An efficient threshold dynamics method for wetting on rough surfaces

TL;DR

This paper introduces an efficient volume-preserving threshold dynamics method for simulating wetting phenomena on rough surfaces, overcoming limitations of previous methods in handling boundary interactions and surface roughness.

Contribution

It develops a novel, stable, and computationally efficient method based on minimization of a weighted surface area functional over an extended domain.

Findings

Method is simple and stable

Achieves $O(N \,\log N)$ complexity per step

Insensitive to boundary roughness and inhomogeneity

Abstract

The threshold dynamics method developed by Merriman, Bence and Osher (MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary. Direct generalization of MBO-type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original MBO method. The dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary. In this paper, we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces. This method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase. The method is simple, stable with $O(N \log N)$ complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary.