Spreading dynamics of a droplet impacting a sphere

TL;DR

This study investigates how droplets spread on curved hydrophobic surfaces, developing a new analytical model that accurately predicts spreading behavior and extends understanding of natural droplet impacts.

Contribution

A novel analytical model for droplet spreading on curved surfaces is introduced, integrating volume conservation and energy balance, and validated against experimental data.

Findings

Droplets spread farther on curved surfaces than on flat ones.

The new model aligns well with experimental measurements across various conditions.

Droplet impact dynamics are better understood through the proposed analytical approach.

Abstract

In nature, high-speed rain drops often impact and spread on curved surfaces e.g. tree leaves. Although a drop impact on a surface is a traditional topic for industrial applications, drop-impact dynamics on curved surfaces in natural situations are less known about. In the present study, we examine the time-dependent spreading dynamics of a drop onto a curved hydrophobic surface. We also observed that a drop on a curved surface is spreads farther than one on a flat surface. To understand the spreading dynamics, a new analytical model is developed based on volume conservation and temporal energy balance. This model converges to previous models at the early stage and in the final stage of droplet impact. We compared the new model with measured spreading lengths on various curved surfaces and impact speeds, which resulted in good agreement.