The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral

Daniel M. Harris, P. T. Brun, Adam Damiano, Luiz M. Faria, John W.M. Bush

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Millimetric droplets may walk across the surface of a vibrating fluid bath, propelled forward by their own guiding or "pilot" wave field. We here consider the interaction of such walking droplets with a submerged circular pillar. While simple scattering events are the norm, as the waves become more pronounced, the drop departs the pillar along a path corresponding to a logarithmic spiral. The system behavior is explored both experimentally and theoretically, using a reduced numerical model in which the pillar is simply treated as a region of decreased wave speed. A trajectory equation valid in the limit of weak droplet acceleration is used to infer an effective force due to the presence of the pillar, which is found to be a lift force proportional to the product of the drop's walking speed and its instantaneous angular speed around the post. This system presents a macroscopic example of pilot-wave-mediated forces giving rise to apparent action at a distance.

Original languageEnglish (US)
Article number096105
JournalChaos
Volume28
Issue number9
DOIs
StatePublished - Sep 1 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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