A 3D sharp and conservative VOF method for modeling the contact line dynamics with hysteresis on complex boundaries

Abstract

We propose a sharp and conservative 3D numerical method for simulating moving contact lines on complex geometries, developed within a coupled geometric Volume-of-Fluid (VOF) and embedded boundary framework. The first major contribution is a modified VOF advection and reconstruction scheme specifically designed for mixed cells containing liquid, gas, and solid phases. This formulation ensures strict local mass conservation in the presence of arbitrarily shaped embedded boundaries. To overcome the severe time-step limitation caused by small cut cells, a redistribution advection strategy is introduced, which completely removes the CFL constraint while preserving both local and global volume conservation. The second key contribution is a novel 3D contact angle imposition technique built upon the height function framework. By incorporating a pre-fitting paraboloid procedure, the method achieves robust curvature estimation and accurate enforcement of contact angle conditions on irregular solid surfaces. In addition, contact angle hysteresis is modeled to capture more realistic wetting dynamics. A series of challenging benchmark tests have been conducted to demonstrate the accuracy, robustness, and superiority of the proposed method compared with existing sharp-interface approaches. This study, for the first time, establishes a fully geometric and conservative VOF-based scheme capable of accurately resolving contact line dynamics on arbitrarily complex 3D surfaces.