Phase-field model for quantitative analysis of droplet wetting

A general phase-field formalism is presented, aimed at capturing the excess surface energies and geometric profiles of three-dimensional, asymmetric liquid droplets on solid surfaces. To ensure strict volume conservation of the droplet, a nonlinear definition is employed for the internal volume. To facilitate modeling in systems where the interface widths approach zero, an extrapolation method is proposed to interpret data obtained at finite interface widths. The numerically tractable algorithm yields accurate predictions for the excess surface energies and state diagrams of known wetting configurations on both the external and internal surfaces of cylinders, demonstrating quantitative agreement with established results from other models and computational techniques.