A Compact-Stencil Wetting Boundary Condition for Three-Dimensional Curved Surfaces in a Phase-Field Lattice Boltzmann Method

Accurate numerical reproduction of contact line dynamics on three-dimensional curved solid surfaces remains a challenging issue in multiphase flow simulations. In this study, a wetting boundary condition applicable to curved surfaces is developed within a three-dimensional phase-field lattice Boltzmann framework. The proposed method extends an existing curved-surface wetting model and focuses on improving the evaluation of interface normals and order-parameter gradients on Cartesian lattices, while preserving the compact computational stencils and efficiency inherent to the lattice Boltzmann method. Three-dimensional simulations of liquid spreading on a concave spherical surface and droplet spreading on a convex solid sphere are performed over a wide range of prescribed contact angles. The results show that the proposed method eliminates nonphysical behaviors observed with conventional staircase-based boundary conditions, such as droplet sliding along the solid surface and droplet detachment into the surrounding gas phase. In the convex spherical surface cases, the droplet height converges stably to equilibrium through damped oscillations, and the equilibrium droplet shapes show good agreement with theoretical predictions derived from geometric considerations under zero-gravity conditions over a broad range of contact angles. These results demonstrate that the proposed wetting boundary condition can accurately reproduce wetting phenomena on three-dimensional curved solid surfaces.