  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 ($\theta^{eq}$) 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 $\theta^{eq}$ 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.
