Onset of thin film meniscus along a fibre

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 l 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 xi(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 theta(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.