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

Carlos Galeano Rios, Paul Milewski, Jean-Marc Vanden-Broeck

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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.
Original languageEnglish
Pages (from-to)856-888
Number of pages32
JournalJournal of Fluid Mechanics
Volume873
Early online date1 Jul 2019
DOIs
Publication statusPublished - 25 Aug 2019

Keywords

  • Capillary waves
  • drops
  • Wave-structure interactions

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