The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral
Author(s)Harris, Daniel M.; Brun, Pierre-Thomas; Damiano, Adam; Maltez Faria, Luiz; Bush, John W. M.
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
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)
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