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Stability and collapse of holes in liquid layers

Published online by Cambridge University Press:  24 September 2018

Cunjing Lv ,
Michael Eigenbrod  and
Steffen Hardt Open the ORCID record for Steffen Hardt [Opens in a new window]
Cunjing Lv
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287 Darmstadt, Germany Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, China
Michael Eigenbrod
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287 Darmstadt, Germany
Steffen Hardt*
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287 Darmstadt, Germany
*
†Email address for correspondence: [email protected]
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Abstract

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that $d_{c}$ increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

JFM classification

Interfacial Flows (free surface): Contact lines Instability: Instability Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 1130 - 1155
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Copyright
© 2018 Cambridge University Press 

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Lv et al. supplementary movie 1

Hole collapse on a superhydrophobic Al plate viewed from the top. Initially, the hole diameter decreases very slowly when adding more water. The dynamics speed up significantly when d reaches dc.

Download Lv et al. supplementary movie 1(Video)
Video 1.8 MB
Supplementary material: PDF

Lv et al. supplementary material

Supplementary material

Download Lv et al. supplementary material(PDF)
PDF 771.4 KB

Lv et al. supplementary movie 2

Same experiment as is movie 1, but captured from the side. This movie starts after instability has already set in. After hole collapse, an air bubble is formed on the surface but finally vanishes in the indentations.

Download Lv et al. supplementary movie 2(Video)
Video 812.6 KB

Lv et al. supplementary movie 3

Hole collapse in a water layer on a Teflon substrate in side view. After the hole is completely closed, there is an air bubble left at the center of the substrate.

Download Lv et al. supplementary movie 3(Video)
Video 608.7 KB

Lv et al. supplementary movie 4

Hole collapse on a hydrophilic silicon wafer in the side view. Different from the other three samples, here an acute angle at the three-phase contact line is observed. Line pinning is observed in the first stage when the hole is stable. However, beyond the stability threshold the hole collapses rather smoothly.

Download Lv et al. supplementary movie 4(Video)
Video 386.1 KB

Lv et al. supplementary movie 5

High-speed video of the final stages of hole collapse on a superhydrophobic Al substrate in side view (recording speed 100 000 fps).

Download Lv et al. supplementary movie 5(Video)
Video 561.9 KB