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A ratchet trap for Leidenfrost drops

Published online by Cambridge University Press:  27 February 2012

Thomas R. Cousins ,
Raymond E. Goldstein ,
Justin W. Jaworski  and
Adriana I. Pesci
Thomas R. Cousins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Raymond E. Goldstein*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Justin W. Jaworski
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Adriana I. Pesci
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

The Leidenfrost effect occurs when a drop of liquid (or a sublimating solid) is levitated above a sufficiently hot surface through the action of an insulating vapour layer flowing from its bottom surface. When such a drop is levitated above a surface with parallel, asymmetric sawtooth-shaped ridges it is known to be propelled in a unique direction, or ratcheted, by the interaction of the vapour layer with the surface. Here we exploit this effect to construct a ‘ratchet trap’ for Leidenfrost drops: a surface with concentric circular ridges, each asymmetric in cross-section. A combination of experiment and theory is used to study the dynamics of drops in these traps, whose centre is a stable fixed point. Numerical analysis of the evaporating flows over a ratchet surface suggests new insights into the mechanism of motion rectification that are incorporated into the simplest equations of motion for ratchet-driven motion of a Leidenfrost body; these resemble a central force problem in celestial mechanics with mass loss and drag. A phase-plane analysis of experimental trajectories is used to extract more detailed information about the ratcheting phenomenon. Orbiting drops are found to exhibit substantial deformations; those with large internal angular momentum can even undergo binary fission. Such ratchet traps may thus prove useful in the controlled study of many properties of Leidenfrost drops.

JFM classification

Phase change: Condensation/evaporation Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 696 , 10 April 2012 , pp. 215 - 227
Copyright
Copyright © Cambridge University Press 2012

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References

1. Adachi, K. & Takaki, R. 1984 Vibration of a flattened drop. Part 1. Observation. J. Phys. Soc. Japan 53, 4184–4191.Google Scholar
2. Bertrand, J. 1873 Théorème relatif au mouvement d’un point attiré vers un centre fixe. C. R. Acad. Sci. 77, 849–853.Google Scholar
3. Biance, A.-L, Clanet, C. & Quéré, D. 2003 Leidenfrost drops. Phys. Fluids 15, 1632–1637.CrossRefGoogle Scholar
4. Brown, R. A. & Scriven, L. E. 1980 The shape and stability of rotating liquid drops. Proc. R. Soc. Lond. A 371, 331–357.Google Scholar
5. Chandrasekhar, S. 1965 The stability of a rotating fluid drop. Proc. R. Soc. Lond. A 286, 1–26.Google Scholar
6. Dupeux, G., Le Merrer, M., Clanet, C. & Quéré, D. 2011a Trapping Leidenfrost drops with crenelations. Phys. Rev. Lett. 107, 114503.CrossRefGoogle ScholarPubMed
7. Dupeux, G., Le Merrer, M., Lagubeau, G., Clanet, C., Hardt, S. & Quéré, D. 2011b Viscous mechanism for Leidenfrost propulsion on a ratchet. Europhys. Lett. 96, 58001.Google Scholar
8. Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625–643.CrossRefGoogle Scholar
9. Lagubeau, G., Le Merrer, M., Clanet, C. & Quéré, D. 2011 Leidenfrost on a ratchet. Nat. Phys. 7, 395–398.CrossRefGoogle Scholar
10. Lebovitz, N. R. & Pesci, A. I. 1995 Dynamic bifurcation in Hamiltonian systems with one degree of freedom. SIAM J. Appl. Maths 55, 1117–1133.Google Scholar
11. Leidenfrost, J. G. 1756 De Aquae Communis Nonnullis Qualitatibus Tractatus. Herman Ovenius.Google Scholar
12. Linke, H., Alemán, B. J., Melling, L. D., Taormina, M. J., Francis, M. J., Dow-Hygelund, C. C., Narayanan, V., Taylor, R. P. & Stout, A. 2006 Self-propelled Leidenfrost droplets. Phys. Rev. Lett. 96, 154502.Google Scholar
13. Myers, T. G. & Charpin, J. P. F. 2009 A mathematical model of the Leidenfrost effect on an axisymmetric droplet. Phys. Fluids 21, 063101.CrossRefGoogle Scholar
14. Ok, J. T., Lopez-Oña, E., Nikitopoulos, D. E., Wong, H. & Park, S. 2011 Propulsion of droplets on micro- and sub-micron ratchet surfaces in the Leidenfrost temperature regime. Microfluid. Nanofluid. 10, 1045–1054.Google Scholar
15. Schlichting, H. 1968 Boundary-Layer Theory, 6th edn. McGraw-Hill.Google Scholar
16. Symon, K. R. 1971 Mechanics, 3rd edn. Addison-Wesley.Google Scholar

Cousins et al. supplementary movie

Supplemental movie 1: Quasi-one-dimensional orbit of a Leidenfrost drop in a ratchet trap. This high-speed movie shows a drop with very small initial orbital angular momentum executing back and forth motion around the trap centre. The drop exhibits noticeable shape deformations near the turning points of the orbit.

Download Cousins et al. supplementary movie(Video)
Video 6.8 MB

Cousins et al. supplementary movie

Supplemental movie 2: Fission of a Leidenfrost drop in a ratchet trap. A drop with large orbital angular momentum is observed to fission as it moves in a roughly circular orbit. The small satellite drop produced during breakup is visible.

Download Cousins et al. supplementary movie(Video)
Video 5.5 MB

Cousins et al. supplementary movie

Supplemental movie 3: Fission and merger of Leidenfrost drops. In this movie a spinning, orbiting drop sheds several small drops, then fissions into two large drops and one smaller one. After continuing to orbit in the trap the large drops then merge.

Download Cousins et al. supplementary movie(Video)
Video 3.7 MB