---
abstract: 'In this work, an analytical Volume Of Fluid (VOF) implementation of the Generalized 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 ($\theta \propto {\text{Ca}}^{1/3}$) can be observed. At later times scaling follows $r \propto t^{1/2}$, suggesting spreading is limited by inertia. These observations are made without any fitting parameters except the slip length.'
author:
- 'A.M.P. Boelens'
- 'J.J. de Pablo'
title: 'Generalized Navier Boundary Condition for a Volume Of Fluid approach using a Finite-Volume method.'
---

Introduction
============

For any multi-phase flow over a wall where dissipation at the contact line becomes of the same order as the bulk dissipation, a good understanding of contact line behavior is essential [@squires2005]. However, despite many investigations [@dussan1979; @degennes1985; @deconinck2008; @eral2013], for applications including adhesion of liquids to a 