Superwalking Droplets

A walker is a droplet of liquid that self-propels on the free surface of an oscillating bath of the same liquid through feedback between the droplet and its wave field. We have studied walking droplets in the presence of two driving frequencies and have observed a new class of walking droplets, which we coin superwalkers. Superwalkers may be more than double the size of the largest walkers, may travel at more than triple the speed of the fastest ones, and enable a plethora of novel multidroplet behaviors.

Figure 1

Comparison of a walker (top), a normal superwalker (middle), and a jumbo superwalker (bottom). Superwalkers emerge when the bath is driven at two frequencies $f$ and $f/2$ with a phase difference $\mathrm{\Delta }\varphi$. They may be significantly larger than walkers and may move significantly faster. Left panels show top views of typical droplets and their wave fields, and side views of the same droplets. Right panels show the bath motion (solid curve) and the typical bouncing motion of the droplets, see text for notation.

Figure 2

Characteristics of a solitary superwalker. (a) Walking speed as a function of droplet radius for fixed values ${\gamma }_{80}=3.8\mathrm{g}$ and $\mathrm{\Delta }\varphi =130°$ and three different values of ${\gamma }_{40}$, specifically ${\gamma }_{40}=0\mathrm{g}$ (blue markers), ${\gamma }_{40}=0.6\mathrm{g}$ (black markers), and ${\gamma }_{40}=1.0\mathrm{g}$ (red markers). Details of the error bars and the theory prediction (solid curve) are explained in the Supplemental Material [27]. Three different bouncing behaviors are indicated for superwalkers: chaotic, (1,2,1), and (1,2,2). Vertical slice-time plots of droplets are shown for (b) chaotic, (c) (1,2,1), and (d) (1,2,2) bouncing modes for ${\gamma }_{40}=0.6\mathrm{g}$ and radii as indicated. These spatiotemporal images are generated by juxtaposing vertical sections one pixel wide passing through the droplet’s center of mass. Panels (e) and (f) show the two extremes of the shape deformations of a jumbo superwalker.

Figure 3

(a) Droplet speed as a function of phase difference $\mathrm{\Delta }\varphi$ for a droplet of radius $R=0.83\pm 0.03\mathrm{mm}$ for ${\gamma }_{80}=3.8\mathrm{g}$ and ${\gamma }_{40}=0.6\mathrm{g}$. The data to the right of the vertical dotted line are repeated. Different behaviors occurring in the $({\gamma }_{80},{\gamma }_{40})/g$ parameter space for a fixed phase difference $\mathrm{\Delta }\varphi =130°$ and three different droplet radii: (b) $R=0.6\pm 0.05\mathrm{mm}$, (c) $R=0.8\pm 0.05\mathrm{mm}$, and (d) $R=1.0\pm 0.05\mathrm{mm}$. Error bars are explained in the Supplemental Material [27].

Figure 4

A plethora of phenomena observed with superwalkers; see text for details.