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The wave-induced added mass of walking droplets

Published online by Cambridge University Press:  22 August 2014

John W. M. Bush*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Anand U. Oza
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Jan Moláček
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
*
Email address for correspondence: bush@math.mit.edu

Abstract

It has recently been demonstrated that droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic realm. The walker, consisting of a droplet plus its guiding wavefield, is a spatially extended object. We here examine the dependence of the walker mass and momentum on its velocity. Doing so indicates that, when the walker’s time scale of acceleration is long relative to the wave decay time, its dynamics may be described in terms of the mechanics of a particle with a speed-dependent mass and a nonlinear drag force that drives it towards a fixed speed. Drawing an analogy with relativistic mechanics, we define a hydrodynamic boost factor for the walkers. This perspective provides a new rationale for the anomalous orbital radii reported in recent studies.

Type
Rapids
Copyright
© 2014 Cambridge University Press 

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