Height functions for applying contact angles to 2D VOF simulations

Abstract

SUMMARYRecent 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

Numerical investigation of elongated drops in a microfluidic T-junction

“…1,[9][10][11] These include level set methods, 12 phase field methods, 13,14 marker methods, 15 and VOF methods, [16][17][18] combined with spatial and temporal discretizations such as the boundary integral formulation, 19 finite elements, and finite differences. [20][21][22] A phase field method was developed in Ref.…”

“…The study includes the range of low capillary numbers that we address, but the presence of crossflow makes their analysis different from ours. Our results are obtained with an in-house code based on a VOF approach, 18,25,26 which provides a simple way for treating topological changes of the interface. We implement the "height function" ͑HF͒ methodology, which yields a consistent representation of surface tension force.…”

“…This enables an accurate computation of interface curvature, which converges with mesh refinement. 18,27,28 Thus, the VOF-HF method is one of the recent developments that has extended the applicability of the VOF method to surface tension dominant phenomena. Below, we briefly describe the implemented VOF-HF methodology in our numerical model.…”

Comparison between numerical models for the simulation of moving contact lines

“…For the transport of the interface, we give here some examples showing that almost all the classical methods are concerned: Boundary Integral methods [1][2][3], adaptive grid methods [4,5], Level-Set methods [6,7], Volume of Fluid methods [8][9][10], Front Tracking Methods [11,12] and coupled Level set and Volume-of-Fluid (CLSVOF) methods [13]. Different methods have also been developed for the modeling of moving contact lines.…”

“…The simplest situation is then to impose a constant angle corresponding to the static angle, i.e. h W ¼ h S [8,11,7,6,9]. When a no-slip condition is imposed on the wall, the stress generated by a contact line moving at velocity U cl , can be estimated as…”