Energy-Based Modeling of Wetting and Contact Angle Hysteresis in a Conservative Diffuse Interface Framework

Abstract

Wetting dynamics and moving contact lines remain difficult to simulate in computational fluid mechanics, despite their importance in applications such as aerospace, bioprinting, and advanced coatings. Both the interface model and the wall boundary treatment strongly influence the results. Among interface-capturing methods, the Conservative Diffuse Interface (CDI) model offers computational efficiency and mass conservation. But it also has a basic limitation: its second-order structure permits only a single boundary condition at solid walls, so enforcing both mass conservation and a prescribed contact angle is not straightforward. Existing approaches address this only partially. Some restore mass conservation only at the global level, others rely on arbitrarily defined slip parameters, and geometric formulations become thermodynamically inconsistent at extreme contact angles. Therefore, a thermodynamically consistent treatment of wetting and contact angle hysteresis within the CDI framework remains limited. To address this, an energy-based wall boundary condition is developed within the CDI framework. It is implemented through a local momentum balance in the near-wall region. Contact Angle Hysteresis (CAH) is incorporated through advancing and receding angle thresholds. This allows the model to capture contact-line pinning and stick–slip behavior on non-ideal surfaces. The governing equations are solved in the in-house solver GenIDLEST on a collocated grid using the fractional-step method. The model is validated against analytical solutions, and three-dimensional droplet impact experiments. These cases cover contact angles from θ = 31° to θ = 156°. Across this range, the model reproduces hydrophilic spreading, hydrophobic recoil, and complete droplet rebound. It also reproduces contact-line pinning and depinning in good agreement with theoretical predictions. Mass conservation is maintained throughout the simulations. In the hydrophobic impact case, the total mass loss is only 0.058%.