Accurate contact angle boundary conditions for the Cahn–Hilliard equations

The contact angle dynamics between a two-phase interface and a solid surface is important in physical interpretations, mathematical modeling, and numerical treatments. We present a novel formulation based on a characteristic interpolation for the contact angle boundary conditions for the Cahn–Hilliard equation. The new scheme inherits characteristic properties, such as the mass conservation, the total energy decrease, and the unconditionally gradient stability. We demonstrate the accuracy and robustness of the proposed contact angle boundary formulation with various numerical experiments. The numerical results indicate a potential usefulness of the proposed method for accurately calculating contact angle problems.