Unveiling crown-finger instability of a non-spherical drop impacting a liquid surface

TL;DR

This study uses 3D simulations to explore how non-spherical droplet shapes affect splash dynamics upon impact, revealing shape-dependent impact regimes, instability mechanisms, and the predictive role of combined Rayleigh-Plateau and Rayleigh-Taylor instabilities.

Contribution

It introduces a comprehensive numerical analysis of non-spherical droplet impacts, linking droplet shape to impact regimes, crown formation, and instability mechanisms, with a stability model predicting finger formation.

Findings

Droplet shape significantly influences impact dynamics and splash regimes.

Higher Weber numbers promote hole instability from lamella rupture.

Rayleigh-Plateau instability primarily determines crown finger number and wavelength.

Abstract

We present a three-dimensional numerical study of the splashing dynamics of non-spherical droplets impacting a quiescent liquid film, covering a wide range of aspect ratios (Ar) and Weber numbers (We). The simulations reveal distinct impact dynamics, such as spreading, splashing type-1, splashing type-2, and canopy formation, which are delineated in a regime map constructed in the Ar-We parameter space. Our results demonstrate that droplet morphology during the impact significantly influences crown evolution and splash initiation, with oblate drops promoting finger growth and fragmentation due to enhanced rim deceleration, while prolate drops tend to form canopies. We observe that the hole instability, which becomes more prominent at higher Weber numbers, arises from lamella rupture in the thinnest region of the film, located just beneath the crown rim. A linear stability analysis, supplemented by the temporal evolution of the crown obtained from the numerical simulations, adequately predicts the number of fingers formed along the crown rim by accounting for both Rayleigh-Plateau (RP) and Rayleigh-Taylor (RT) instabilities. The theoretical analysis demonstrates the dominant role of the Rayleigh-Plateau instability in determining the number and wavelength of early undulations, with the Rayleigh-Taylor instability serving to amplify the growth rate of the disturbances. Our findings highlight the critical role of the droplet shape in splash dynamics, which is relevant to a range of applications involving droplet impact.