Volume-filtered Surface Forces for the Simulation of Contact Lines

Although contact lines are present in many industrial processes, there is no universal agreement how to implement these singularities in numerical simulations. Often a dynamic contact-angle law is applied with a slip boundary condition at the contact line. However, most slip boundary conditions require realistic slip lengths much smaller than the largest length scale. At a sufficient numerical grid resolution, this multi-scale problem have a prohibitive computational expense. In this study, volume-averaged source terms are constructed for both a contact-angle restoring surface force and the viscous dissipation in the vicinity of the contact line. Closure terms are proposed for the unresolved slip length scales. Unlike previous studies, no a-priori angle relation is applied and the contact angle evolves naturally from the explicitly represented physics. Simulations of fluid displacement in a channel and droplet spreading are demonstrated with this new framework.