Dynamic behavior and maximum spreading of droplets impacting concave spheres

Droplet impact is omnipresent in nature and industry, and it is affected by the surface shape. Here, experiments, simulations, and theoretical analyses are conducted to explore the impact behaviors of water droplets on the concave spheres, especially the maximum spreading. The simulation model using the volume of fluid method is validated by comparing the temporal droplet profiles and spreading factors yielded by the simulation and experiment. The effects of the Weber number, contact angle, and sphere-to-droplet diameter ratio on the maximum spreading are exhaustively investigated. The results indicate that both the maximum spreading factor and arc angle increase with the increase in the Weber number and the decrease in the contact angle. The maximum spreading factor and area on the concave sphere generally first increase slightly and then decrease with the reduction in the diameter ratio owing to the combined action of the gravity and the surface shape. As the diameter ratio decreases, the maximum spreading arc angle increases and the maximum diameter of the contact line decreases. For a fixed diameter ratio, the droplet generally spreads less on a concave surface than on a convex one. Based on the energy conservation, a theoretical model is further established to predict the changing trend of the maximum spreading factor with the Weber number, contact angle, and diameter ratio, which yields a ±15% deviation over 93% of all the data points. This work may deepen our understanding of the mechanism of droplet impact on concave spheres and contribute to the associated applications.