Emergence of superwalking droplets

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. 2019). 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.

arXiv comment27 pages, 10 figures

References in corpus (7)

• Path-memory induced quantization of classical orbits
• Self-organization into quantized eigenstates of a classical wave driven particle
• Chaos driven by interfering memory
• Superwalking droplets
• Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits
• Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers
• Hong-Ou-Mandel-like two-droplet correlations

Cited by in corpus (10)

• Unsteady dynamics of a classical particle-wave entity
• Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
• Attractor-driven matter
• Anomalous transport of a classical wave-particle entity in a tilted potential
• Pseudo-laminar chaos from on-off intermittency
• Faraday waves under perpendicular electric field
• Liquid Time Crystals
• Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave-particle entity in a periodic potential
• Stop-and-go locomotion of superwalking droplets
• Quantum-like behavior of an active particle in a double-well potential