The interaction of a walking droplet and a pillar

ORAL

Abstract

Droplets may bounce on the surface of a vibrating fluid bath, propelled forward by their own pilot-wave field. With a view to better understanding the interaction of such walking droplets with boundaries, we consider their impact on a submerged circular pillar. While simple scattering events are the norm, as the Faraday threshold is approached, the drop departs the pillar along a path corresponding to a logarithmic spiral. An effective wave force resulting from the pillar is inferred from the spiral, and takes the form of the Coriolis force that would arise in a frame of reference rotating with the instantaneous angular momentum of the drop about the pillar. An electromagnetic analog is explored.

Authors

  • John Bush

    MIT, MIT, Department of Mathematics

  • Daniel Harris

    UNC, UNC, Chapel Hill

  • Pierre-Thomas Brun

    MIT, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA, Massachusetts Institute of Technology