Wetting boundary scheme implemented in three-dimensional phase-field lattice Boltzmann model with large density ratios and complex solid boundaries

The phase-field lattice Boltzmann (LB) method is a powerful tool for simulating two-phase flows. However, for gas-liquid-solid systems with large density ratios, the accurate and systematic treatment of three-dimensional curved solid surfaces remains a challenge. In this work, we propose a wetting boundary scheme within the phase-field LB framework to address this problem. First, a phase-field LB model is developed for simulating multiphase flows with the density ratio up to 1000. Then, based on the free-energy approach, a method is introduced to determine the location of solid boundaries and their normal vectors. Finally, depending on the spatial position of the solid surface, the wetting condition is imposed using different interpolation schemes. The proposed method is validated through three benchmark cases: a droplet resting on a spherical surface, capillary rise in cylindrical tubes, and self-propelled droplet on conical fibers. Simulation results demonstrate that the method achieves high accuracy in both static and dynamic processes and is capable of handling arbitrarily complex curved surfaces in three-dimensional space. Moreover, to the best of our knowledge, two new power-law behaviors are observed in the third case, indicating the potential of the model for discovering novel wetting dynamics.