Three-dimensional lattice Boltzmann simulations for droplet impact and freezing on ultra-cold superhydrophobic surfaces

Droplet impact and freezing on cold surfaces is a widely encountered multi-physical phenomenon involving droplet deformation and the liquid–solid phase change. Due to its complexity in nature, it is challenging to simulate the three-dimensional (3D) droplet impact and freezing process. Furthermore, due to the limitation of experimental techniques, it is not easy to experimentally investigate the impact of liquid droplets on ultra-cold superhydrophobic surfaces, which is crucial in some applications. Thus, in the present work, a 3D lattice Boltzmann (LB) method is developed to simulate the droplet impact and freezing on an ultra-cold superhydrophobic surface, in which an enhanced cascaded LB method is used to solve the multiphase flow field, and a multi-relaxation-time scheme is applied to solve the liquid–solid phase change model. The previous experimental results are numerically reproduced, proving that the present model can satisfactorily describe the droplet impact and solidification. The surface temperatures have no significant influence on droplet spreading. However, during the droplet retraction, a rim of ice first appears near the three-phase contact line, and then, the droplet bottom will completely solidify into ice. The occurrence of solidification at the bottom of the droplet will lead the droplet to break at a lower impact velocity, which can only be observed at a high Weber number on the room-temperature superhydrophobic surface. In addition, the effects of surface temperatures and Weber numbers on the evolution of spreading factors and space-averaged heat flux are also quantitatively analyzed in detail.