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Emergence of superwalking droplets

Published online by Cambridge University Press:  09 November 2020

Rahil N. Valani Open the ORCID record for Rahil N. Valani [Opens in a new window] ,
Jack Dring ,
Tapio P. Simula Open the ORCID record for Tapio P. Simula [Opens in a new window]  and
Anja C. Slim
Rahil N. Valani*
Affiliation:
School of Physics and Astronomy, Monash University, Victoria3800, Australia
Jack Dring
Affiliation:
School of Mathematics, Monash University, Victoria3800, Australia
Tapio P. Simula
Affiliation:
Optical Sciences Centre, Swinburne University of Technology, Melbourne3122, Australia
Anja C. Slim
Affiliation:
School of Mathematics, Monash University, Victoria3800, Australia School of Earth, Atmosphere and Environment, Monash University, Victoria3800, Australia
*
†Email address for correspondence: rahil.valani@monash.edu
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Abstract

A new class of self-propelled droplets, coined superwalkers, has been shown to emerge when a bath of silicone oil is vibrated simultaneously at a given frequency and its subharmonic tone with a relative phase difference between them (Valani et al., Phys. Rev. Lett., vol. 123, 2019, 024503). To understand the emergence of superwalking droplets, we explore their vertical and horizontal dynamics by extending previously established theoretical models for walkers driven by a single frequency to superwalkers driven by two frequencies. Here, we show that driving the bath at two frequencies with an appropriate phase difference raises every second peak and lowers the intermediate peaks in the vertical periodic motion of the fluid surface. This allows large droplets that could otherwise not walk to leap over the intermediate peaks, resulting in superwalking droplets whose vertical dynamics is qualitatively similar to normal walkers. We find that the droplet's vertical and horizontal dynamics are strongly influenced by the relative height difference between successive peaks of the bath motion, a parameter that is controlled by the phase difference. Comparison of our simulated superwalkers with the experiments of Valani et al. (2019) shows good agreement for small- to moderate-sized superwalkers.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Faraday waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A3
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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