An Adaptive Threshold Dynamics Method for Three-Dimensional Wetting on Rough Surfaces

Abstract

We propose an adaptive threshold dynamics method for wetting problems in three space dimensions. The method is based on solving a linear heat equation and a thresholding step in each iteration. The heat equation is discretized by a cellcentered finite volume method on an adaptively refined mesh. An efficient technique for volume conservation is developed on the nonuniform meshes based on a quicksorting operation. By this method, we compute some interesting wetting problems on complicated surfaces. Numerical results verify some recent theory for the apparent contact angle on rough and chemically patterned surfaces. AMS subject classifications: 65M08, 65M50, 76T10