Lubrication-mediated rebounds off fluid baths

TL;DR

This paper develops a lubrication-mediated quasi-potential model to simulate droplet rebounds off liquid baths, offering a computationally efficient alternative to DNS and capturing micro-scale lubrication effects.

Contribution

The paper introduces a novel lubrication-mediated model for droplet rebounds, bridging micro-scale lubrication physics with macro-scale impact dynamics.

Findings

The LM model accurately matches experimental data in low-speed impacts.

It is significantly more computationally efficient than direct numerical simulations.

The model reveals detailed behavior within the thin lubrication layer.

Abstract

We present herein the derivation of a lubrication-mediated (LM) quasi-potential model for droplet rebounds off deep liquid baths, assuming the presence of a persistent dynamic air layer which acts as a lubricating pressure transfer. We then present numerical simulations of the LM model for axisymmetric rebounds of solid spheres and compare quantitatively to current results in the literature, including experimental data in the low speed impact regime. In this regime the LM model has the advantage of being far more computationally tractable than DNS and is also able to provide detailed behaviour within the micro-metric thin lubrication region. The LM system has an interesting mathematical structure, with the lubrication layer providing a free boundary elliptic problem mediating the drop and bath free-boundary evolutionary equations.