Fate of Secondary Droplets Produced by High-speed Raindrops Interacting with a Liquid Pool

TL;DR

This study uses direct numerical simulations to analyze how high-speed raindrops interacting with a liquid pool generate secondary droplets, revealing a new scaling law for droplet size distribution and detailed interaction dynamics.

Contribution

The paper introduces a novel scaling law for secondary droplet size distribution and provides detailed insights into the interaction stages and breakup mechanisms during raindrop-liquid pool impacts.

Findings

Secondary droplet size distribution scales as $N_d(r_s) \,\propto\, r_s^{-5/2}$.

Normalized distributions from different parameters collapse onto a single curve.

Impact morphology analysis identifies distinct interaction stages and central liquid film formation.

Abstract

Secondary droplets produced by interactions between falling fluid drops and a liquid pool play a significant role in engineering applications and geophysical processes in nature. This study uses direct numerical simulations to investigate the dynamics of secondary droplets generated by raindrop-liquid pool interactions, with varying parameters including the number of raindrops, their diameters, surface tension, and inter-raindrop distance. The secondary droplet size distribution, $N_d$, is found to scale with the droplet radius, $r_s$, as $N_d(r_s)\propto r_s^{-5/2}$, with additional dependencies on surface tension and raindrop diameter. When normalized according to this new scaling law, the $N_d(r_s)$ obtained from simulations with different parameter values collapses onto a single curve. Analysis of the impact morphology reveals distinct stages of raindrop interactions and identifies the formation and breakup of a central liquid film. Spatial and temporal analyses of the secondary droplets show that raindrop interaction can influence both the percentage of droplets captured by the cavity and the duration over which they re-merge with the pool. These behaviors arise from the combined effects of differences in the birth times of secondary droplets of various sizes and cavity secondary flows modulated by the central liquid film.