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Onset of thin film meniscus along a fibre

  • Shuo Guo (a1), Xianmin Xu (a2), Tiezheng Qian (a3), Yana Di (a2), Masao Doi (a4) and Penger Tong (a1)...

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.

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Corresponding author

Email address for correspondence: penger@ust.hk

References

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