Lattice Boltzmann modelling of droplet impact and splashing at high Reynolds and Weber numbers

We developed a two-phase lattice Boltzmann model by coupling the entropic multiple-relaxation-time (EMRT or KBC) collision operator enabling low fluid viscosity, with a source term (Wang et al. 2022, Phys. Rev. E vol. 105, no 4) to independently adjust surface tension. The coupling is implemented via the exact difference method (EDM), which allows full consideration of external-force effects on the entropic stabiliser in KBC, in contrast to the recent work of Wang et al. (2022 Phys. Rev. E vol. 105) and Xu et al. (2024 Comput. Math. Appl . vol. 159, 92–101). More importantly, we address a major drawback of the EDM by explicitly demonstrating how its high-order error terms influence the pressure tensor and surface tension. Using the developed model, we investigated droplet impact and splashing on a thin liquid film at a remarkably high Weber number of ${\textit{We}} = 5000$ and Reynolds number of ${\textit{Re}} = 5000$ . Droplet impact and splashing on flat surfaces and mesh structures at very high ${\textit{Re}}$ (15 200) and ${\textit{We}}$ (1020) are also studied after validating four representative cases against experiments. For droplet impact on flat surfaces, hydrophobicity promotes the growth of peripheral instabilities, leading to fingering splashing. Corona splashing transitions to fingering splashing as the liquid–gas viscosity ratio increases. For droplet impact on mesh structures, large openings promote liquid penetration, whereas small openings enhance spreading. As the solid ratio increases, the maximum spreading ratio increases monotonically but nonlinearly, whereas the maximum penetrated liquid pillar length first rises and then drops. These simulations demonstrate the proposed model offers significant advantages for accurately capturing and elucidating complex droplet impact and splashing dynamics at high ${\textit{Re}}$ and ${\textit{We}}$ .