Growth and instability of the liquid rim in the crown splash regime

TL;DR

This study combines numerical simulations and linear stability theory to analyze the formation, growth, and breakup of liquid rims in crown splash regimes, providing scaling laws and predictions aligned with experimental data.

Contribution

It introduces a comprehensive approach integrating simulations and stability analysis to predict droplet formation in splash phenomena, advancing understanding of instability mechanisms.

Findings

Simulations match high-speed X-ray imaging profiles.

Predicted most unstable wavelengths agree with experiments.

Deceleration enhances rim instability leading to droplet formation.

Abstract

We study the formation, growth, and disintegration of jets following impact of a drop on a thin film of the same liquid for We < 1000 and Re < 2000 using a combination of numerical simulations and linear stability theory (Agbaglah et al. 2013). Our simulations faithfully capture this phenomena and are in good agreement with experimental profiles obtained from high-speed X-ray imaging.We obtain scaling relations from our simulations and use these as inputs to our stability analysis. The resulting prediction for the most unstable wavelength are in excellent agreement with experimental data. Our calculations show that the dominant destabilizing mechanism is a competition between capillarity and inertia but that deceleration of the rim provides an additional boost to growth. We also predict over the entire parameter range of our study the number and timescale for formation of secondary droplets formed during a splash, based on the assumption that the most unstable mode sets the droplet number.