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Explicit theory of moving contact lines

Part of: JFM Notebooks

Published online by Cambridge University Press:  23 September 2025

Jun Luo  and
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]
Jun Luo
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Peng Gao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
Corresponding author: Peng Gao, gaopeng@ustc.edu.cn
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Abstract

The interface shape near a moving contact line is described by the Cox–Voinov theory, which contains a constant term that is not trivially obtained. In this work, an approximate expression of this term in explicit form is derived under the condition of a Navier slip. Introducing the approximation of a local slippery wedge flow, we first propose a novel form of the generalised lubrication equation. A matched asymptotic analysis of this equation yields the Cox–Voinov relation with the constant term expressed in elementary functions. For various viscosity ratios and contact angles, the theoretical predictions are rigorously validated against full numerical solutions of the Stokes equations and available asymptotic results.

JFM classification

Interfacial Flows (free surface): Contact lines Low-Reynolds-number flows: Lubrication theory

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1019 , 25 September 2025 , A52
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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