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Onset of thin film meniscus along a fibre

Published online by Cambridge University Press:  22 February 2019

Shuo Guo ,
Xianmin Xu ,
Tiezheng Qian ,
Yana Di ,
Masao Doi  and
Penger Tong Open the ORCID record for Penger Tong [Opens in a new window]
Shuo Guo
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Xianmin Xu
Affiliation:
LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Tiezheng Qian
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Yana Di
Affiliation:
LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Masao Doi
Affiliation:
Interdisciplinary Research Center, Beihang University, Beijing 100191, China
Penger Tong*
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
*
†Email address for correspondence: penger@ust.hk
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Abstract

The dynamics of spreading of a macroscopic liquid droplet over a wetting surface is often described by a power-law relaxation, namely, the droplet radius increases as $t^{m}$ for time $t$, which is known as Tanner’s law. Here we show, by both experiments and theory, that when the liquid spreading takes place between a thin soap film and a glass fibre penetrating the film, the spreading is significantly slowed down. When the film thickness $\ell$ becomes smaller than the fibre diameter $d$, the strong hydrodynamic confinement effect of the soap film gives rise to a logarithmic relaxation with fibre creeping time $t$. Such a slow dynamics of spreading is observed for hours both in the measured time-dependent height of capillary rise $h(t)$ on the fibre surface and viscous friction coefficient $\unicode[STIX]{x1D709}_{s}(t)$ felt by the glass fibre in contact with the soap film. A new theoretical approach based on the Onsager variational principle is developed to describe the dynamics of thin film spreading along a fibre. The newly derived equations of motion provide the analytical solutions of $h(t)$ and contact angle $\unicode[STIX]{x1D703}(t)$, which are found to be in good agreement with the experimental results. Our work thus provides a common framework for understanding the confinement effect of thin soap films on the dynamics of spreading along a fibre.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 650 - 680
Copyright
© 2019 Cambridge University Press 

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