Volume-conserving method for dynamic contact line on complex surfaces

In this study, we aim to improve the volume conservation of the interface advection method and the behavior of the triple point at small contact angles on arbitrary solid surfaces in a framework where volume-of-fluid methods and embedded solid representations are used to describe fluid and solid domains. We present a method with improved volume-conservation properties allowing for general solid boundaries. The method calculates the exact advected volume while accounting for the solid presence. In cases without solids, the existing method already maintains very good conservation. For configurations involving small contact angles, the solution focuses on accurately locating the triple point by identifying the intersection of the solid surface with the gas–liquid interface. To validate our approach, we tested the method with a relaxing sessile drop on both flat and cylindrical surfaces. Results demonstrate a significant improvement in accuracy, with a relative mass error reduced from 14% to 0.02%, and precise contact angles successfully achieved in the range of 5° to 165°.