Generalised Navier boundary condition for a volume of fluid approach using a finite-volume method

In this work, an analytical volume of fluid implementation of the generalised Navier boundary condition is presented based on the Brackbill surface tension model. The model is validated by simulations of droplets on a smooth surface in a planar geometry. Looking at the static behavior of the droplets, it is found that there is a good match between the droplet shape resolved in the simulations and the theoretically predicted shape for various values of the Young's angle. Evaluating the spreading of a droplet on a completely wetting surface, the Voinov-Tanner-Cox law (theta proportional to Ca-1/3) can be observed. In addition, the scaling of the droplet radius as a function of time follows r proportional to t(1/2), suggesting that spreading is limited by inertia. These observations are made without any fitting parameters except the slip length. Published under license by AIP Publishing.