Damped-driven system of bouncing droplets leading to deterministic diffusive behavior

TL;DR

This study investigates a fluidic droplet on a vibrating bath, revealing that deterministic damping and driving can produce complex, Brownian-like diffusive behavior through chaotic velocity changes.

Contribution

It combines experimental and theoretical analysis of a droplet system, demonstrating how simple deterministic interactions can lead to complex diffusive phenomena.

Findings

Droplet velocities follow a Gaussian distribution.

Chaotic velocity changes mimic Brownian motion.

Deterministic damping and driving produce Levy-like behavior.

Abstract

Damped-driven systems are ubiquitous in science, however the damping and driving mechanisms are often quite convoluted. This manuscript presents an experimental and theoretical investigation of a fluidic droplet on a vertically vibrating fluid bath as a damped-driven system. We study a fluidic droplet in an annular cavity with the fluid bath forced above the Faraday wave threshold. We model the droplet as a kinematic point particle in air and as inelastic collisions during impact with the bath. In both experiments and the model the droplet is observed to chaotically change velocity with a Gaussian distribution. Finally, the statistical distributions from experiments and theory are analyzed. Incredibly, this simple deterministic interaction of damping and driving of the droplet leads to more complex Brownian-like and Levy-like behavior.