Geometrical wetting boundary condition for complex geometries in lattice Boltzmann color-gradient model

A wetting boundary condition for dealing with moving contact lines on complex surfaces is developed in the lattice Boltzmann color-gradient model. The wetting boundary condition is implemented by combining the geometrical formulation of contact angle and the idea of the prediction-correction wetting scheme, which not only produces the desired contact angles with high accuracy but also avoids the necessity to select an appropriate interface normal vector from multiple solutions that satisfy the contact angle condition. Through the implementation in the framework of color-gradient model, the developed wetting boundary condition is validated against analytical solutions by a series of benchmark cases, including a droplet resting on a cylindrical surface and on a tilt wall, a liquid film migrating between two parallel plates, and the forced imbibition into a pore doublet. The simulation results of static contact angles show that the wetting boundary condition is able to simulate arbitrary values of contact angle and leads to negligible mass leakage across the boundary. For dynamic problems, the wetting boundary condition is found to correctly capture the imbibition dynamics under various flow and viscosity ratio conditions and produce dynamic contact angles that match well with the Cox-Voinov law.