A three-dimensional numerical scheme for modeling discontinuous pinning at sharp edges using the Volume-of-Fluid method

Abstract

We present a novel three-dimensional (3D) numerical scheme for modeling the discontinuous contact line pinning along sharp straight edges. The proposed scheme is devised for multi-phase flow solvers that rely on the Volume-of-Fluid (VOF) method, although its fundamental concepts can be extended and applied to other methods. Following the Piecewise-Linear-Interface-Construction (PLIC) approach in VOF, the discontinuous pinning is modeled by adjusting the orientation of PLIC polygons located near a sharp edge according to the pinning stage. That is achieved by solving a root-finding problem and using a 3D geometrical toolbox, where the advancing contact angle determines critical volume fractions in numerical cells neighboring the sharp edge. Implementing the proposed scheme in our multi-phase flow solver, we assessed its performance using several test cases where contact line pinning effects dominate. To demonstrate the scheme's efficacy, we present quantitative comparisons of our results at various grid resolutions and with a theoretical study. Furthermore, we show quantitatively that without a numerical treatment of contact line pinning, the simulation results will be drastically different. Contact line pinning plays a critical role in several technologies including separation, lithography, lens fabrication, micro-fluidic flow control among numerous others. The proposed scheme will help to accurately capture the pinning effects in computational simulations of such applications.