Spreading dynamics of a droplet impacting a sphere

Abstract

In nature, high-speed rain drops often impact and spread on curved surfaces, e.g., leaves and animal bodies. Although a drop's impact on a surface is a traditional topic for industrial applications, drop-impact dynamics on curved surfaces are less known. 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 spreads farther than one on a flat surface. To further 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 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.