The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral
Name
Harris-SPIRAL.pdf
Description
Published version
Size
1.38 MB
Format
Adobe PDF
Checksum (MD5)
cc0b6c4b188ace58244f14d69fbf3c91
Author(s)
Harris, Daniel M.
Brun, Pierre-Thomas
Damiano, Adam
Maltez Faria, Luiz
Bush, John W. M.
Date Issued
September 2018
Journal
Chaos
Publisher
AIP Publishing
Citation
Harris, Daniel M. et al. "The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral." Chaos 28, 9 (September 2018): 096105 © 2018 Author(s)
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/1.5031022
