  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.
