# A solvable model of axisymmetric and non-axisymmetric droplet bouncing

## TL;DR

This paper presents a solvable Lagrangian model for droplet bouncing that explains how asymmetries in shape and velocity influence contact time and the dynamics of non-axisymmetric bouncing, aligning qualitatively with experimental observations.

## Contribution

The paper introduces a new solvable model capturing both axisymmetric and asymmetric droplet bouncing, elucidating the role of surface tension and asymmetries in reducing contact time.

## Key findings

- Contact time decreases to a constant with increasing Weber number for axisymmetric drops.
- Asymmetries can lead to reduced contact time and elongated bounce shapes.
- Surface tension forces explain non-axisymmetric bouncing mechanisms.

## Abstract

We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in terms of surface tension forces. Once the drop has an elliptical footprint the surface tension force acting on the longer sides is greater. Therefore the shorter axis retracts faster and, due to the incompressibility constraints, pumps fluid along the more extended droplet axis. This leads to a positive feedback, allowing the drop to jump in an elongated configuration, and more quickly.