Numerical and Theoretical Modeling of Droplet Impact on Spherical Surfaces

Abstract

Droplet impact on solid surfaces is a fluid phenomenon widely involved in additive manufacturing, heat management, and coating, in which the ability to exert control over the impact dynamics and duration is critical. While past studies have established a comprehensive understanding of the impact on flat substrates, what we know about the impact dynamics on curved solid surfaces is still limited. This work aims to elucidate the physics of droplet impact on spherical surfaces with different Weber numbers ($We$), radii ($R_s$), and surface wettability ($θ^{eq}$) using a combination of axisymmetric lattice Boltzmann method (LBM) and theoretical analysis. The model developed in our previous work [H. Dalgamoni and X. Yong, Phys. Rev. E 98, 13102 (2018)] was extended and modified for simulating the normal impact of droplet on curved substrates in the low Weber number regime (i.e., $We \leq 15$), in which axisymmetric assumption of droplet deformation holds. The LBM simulations show that $We$, $R_s$, and $θ^{eq}$ significantly affect the spreading and recoiling of droplet during impact. The parametric studies uncover five outcomes of impact, which range from complete deposition to total rebound. A simulation-predicted phase diagram was constructed and correlated with the total time that the droplet was in contact with the solid. In addition, a theoretical model based on energy budget during impact was developed to predict the rebound threshold for impact on spherical targets when varying We, and independently, which agrees well with simulation observations. These findings provide fundamental insight into surface structure design for controlling droplet hydrodynamics and the contact time during impact.