Resonant and rolling droplet

TL;DR

This paper investigates how vibrated oil droplets bounce, deform, and roll on a vibrating bath, revealing resonant effects and a new self-propulsion mode influenced by droplet deformation modes.

Contribution

It introduces the role of spherical harmonic deformation modes in droplet bouncing and identifies a novel rolling self-propulsion mode induced by specific mode excitation.

Findings

Resonant effects reduce the threshold acceleration for bouncing.

Certain deformation modes facilitate droplet rolling without contact.

Mode b1=2, m=1 induces a self-propulsion rolling behavior.

Abstract

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.