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Quasi-normal free-surface impacts, capillary rebounds and application to Faraday walkers

Published online by Cambridge University Press:  01 July 2019

C. A. Galeano-Rios Open the ORCID record for C. A. Galeano-Rios [Opens in a new window] ,
P. A. Milewski Open the ORCID record for P. A. Milewski [Opens in a new window]  and
J.-M. Vanden-Broeck
C. A. Galeano-Rios*
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
P. A. Milewski
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present a model for capillary-scale objects that bounce on a fluid bath as they also translate horizontally. The rebounding objects are hydrophobic spheres that impact the interface of a bath of incompressible fluid whose motion is described by linearised quasi-potential flow. Under a quasi-normal impact assumption, we demonstrate that the problem can be decomposed into an axisymmetric impact onto a quiescent bath surface, and the unforced evolution of the surface waves. We obtain a walking model that is free of impact parametrisation and we apply this formulation to model droplets walking on a vibrating bath. We show that this model accurately reproduces experimental reports of bouncing modes, impact phases and time-dependent wave field topography for bouncing and walking droplets. Moreover, we revisit the modelling of horizontal drag during droplet impacts to incorporate the effects of the changes in the pressed area during droplet–surface contacts. Finally, we show that this model captures the recently discovered phenomenon of superwalkers.

JFM classification

Waves/Free-surface Flows: Capillary waves Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 856 - 888
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Copyright
© 2019 Cambridge University Press 

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Galeano-Rios et al. supplementary movie 1

Bouncer: Drop and waves (Fig. 4a)

Download Galeano-Rios et al. supplementary movie 1(Video)
Video 1.4 MB

Galeano-Rios et al. supplementary movie 2

Bouncer: Wave field (Fig. 4a)

Download Galeano-Rios et al. supplementary movie 2(Video)
Video 1.5 MB

Galeano-Rios et al. supplementary movie 3

Walker: Drop and waves (Fig. 4b)

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Video 44.2 MB

Galeano-Rios et al. supplementary movie 4

Walker: Wave field (Fig. 4b)

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Video 11.7 MB

Galeano-Rios et al. supplementary movie 5

Superbouncer: Drop and waves (Fig. 12a)

Download Galeano-Rios et al. supplementary movie 5(Video)
Video 1.5 MB

Galeano-Rios et al. supplementary movie 6

Superbouncer: Wave field (Fig. 12a)

Download Galeano-Rios et al. supplementary movie 6(Video)
Video 1.8 MB

Galeano-Rios et al. supplementary movie 7

Superwalker: Drop and waves (Fig. 12b)

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Video 19.9 MB

Galeano-Rios et al. supplementary movie 8

Superwalker: Wave field (Fig. 12b)

Download Galeano-Rios et al. supplementary movie 8(Video)
Video 5.4 MB