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Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid

Published online by Cambridge University Press:  19 July 2021

Andrey Pototsky Open the ORCID record for Andrey Pototsky [Opens in a new window] ,
Alexander Oron Open the ORCID record for Alexander Oron [Opens in a new window]  and
Michael Bestehorn Open the ORCID record for Michael Bestehorn [Opens in a new window]
Andrey Pototsky*
Affiliation:
Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria3122, Australia
Alexander Oron
Affiliation:
Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa3200003, Israel
Michael Bestehorn
Affiliation:
Institute of Physics, Brandenburg University of Technology, 03013Cottbus-Senftenberg, Germany
*
†Email address for correspondence: [email protected]
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Abstract

A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show that such a floating liquid drop with a sufficiently small volume has two distinct equilibrium shapes at terrestrial gravity: one with a larger and one with a smaller radius of the triple-phase contact line. Static stability analysis reveals that both shapes could be stable if the drop volume is below a certain critical value. Experiments conducted with $\mathrm {\mu }\textrm {L}$-sized water drops floating on commercial oil support the existence of multiple contact line radii for a drop with fixed volume. Next, we experimentally study the floatability of a less viscous water drop on the surface of a more viscous and less dense oil, subjected to a low-frequency (Hz-order) vertical vibration. We find that in a certain range of amplitudes, vibration helps heavy liquid drops to stay afloat. The physical mechanism of the increased floatability is explained by the horizontal elongation of the drop driven by subharmonic Faraday waves. The average length of the triple-phase contact line increases as the drop elongates that leads to a larger average lifting force produced by the surface tension.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Faraday waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A31
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Pototsky et al. supplementary movie 1

Two stable shapes of a 5 micro liter water drop floating on the surface of commercial vegetable oil. All fluid parameters are as in Fig.5 in the main.

Download Pototsky et al. supplementary movie 1(Video)
Video 1.8 MB

Pototsky et al. supplementary movie 2

200fps slow motion video of a 0.12 milliliter water drop floating on the surface of olive oil vibrated at 60 Hz with amplitude a=5.5g. Drop shape and dimensions are described in Fig.7 in the main text.

Download Pototsky et al. supplementary movie 2(Video)
Video 1.1 MB

Pototsky et al. supplementary movie 3

200 fps slow motion video of a 0.15 milliliter water puddle in 5 mm layer of olive oil layer vibrated at 60 Hz with amplitude of a=5g. As the puddle undergoes a spontaneous horizontal elongation, driven by Faraday waves, the water is drawn by the increased surface tension forces towards the oil-air interface

Download Pototsky et al. supplementary movie 3(Video)
Video 5.2 MB

Pototsky et al. supplementary movie 4

5-6 micro-litter water drop floating on the surface of commercial cooking oil. After a needle is immersed into the upper part of the drop, the contact radius is increased. Horizontal bar is 5 mm.

Download Pototsky et al. supplementary movie 4(Video)
Video 72.7 KB

Pototsky et al. supplementary movie 5

0.12 milliliter water drop floating on the surface of olive oil vibrated at 50 Hz with amplitude a=5.5g. The first 11 seconds of the video are in slow motion (200 fps) the remaining part of the video is in real time. When vibration stops, the drop can no longer be supported by surface tension forces and sinks.

Download Pototsky et al. supplementary movie 5(Video)
Video 385.3 KB