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Floating under a levitating liquid

An Author Correction to this article was published on 23 September 2020

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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.

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Data availability

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

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References

  1. Lord Rayleigh. Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177 (1883).

    MathSciNet  MATH  Google Scholar 

  2. Lewis, D. J. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II. Proc. R. Soc. Lond. A 202, 81–96 (1950).

    Article  ADS  CAS  Google Scholar 

  3. Burgess, J. M., Juel, A., McCormick, W. D., Swift, J. B. & Swinney, H. L. Suppression of dripping from a ceiling. Phys. Rev. Lett. 86, 1203–1206 (2001).

    Article  ADS  CAS  Google Scholar 

  4. Cimpeanu, R., Papageorgiou, D. T. & Petropoulos, P. G. On the control and suppression of the Rayleigh–Taylor instability using electric fields. Phys. Fluids 26, 022115 (2014).

    MATH  Google Scholar 

  5. Rannacher, D. & Engel, A. Suppressing the Rayleigh–Taylor instability with a rotating magnetic field. Phys. Rev. E 75, 016311 (2007).

    Article  ADS  Google Scholar 

  6. Tao, J. J., He, X. T., Ye, W. H. & Busse, F. H. Nonlinear Rayleigh–Taylor instability of rotating inviscid fluids. Phys. Rev. E 87, 013001 (2013).

    Article  ADS  CAS  Google Scholar 

  7. Wolf, G. H. The dynamic stabilization of the Rayleigh–Taylor instability and the corresponding dynamic equilibrium. Z. Phys. 227, 291–300 (1969).

    Article  ADS  Google Scholar 

  8. Wolf, G. H. Dynamic stabilization of the interchange instability of a liquid–gas interface. Phys. Rev. Lett. 24, 444–446 (1970).

    Article  ADS  CAS  Google Scholar 

  9. Lapuerta, V., Mancebo, F. J. & Vega, J. M. Control of Rayleigh–Taylor instability by vertical vibration in large aspect ratio containers. Phys. Rev. E 64, 016318 (2001).

    Article  ADS  CAS  Google Scholar 

  10. Kumar, S. Mechanism for the Faraday instability in viscous liquids. Phys. Rev. E 62, 1416–1419 (2000).

    Article  ADS  CAS  Google Scholar 

  11. Pototsky, A. & Bestehorn, M. Faraday instability of a two-layer liquid film with a free upper surface. Phys. Rev. Fluids 1, 023901 (2016).

    Article  ADS  Google Scholar 

  12. Pototsky, A., Oron, A. & Bestehorn, M. Vibration-induced floatation of a heavy liquid drop on a lighter liquid film. Phys. Fluids 31, 087101 (2019).

    Article  ADS  Google Scholar 

  13. Sterman-Cohen, E., Bestehorn, M. & Oron, A. Rayleigh–Taylor instability in thin liquid films subjected to harmonic vibration. Phys. Fluids 29, 052105 (2017); correction 29, 109901 (2017).

    Article  ADS  Google Scholar 

  14. Baird, M. H. I. Resonant bubbles in a vertically vibrating liquid column. Can. J. Chem. Eng. 41, 52–55 (1963).

    CAS  Google Scholar 

  15. Jameson, G. J. The motion of a bubble in a vertically oscillating viscous liquid. Chem. Eng. Sci. 21, 35–48 (1966).

    Article  CAS  Google Scholar 

  16. Sorokin, V. S., Blekhman, I. I. & Vasilkov, V. B. Motion of a gas bubble in fluid under vibration. Nonlinear Dyn. 67, 147–158 (2012).

    Article  MathSciNet  Google Scholar 

  17. Blekhman, I. I., Blekhman, L. I., Vaisberg, L. A., Vasil’kov, V. B. & Yakimova, K. S. “Anomalous” phenomena in fluid under the action of vibration. Dokl. Phys. 53, 520–524 (2008).

    Article  ADS  CAS  Google Scholar 

  18. Blekhman, I. I., Blekhman, L. I., Sorokin, V. S., Vasilkov, V. B. & Yakimova, K. S. Surface and volumetric effects in a fluid subjected to high-frequency vibration. Proc. Inst. Mech. Eng. C 226, 2028–2043 (2012).

    Article  Google Scholar 

  19. Zen’kovskaja, S. M. & Novosjadlyj, V. A. Vlijanie vertikal'nyh kolebanij na dvuhslojnuju sistemu s deformiruemoj poverhnost'ju razdela [Influence of vertical oscillations on a bilaminar system with a non-rigid interface.] Zh. Vychisl. Mat. Mat. Fiz. 48, 1710–1720 (2008).

    Google Scholar 

  20. Chelomei, V. N. Mechanical paradoxes caused by vibrations. Sov. Phys. Dokl. 28, 387–390 (1983).

    ADS  Google Scholar 

  21. Young, T. III. An essay on the cohesion of fluids. Philos. Trans. R. Soc. Lond. 95, 65–87 (1805).

    ADS  Google Scholar 

  22. Thomson, W. LX. On the equilibrium of vapour at a curved surface of liquid. Lond. Edinb. Dublin Philos. Mag. J. Sci. 42, 448–452 (1871).

    Article  Google Scholar 

  23. de Gennes, P.-G., Brochard-Wyart, F. & Quere, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer Science & Business Media, 2013).

  24. Fermigier, M., Limat, L., Wesfreid, J. E., Boudinet, P. & Quilliet, C. Two-dimensional patterns in Rayleigh–Taylor instability of a thin layer. J. Fluid Mech. 236, 349–383 (1992).

    Article  ADS  CAS  Google Scholar 

  25. Myshkis, A. D., Babskii, V. G., Kopachevskii, N. D., Slobozhanin, L. A. & Tyuptsov, A. Low-Gravity Fluid Mechanics. Mathematical Theory of Capillary Phenomena (Springer, 1987).

  26. Faraday, M. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. Lond. 121, 299–340 (1831).

    ADS  Google Scholar 

  27. Douady, S. Experimental study of the Faraday instability. J. Fluid Mech. 221, 383–409 (1990).

    Article  ADS  Google Scholar 

  28. Kumar, K. & Tuckerman, L. S. Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 49–68 (1994).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. Elbing, B. R., Still, A. L. & Ghajar, A. J. Review of bubble column reactors with vibration. Ind. Eng. Chem. Res. 55, 385–403 (2016).

    Article  CAS  Google Scholar 

  30. Bjerknes, V. F. K. Fields of Force: Supplementary Lectures, Applications to Meteorology (Columbia Univ. Press and Macmillan, 1906).

  31. Kapitza, P. L. Dynamic stability of a pendulum when its point of suspension vibrates. Sov. Phys. JETP 21, 588–597 (1951).

    Google Scholar 

  32. Krieger, M. S. Interfacial fluid instabilities and Kapitsa pendula. Eur. Phys. J. E 40, 67 (2017).

    Article  Google Scholar 

  33. Landau, L. D. & Lifshitz, E. M. Mechanics (Pergamon, 1969).

Download references

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.

Author information

Authors and Affiliations

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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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