An improved threshold dynamics method for wetting dynamics

Abstract

We propose a modified threshold dynamics method for wetting dynamics, which significantly improves the behavior near the contact line compared to the previous method (J. Comput. Phys. 330 (2017) 510–528). The new method is also based on minimizing the functional consisting of weighted interface areas over an extended domain including the solid phase. However, each interface area is approximated by the Lyapunov functional with a different Gaussian kernel. We show that a correct contact angle (Young's angle) is obtained in the leading order by choosing correct Gaussian kernel variances. We also show the Gamma convergence of the functional to the total surface energy. The method is simple, unconditionally stable with O(NlogN) computational complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid surface. It is also shown that the dynamics of the contact point is consistent with the dynamics of the interface away from the contact point. Numerical examples have shown significant improvements in the accuracy of the contact angle and the hysteresis behavior of the contact angle.