Superwalking Droplets

Abstract

A new class of travelling droplets, coined superwalkers, have recently 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 (Valani et al. 2019). To understand the emergence of superwalking droplets, here we explore their vertical and horizontal dynamics using an extension of the theoretical model for walking droplets of Moláček & Bush (2013a,b). We show that driving the bath at two frequencies with an appropriate phase difference lowers every second peak and raises the intermediate peaks in the bath motion, allowing large droplets that could otherwise not walk to clear every second peak and bounce and walk in a similar manner 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 speed-size characteristics between simulations and experiments shows good agreement for small-to moderate-sized superwalkers. A novel behaviour of superwalking droplets, stop-and-go motion, is also captured in our simulations. Key words:Recently, a new class of walking droplets, coined superwalkers, have been observed (Valani et al. 2019). These emerge when the bath is driven simultaneously at two frequencies, f and f /2, with a relative phase difference ∆φ. For a commonly studied †

Walking droplets through the lens of dynamical systems

“…There is also the quasi-potential model numerical of Galeano-Rios et al [60,63] performed using a combination of finite differences and a semi-implicit Euler method that produces dynamics that are in very good agreement with the experimental and theoretical results in Wind-Willassen et al [35] and some of the other dynamical findings mentioned above. They also investigated a new dynamical regime called superwalkers, which was first observed by Valani et al [62], wherein the droplet bounces in place when the bath container is subject to a simple harmonic vertical motion, but tends to walk exceptionally fast for mixed harmonic oscillations.…”

Emergence of superwalking droplets

“…Using sophisticated numerical simulations, Galeano-Rios, Milewski & Vanden-Broeck (2019) were able to replicate superwalking behaviour for a single droplet of moderate radius mm, and reported a good match in the superwalking speed between their simulation and the experiments of Valani et al. (2019). Although these two studies describe the characteristics of superwalkers, an understanding of the mechanism that enables superwalking is still lacking.…”

“…Recently, a new class of walking droplets, coined superwalkers, has been observed (Valani, Slim & Simula 2019). These emerge when the bath is driven simultaneously at two frequencies, and , with a relative phase difference .…”

“…In the same system with two-frequency driving at and Hz, superwalkers can be significantly larger than walkers with radii up to and walking speeds up to (Valani et al. 2019). Intriguingly, the walking speed and the vertical dynamics of superwalkers are strongly dependent on the phase difference , with peak superwalking speed occurring near , while near they only bounce or may even coalesce.…”

Wave fields in double-slit experiments with wave-driven droplets

“…Surprisingly, at vibration amplitudes just below the threshold for Faraday surface waves, a droplet can self-propel horizontally over the surface due to the waves that are generated as it bounces [2]. Such wave-driven droplets have recently been the subject of intense studies to explore both their fascinating fluid dynamics [3][4][5][6][7][8][9][10][11][12][13][14] and their thought-provoking relation to quantum mechanics [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The exploration of the relation to quantum mechanics was pioneered by Couder and Fort, who pointed out the similarity between wave-driven droplets and de Broglie's picture of quantum particles propelled by "pilot-waves" [15].…”