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Axisymmetric evolution of gravity-driven thin films on a small sphere

Published online by Cambridge University Press:  17 November 2020

Jian Qin ,
Yu-Ting Xia  and
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]
Jian Qin
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China
Yu-Ting Xia
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China
Peng Gao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui230026, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We study the axisymmetric evolution of a liquid film on a solid sphere governed by gravity, capillarity and viscous forces. The lubrication equations established in spherical coordinates are numerically solved using finite elements and local similarity solutions are obtained. Results show that the evolution behaves differently at early and late stages. At the early stage, the interface evolves in such a way that the capillary effect can be ignored. At the late stage, there emerge four zones from top to bottom: a thin film, a ridge ring, a dimple ring and a pendant drop. Each zone is governed by the balance of different forces, and hence is characterized by an individual physical mechanism. Consequently, the pendant drop is quasi-static, and the film thicknesses of other regions follow different scaling laws. The position of the dimple remains unchanged at the late stage.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A4
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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