Resonant and rolling droplet

When an oil droplet is placed on a quiescent oil bath, it eventually collapses into the bath due to gravity. The resulting coalescence may be eliminated when the bath is vertically vibrated. The droplet bounces periodically on the bath, and the air layer between the droplet and the bath is replenished at each bounce. This sustained bouncing motion is achieved when the forcing acceleration is higher than a threshold value. When the droplet has a sufficiently low viscosity, it significantly deforms : spherical harmonic \boldmath{$Y_{\ell}^m$} modes are excited, resulting in resonant effects on the threshold acceleration curve. Indeed, a lower acceleration is needed when $\ell$ modes with $m=0$ are excited. Modes $m \ne 0$ are found to decrease the bouncing ability of the droplet. When the mode $\ell=2$ and $m=1$ is excited, the droplet rolls on the vibrated surface without touching it, leading to a new self-propulsion mode.