The role of the droplet deformations in the bouncing droplet dynamics

TL;DR

This study investigates how droplet deformations influence bouncing dynamics on a vibrated liquid bath, using experiments and a spring-mass-damper model to understand complex behaviors and predict various bouncing modes.

Contribution

It introduces a deformable droplet model with a spring-mass-damper system to explain bouncing behaviors, validated by experimental bifurcation diagrams.

Findings

Spring model accurately predicts multi-periodic bouncing modes

Droplet deformation plays a key role in energy storage and dissipation

Experimental bifurcation diagrams match model predictions

Abstract

Droplets bouncing on a vibrated liquid bath open ways to methods of manipulating droplets, creating double emulsion and performing pilot wave model experiments. In this work, we focus on the role of the droplet deformations in the vertical bouncing dynamics by neglecting the deformation of the surface of the bath. To be under this favorable conditions, low viscous oil droplet are dropped over a highly viscous oil bath. These droplets bounce vertically on the surface of the bath and exhibit many periodic trajectories and resonant modes when tuning the forcing parameters, i.e. the oscillation of the bath. This complex dynamics emphasizes the interplay between elastic energy storage and energy dissipation in droplets at each bounce. We propose to model droplets using a bouncing mass-spring-damper system that mimics a deformable droplet bouncing on a non-deformable liquid bath. From the experimental measurements, we constructed bifurcation diagrams of the bouncing trajectories and challenged our bouncing spring model. The agreement between experiment and the spring model reveals that this model can be used to rationalize and predict a variety of bouncing droplets behaviors involving multi-periodicities.