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Numerical simulations of self-propelled jumping upon drop coalescence on non-wetting 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 addresses for correspondence: jfeng@math.ubc.ca, chuanhua.chen@duke.edu
†Email addresses for correspondence: jfeng@math.ubc.ca, chuanhua.chen@duke.edu
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Abstract

Coalescing drops spontaneously jump out of plane on a variety of biological and synthetic superhydrophobic surfaces, with potential applications ranging from self-cleaning materials to self-sustained condensers. To investigate the mechanism of self-propelled jumping, we report three-dimensional phase-field simulations of two identical spherical drops coalescing on a flat surface with a contact angle of 180°. The numerical simulations capture the spontaneous jumping process, which follows the capillary–inertial scaling. The out-of-plane directionality is shown to result from the counter-action of the substrate to the impingement of the liquid bridge between the coalescing drops. A viscous cutoff to the capillary–inertial velocity scaling is identified when the Ohnesorge number of the initial drops is around 0.1, but the corresponding viscous cutoff radius is too small to be tested experimentally. Compared to experiments on both superhydrophobic and Leidenfrost surfaces, our simulations accurately predict the nearly constant jumping velocity of around 0.2 when scaled by the capillary–inertial velocity. By comparing the simulated drop coalescence processes with and without the substrate, we attribute this low non-dimensional velocity to the substrate intercepting only a small fraction of the expanding liquid bridge.

JFM classification

Drops and Bubbles: Breakup/coalescence Mathematical Foundations: Computational methods Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 752 , 10 August 2014 , pp. 39 - 65
Copyright
© 2014 Cambridge University Press 

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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.

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Liu et al. supplementary movie

Coalescence on the substrate (figure 3a): Oh=0.00375, xz view (duration T*=6).

Download Liu et al. supplementary movie(Video)
Video 1.5 MB

Liu et al. supplementary movie

Coalescence in the air (figure 3b): Oh=0.00375, xz/xy view (duration T*=6).

Download Liu et al. supplementary movie(Video)
Video 1.8 MB

Liu et al. supplementary movie

Coalescence in the air (figure 3b): Oh=0.00375, xz/xy view (duration T*=6).

Download Liu et al. supplementary movie(Video)
Video 3.3 MB

Liu et al. supplementary movie

Coalescence on the substrate (figure 4a): Oh=0.00375, yz view (duration T*=6).

Download Liu et al. supplementary movie(Video)
Video 1.5 MB

Liu et al. supplementary movie

Coalescence on the substrate (figure 4b): Oh=0.00375, xy view (duration T*=6).

Download Liu et al. supplementary movie(Video)
Video 1.5 MB

Liu et al. supplementary movie

Coalescence on the substrate (figure 9a): Oh=0.375, xz view (duration T*=8).

Download Liu et al. supplementary movie(Video)
Video 1.9 MB

Liu et al. supplementary movie

Coalescence in the air (figure 9b): Oh=0.375, xz/xy view (duration T*=8).

Download Liu et al. supplementary movie(Video)
Video 1.7 MB