Maximum spreading of droplets impacting spherical surfaces

Experimental observations, numerical simulations, and theoretical analysis are conducted to investigate the impacting dynamics of water droplets on spherical surfaces. A volume of fluid numerical model coupled with a dynamic contact angle model with consideration of the gravity effect is established and validated by comparing the evolutions of droplet profiles and spreading factors obtained from the simulations and the experiments in both the present work and literature. The effects of the Weber number, contact angle, and sphere-to-droplet diameter ratio (D*) on the droplet impacting on a spherical surface are further studied by numerically calculating the spreading factor and the spreading arc angle corresponding to the two-dimensional wetting arc at the maximum spreading state. The results indicate that both the maximum spreading factor and arc angle increase with increasing Weber number and reducing contact angle. When the sphere-to-droplet diameter ratio is reduced, the maximum spreading factor remains almost unchanged for D*≳10 but it shows a significant increase for D*10. The maximum spreading arc angle keeps going up with reducing diameter ratio under all conditions even for D*≳10. As the Weber number increases and the contact angle decreases, the effect of the diameter ratio on the maximum spreading becomes more conspicuous. Based on the energy conservation, a theoretical model considering the gravity effect is developed to describe the maximum spreading factor of an impacting droplet on a spherical surface. The maximum spreading factors obtained from the theoretical model yield a deviation of ±15% as compared with those from the experiments and simulations.