Height functions for applying contact angles to 2D VOF simulations

Recent work on a consistent representation of surface tension and on the accurate computation of interface curvature has extended the applicability of the volume-of-fluid, or VOF, method to surface tension-driven phenomena. We have extended these methodologies to interfaces near solid surfaces; specifically, we show how height functions can be used to enforce a contact angle boundary condition at a contact line, for the full range of contact angles. As such, this work may be viewed as following up on the methodology of Renardy et al. (J. Comput. Phys. 2001; 171:243-263). This approach yields accurate values of curvature and the surface tension force at contact lines, values that converge with mesh refinement. The efficacy of the methodology is demonstrated using 21) examples of static fluid configurations in equilibrium and dynamic contact line phenomena that approach known equilibrium configurations. Copyright (C) 2007 John Wiley & Sons, Ltd.