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.
LanguageEnglish
Number of pages32
JournalJournal of Fluid Mechanics
StatusAccepted/In press - 3 May 2019

Keywords

  • Capillary waves
  • drops
  • Wave-structure interactions

Cite this

@article{2ed2259364c64336936a92d0293facdd,
title = "Quasi-normal free-surface impacts, capillary rebounds and application to Faraday walkers.",
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.",
keywords = "Capillary waves, drops, Wave-structure interactions",
author = "{Galeano Rios}, Carlos and Paul Milewski and Jean-Marc Vanden-Broeck",
year = "2019",
month = "5",
day = "3",
language = "English",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Quasi-normal free-surface impacts, capillary rebounds and application to Faraday walkers.

AU - Galeano Rios, Carlos

AU - Milewski, Paul

AU - Vanden-Broeck, Jean-Marc

PY - 2019/5/3

Y1 - 2019/5/3

N2 - 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.

AB - 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.

KW - Capillary waves

KW - drops

KW - Wave-structure interactions

M3 - Article

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -