boundary conditions at a liquid–solid interface are crucial to dynamics of a liquid film coated on a fibre. Here, a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid–solid slip on the Rayleigh–Plateau instability of a cylindrical film on a fibre. The new model not only shows that the slip-enhanced growth rate of perturbations is overestimated by the classical lubrication model, but also indicates a slip-dependent dominant wavelength, instead of a constant value obtained by the lubrication method, which leads to larger drops formed on a more slippery fibre. The theoretical findings are validated by direct numerical simulations of Navier–Stokes equations via a volume-of-fluid method. Additionally, the slip-dependent dominant wavelengths predicted by our model agree with the experimental results provided by Haefner et al. (Nat. Commun., vol. 6, issue 1, 2015, 7409).

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A46
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© The Author(s), 2023. Published by Cambridge University Press

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