A coupling VOF/embedded boundary to model arbitrary contact angles on solid surfaces

Two-phase flows in presence of solid boundaries are present in numerous natural environment and industrial applications. In the past decades, a lot of experimental and numerical studies has been carried out to deal with the dynamics of the contact angles at the triple point between the two fluids and the solid. From a numerical point of view, there is still a remaining challenge for the triple point computation depending on the tracking interface method (VOF, level-set...) used  and how the solid surface is taken into account (boundary conditions...) for the contact angle imposition. 

A numerical methodology is presented here for simulating contact angles on solid surfaces. We use the Basilisk solver where a 2nd order conservative cartesian embedded boundary method is used to tackle with solid geometries. The fluid-fluid interface is tracked by a conservative volume of fluid VOF method. In our method, an apparent contact angle is implicitly imposed by setting the right conditions in ghost fluid cells in the embed solid.  The developed methodology is validated in different test cases with several geometry shapes including the droplet on a fiber. The results obtained show that the present method works well and stay robust in a wide range of contact angles and geometry configurations.