Floating under a levitating liquid

Abstract

When placed over a less dense medium, a liquid layer will typically collapse downwards if it exceeds a certain size, as gravity acting on the lower liquid interface triggers a destabilizing effect called a Rayleigh–Taylor instability1,2. Of the many methods that have been developed to prevent the liquid from falling3,4,5,6, vertical shaking has proved to be efficient and has therefore been studied in detail7,8,9,10,11,12,13. Stabilization is the result of the dynamical averaging effect of the oscillating effective gravity. Vibrations of liquids also induce other paradoxical phenomena such as the sinking of air bubbles14,15,16,17,18,19 or the stabilization of heavy objects in columns of fluid at unexpected heights20. Here we take advantage of the excitation resonance of the supporting air layer to perform experiments with large levitating liquid layers of up to half a litre in volume and up to 20 centimetres in width. Moreover, we predict theoretically and show experimentally that vertical shaking also creates stable buoyancy positions on the lower interface of the liquid, which behave as though the gravitational force were inverted. Bodies can thus float upside down on the lower interface of levitating liquid layers. We use our model to predict the minimum excitation needed to withstand falling of such an inverted floater, which depends on its mass. Experimental observations confirm the possibility of selective falling of heavy bodies. Our findings invite us to rethink all interfacial phenomena in this exotic and counter-intuitive stable configuration.

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Fig. 1: Levitating liquid layer stabilized by the Kapitza effect.
Fig. 2: Archimedes’ principle over and under a levitating liquid layer.
Fig. 3: Stability of the floater and the liquid layer.

Data availability

All the datasets generated during the current study are available in the Supplementary Information.

Change history

  • 23 September 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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Acknowledgements

We thank S. Protière, A. Lazarus, S. Wildeman and the staff and students of ‘Projets Scientifiques en Equipes’ for insightful discussions. We thank the AXA research fund and the French National Research Agency LABEX WIFI (ANR-10-LABX-24) for support.

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Authors

Contributions

All the authors discussed, interpreted the results and conceived the theoretical framework. E.F. devised the initial idea. B.A. and F.N. designed and performed the experiments. B.A., F.N. and E.F. wrote the paper. All authors reviewed the manuscript.

Corresponding author

Correspondence to Emmanuel Fort.

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The authors declare no competing interests.

Additional information

Peer review information Nature thanks Koji Hasegawa, Vladislav Sorokin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Models and Supplementary Raw Data.

Video 1

Controlling the position of an air bubble in an oscillating bath The liquid is silicon oil shaken at a frequency of 100 Hz by changing the forcing amplitude A. The critical depth d* above which the bubble starts to sink decreases when the forcing amplitude is increased. Hence, the bubble can go up or down depending on the vibration. The frame is tuned to strobe the bath oscillation. The container has a horizontal section of 11×11 cm2.

Video 2

Making the liquid layer levitate. The air layer is obtained by blowing air at the bottom of the oscillating liquid bath through a needle. The sinking bubble grows up to completely fill the bottom of the bath. The liquid is silicon oil, the forcing frequency is 100 Hz. The forcing amplitude is initially 3 mm and is decreased after the creation of the levitating layer to avoid Faraday instability. The container has a horizontal section of 5×4 cm2.

Video 3

Faraday instability at the two interfaces of the levitating liquid layer. The liquid is silicon oil, the forcing frequency is 100 Hz. The forcing amplitude is tuned to start the Faraday instability. The container has a horizontal section of 5×4 cm2.

Video 4

Making two liquid layer levitate. The liquid is silicon oil, the forcing frequency is 100 Hz. The forcing amplitude is tuned during the process to control the size of the liquid layers. The container has a horizontal section of 5×4 cm2.

Video 5

Stabilization of a liquid layer. The liquid is silicon oil with a horizontal section of 18×2 cm2. The forcing frequency is 80 Hz.

Video 6

Boats floating at the interfaces of the levitating liquid layer. The liquid is silicon oil, the forcing frequency is 60 Hz. The container has a horizontal section of 14×2 cm2. The boat are made a light foam with a width of 1.5 cm and length of approximately 3 cm.

Video 7

Relative stability between a floater and the liquid layer. The liquid is silicon oil, the forcing frequency is 80 Hz. The container has a horizontal section of 5×4 cm2. The floater is a sphere with a diameter of 2.5 cm.

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Apffel, B., Novkoski, F., Eddi, A. et al. Floating under a levitating liquid. Nature 585, 48–52 (2020). https://doi.org/10.1038/s41586-020-2643-8

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