Comptes Rendus
no. 11-12
The Leidenfrost effect: From quasi-spherical droplets to puddles
Yves Pomeau1 ; Martine Le Berre2  ; Franck Celestini3 ; Thomas Frisch4
1 Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089, USA
2 Institut des sciences moléculaires dʼOrsay ISMO-CNRS, Univ. Paris-Sud, bâtiment 210, 91405 Orsay cedex, France
3 Laboratoire de physique de la matière condensée, CNRS UMR 7366, université de Nice Sophia-Antipolis, parc Valrose 06108 Nice cedex 2, France
4 Institut non linéaire de Nice, CNRS UMR 7735, université de Nice Sophia-Antipolis, 1361, routes des lucioles, Sophia Antipolis, 06560 Valbonne, France
Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 867-881.

In the framework of the lubrication approximation, we derive a set of equations describing the steady bottom profile of Leidenfrost drops coupled with the vapor pressure. This allows us to derive scaling laws for the geometry of the concave bubble encapsulated between the drop and the hot plate under it. The results agree with experimental observations in the case of droplets with radii smaller than the capillary length Rc as well as in the case of puddles with radii larger than Rc.

Publié le :
DOI : 10.1016/j.crme.2012.10.034
Mots clés : Leidenfrost effect
Yves Pomeau 1 ; Martine Le Berre 2 ; Franck Celestini 3 ; Thomas Frisch 4

1 Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089, USA
2 Institut des sciences moléculaires dʼOrsay ISMO-CNRS, Univ. Paris-Sud, bâtiment 210, 91405 Orsay cedex, France
3 Laboratoire de physique de la matière condensée, CNRS UMR 7366, université de Nice Sophia-Antipolis, parc Valrose 06108 Nice cedex 2, France
4 Institut non linéaire de Nice, CNRS UMR 7735, université de Nice Sophia-Antipolis, 1361, routes des lucioles, Sophia Antipolis, 06560 Valbonne, France 
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Yves Pomeau; Martine Le Berre; Franck Celestini; Thomas Frisch. The Leidenfrost effect: From quasi-spherical droplets to puddles. Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 867-881. doi : 10.1016/j.crme.2012.10.034. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.034/

[1] J.G. Leidenfrost, De aquae communis nonnullis qualitatibus tractatus, Duisburg, 1756; English translation by C. Wares in Int. Heat Mass Transfer 15 (1966) 1153–1166. See also M. Boutigny, Sur les phénomenes que présentent les corps projettés sur des surfaces chaudes, Annales de Chimie et de Physique 3 (IX) (1843) 350–370 and 3 (XI) (1844) 16–39.

[2] J. Tyndall Heat: A Mode of Motion, D. Appleton and Co. Publisher, 1890

[3] F. Celestini; T. Frisch; Y. Pomeau Take-off of small Leidenfrost droplets, Phys. Rev. Lett., Volume 109 (2012) 034501(1–4)

[4] A.L. Biance; C. Clanet; D. Quéré Leidenfrost drops, Phys. Fluid, Volume 15 (2003), pp. 1632-1637 (and references therein)

[5] J.H. Snoeijer; P. Brunet; J. Eggers Maximum size of drops levitated by an air cushion, Phys. Rev. E, Volume 79 (2009) 036307(1–13)

[6] F. Celestini; G. Kirstetter Effect of the electric field on a Leidenfrost droplet, Soft Matter, Volume 8 (2012), p. 5992

[7] J.C. Burton; A.L. Sharpe; R.C.A. van der Veen; A. Franco; S.R. Nagel The geometry of a vapor layer under a Leidenfrost drop, Phys. Rev. Lett., Volume 109 (2012) 074301(1–4)

[8] Lei Xu; W.W. Zhang; S.R. Nagel Drop splashing on a dry smooth surface, Phys. Rev. Lett., Volume 94 (2005) 184505(1–4)

[9] P.L. Bhatnagar; E.P. Gross; M.A. Krook A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., Volume 94 (1954), pp. 511-525

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