Exploratory Study of Chaotic Behavior in Walking Droplets

TL;DR

This study explores chaotic behaviors of walking droplets interacting with supercritical Faraday waves, revealing complex trajectories, clustering, and boundary effects, advancing understanding of hydrodynamic quantum analogs.

Contribution

It provides experimental insights into walking droplet dynamics in supercritical Faraday wave regimes, including boundary influences and partial wave effects, which were not previously studied.

Findings

Walking droplets exhibit erratic trajectories in supercritical Faraday waves.

Droplets tend to cluster due to capillary effects.

Partial Faraday wave regimes influence droplet behavior and trajectories.

Abstract

The interaction of 'walking droplets' and capillary waves in a weakly subcritical Faraday wave experiment has been studied as a hydrodynamic analog to Bohmian quantum mechanics (see "Hydrodynamic Quantum Analogs", J. Bush and A. Oza, Rep. Prog. Physics (2021)). We report here experimental results of walking droplets interacting with supercritical Faraday waves with dimensionless acceleration of approximately 7.7, where the onset of Faraday instability occurs at dimensionless acceleration 6.3, in flat bath topography. Our working fluid is silicone oil with a kinematic viscosity of 20 cst that is placed as a 4.2 mm horizontal liquid layer in an intermediate-aspect-ratio circular bath with a radius to Faraday wavelength ratio of 5.8. We also use different 3D-printed subsurfaces that act as slit structures with local oil depth of 0.7 mm. We confirm expected behavior for walking droplets in the supercritical Faraday regime, such as erratic trajectories, droplets clustering together due to capillary effects, and spontaneous drop creation. We note a special case of walking-droplet behavior when the bath only partially displays Faraday waves. We discuss the influence of the lateral boundaries and slits on droplet trajectory in this chaotic regime and compare the measured trajectories found here to those single and double slit experiments previously studied in the subcritical Faraday regime.