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Drops bouncing on a vibrating bath

Published online by Cambridge University Press:  28 June 2013

Jan Moláček  and
John W. M. Bush
Jan Moláček
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
John W. M. Bush*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: bush@math.mit.edu
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Abstract

We present the results of a combined experimental and theoretical investigation of millimetric droplets bouncing on a vertically vibrating fluid bath. We first characterize the system experimentally, deducing the dependence of the droplet dynamics on the system parameters, specifically the drop size, driving acceleration and driving frequency. As the driving acceleration is increased, depending on drop size, we observe the transition from coalescing to vibrating or bouncing states, then period-doubling events that may culminate in either walking drops or chaotic bouncing states. The drop’s vertical dynamics depends critically on the ratio of the forcing frequency to the drop’s natural oscillation frequency. For example, when the data describing the coalescence–bouncing threshold and period-doubling thresholds are described in terms of this ratio, they collapse onto a single curve. We observe and rationalize the coexistence of two non-coalescing states, bouncing and vibrating, for identical system parameters. In the former state, the contact time is prescribed by the drop dynamics; in the latter, by the driving frequency. The bouncing states are described by theoretical models of increasing complexity whose predictions are tested against experimental data. We first model the drop–bath interaction in terms of a linear spring, then develop a logarithmic spring model that better captures the drop dynamics over a wider range of parameter space. While the linear spring model provides a faster, less accurate option, the logarithmic spring model is found to be more accurate and consistent with all existing data.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Faraday waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 582 - 611
Copyright
©2013 Cambridge University Press 

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