Emergence of superwalking droplets

TL;DR

This paper extends theoretical models to explain the emergence of superwalking droplets driven by two-frequency vibrations, showing how phase differences influence their vertical and horizontal dynamics, aligning well with experimental observations.

Contribution

It introduces a modified theoretical framework for superwalkers driven by two frequencies, highlighting the role of phase difference in their dynamics, which was not previously modeled.

Findings

Vertical motion peaks are altered by phase difference, enabling larger droplets to leap over peaks.

Superwalkers exhibit vertical dynamics similar to normal walkers despite larger size.

Model predictions align with experimental data for small to moderate superwalkers.

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.