Droplets can exhibit complex dynamics when vertically and sinusoidally forced by a liquid surface from which they remain separated by a thin air cushion. Here we extend previous studies to include a family of periodic forcing functions that vary smoothly from sinusoidal to square wave by changing a single parameter. Through analytical and numerical work we find that the dynamics of the droplets and transitions between regular and chaotic regimes are effectively controlled by the impulse imparted on the droplets over a half-period. We also find that having nonsinusoidal forcing lowers the threshold amplitudes for most of the dynamical regimes. This is explained on the basis of a correlation between impulse increases and subsequent energy increases.

• Received 29 May 2018

DOI:https://doi.org/10.1103/PhysRevE.98.042215