Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T21:38:34.112Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-propelled jumping upon drop coalescence on Leidenfrost surfaces

Published online by Cambridge University Press:  02 July 2014

Fangjie Liu ,
Giovanni Ghigliotti ,
James J. Feng Open the ORCID record for James J. Feng [Opens in a new window]  and
Chuan-Hua Chen
Fangjie Liu
Affiliation:
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA
Giovanni Ghigliotti
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2
James J. Feng
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2 Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z3
Chuan-Hua Chen*
Affiliation:
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Self-propelled jumping upon drop coalescence has been observed on a variety of textured superhydrophobic surfaces, where the jumping motion follows the capillary–inertial velocity scaling as long as the drop radius is above a threshold. In this paper, we report an experimental study of the self-propelled jumping on a Leidenfrost surface, where the heated substrate gives rise to a vapour layer on which liquid drops float. For the coalescence of identical water drops, we have tested initial drop radii ranging from 20 to $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}500\ \mu \mathrm{m}$, where the lower bound is related to the spontaneous takeoff of individual drops and the upper bound to gravitational effects. Regardless of the approaching velocity prior to coalescence, the measured jumping velocity is around 0.2 when scaled by the capillary–inertial velocity. This constant non-dimensional velocity holds for the experimentally accessible range of drop radii, and we have found no cutoff radius for the scaling, in contrast to prior experiments on textured superhydrophobic surfaces. The Leidenfrost experiments quantitatively agree with our numerical simulations of drop coalescence on a flat surface with a contact angle of 180°, suggesting that the cutoff is likely to be due to drop–surface interactions unique to the textured superhydrophobic surfaces.

JFM classification

Drops and Bubbles: Breakup/coalescence Phase change: Condensation/evaporation Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 752 , 10 August 2014 , pp. 22 - 38
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice CEDEX 2, France.

References

Bernardin, J. D. & Mudawar, I. 1999 The Leidenfrost point: experimental study and assessment of existing models. Trans. ASME: J. Heat Transfer 121, 894–903.CrossRefGoogle Scholar
Biance, A. L., Chevy, F., Clanet, C., Lagubeau, G. & Quéré, D. 2006 On the elasticity of an inertial liquid shock. J. Fluid Mech. 554, 47–66.CrossRefGoogle Scholar
Biance, A. L., Clanet, C. & Quéré, D. 2003 Leidenfrost drops. Phys. Fluids 15, 1632–1637.CrossRefGoogle Scholar
Boreyko, J. B.2012 From dynamical superhydrophobicity to thermal diodes. PhD thesis, Duke University, Durham, NC.Google Scholar
Boreyko, J. B. & Chen, C. H. 2009 Self-propelled dropwise condensate on superhydrophobic surfaces. Phys. Rev. Lett. 103, 184501.CrossRefGoogle ScholarPubMed
Boreyko, J. B. & Chen, C. H. 2010 Self-propelled jumping drops on superhydrophobic surfaces. Phys. Fluids 22, 091110.CrossRefGoogle Scholar
Burton, J. C., Sharpe, A. L., van der Veen, R. C. A., Franco, A. & Nagel, S. R. 2012 Geometry of the vapor layer under a Leidenfrost drop. Phys. Rev. Lett. 109, 074301.CrossRefGoogle Scholar
Celestini, F., Frisch, T. & Pomeau, Y. 2012 Take off of small Leidenfrost droplets. Phys. Rev. Lett. 109, 034501.CrossRefGoogle ScholarPubMed
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.CrossRefGoogle Scholar
Gottfried, B. S., Lee, C. J. & Bell, K. J. 1966 The Leidenfrost phenomenon: film boiling of liquid droplets on a flat plate. Intl J. Heat Mass Transfer 9, 1167–1188.CrossRefGoogle Scholar
Leidenfrost, J. G. 1756 De Aquae Communis Nonnullis Qualitatibus Tractatus. Johann Straube, Duisburg (translation: 1966 Intl J. Heat Mass Transfer 9, 1153–1166).CrossRefGoogle Scholar
Liu, F.2013 Self-propelled jumping upon coalescence on Leidenfrost surfaces. MS thesis, Duke University, Durham, NC.CrossRefGoogle Scholar
Liu, F., Ghigliotti, G., Feng, J. J. & Chen, C.-H. 2014 Numerical simulations of self-propelled jumping upon drop coalescence on non-wetting surfaces. J. Fluid Mech. 752, 39–65.CrossRefGoogle Scholar
Neitzel, G. P. & Dell’Aversana, P. 2002 Noncoalescence and nonwetting behavior of liquids. Annu. Rev. Fluid Mech. 34, 267–289.CrossRefGoogle Scholar
Pomeau, Y., Le Berre, M., Celestini, F. & Frisch, T. 2012 The Leidenfrost effect: from quasi-spherical droplets to puddles. C. R. Méc. 340, 867–881.CrossRefGoogle Scholar
Qian, J. & Law, C. K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80.CrossRefGoogle Scholar
Quéré, D. 2005 Non-sticking drops. Rep. Prog. Phys. 68, 2495–2532.Google Scholar
Quéré, D. 2013 Leidenfrost dynamics. Annu. Rev. Fluid Mech. 45, 197–215.CrossRefGoogle Scholar
Snoeijer, J. H., Brunet, P. & Eggers, J. 2009 Maximum size of drops levitated by an air cushion. Phys. Rev. E 79, 036307.CrossRefGoogle ScholarPubMed
Tran, T., de Maleprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.CrossRefGoogle Scholar
Tran, T., Staat, H. J. J., Prosperetti, A., Sun, C. & Lohse, D. 2012 Drop impact on superheated surfaces. Phys. Rev. Lett. 108, 036101.CrossRefGoogle ScholarPubMed
Zhang, F. H., Li, E. Q. & Thoroddsen, S. T. 2009 Satellite formation during coalescence of unequal size drops. Phys. Rev. Lett. 102, 104502.CrossRefGoogle ScholarPubMed

Liu et al. supplementary movie

Coalescence on a Leidenfrost surface (figure3a): r=22um, duration=10ms.

Download Liu et al. supplementary movie(Video)
Video 12.5 KB

Liu et al. supplementary movie

Coalescence on a Leidenfrost surface (figure 4): r=380um, duration=13.3ms.

Download Liu et al. supplementary movie(Video)
Video 212.2 KB

Liu et al. supplementary movie

Simulated coalescence on a non-wetting surface (figure 6): r=380um, duration=6.6ms.

Download Liu et al. supplementary movie(Video)
Video 799.4 KB

Liu et al. supplementary movie

Simulated coalescence on a non-wetting surface (figure 6): r=380um, duration=6.6ms.

Download Liu et al. supplementary movie(Video)
Video 975.8 KB

Liu et al. supplementary movie

Spontaneous takeoff of an individual Leidenfrost drop (figure 9): r=13um, duration=6.5ms.

Download Liu et al. supplementary movie(Video)
Video 27.3 KB

Liu et al. supplementary movie

Asymmetric coalescence on a Leidenfrost surface (figure 10): r0=330um, r1=190um, duration=13.75ms.

Download Liu et al. supplementary movie(Video)
Video 76.4 KB