Analysis and Computations for Wetting Problem on Rough Surface

Xu,Xianmin
Institute of Computational Mathematics, CAS

2017-05-24 15:10-17:40 Teaching building No. 3 507


Abstract: Wetting on rough surfaces is common in nature and some industry applications. It is a two-phase flow problem with complicated boundary conditions. Mathematically, it can be modeled by a free interface problem in a domain with rough boundaries. In this talk, we will introduce some recent analysis and computations for this problem. We first show some multi-scale analysis for the problem. Basically, we derive a homogenized equation to describe the macroscopic contact angle on rough surface. The equation describes the local minimizers in the system and thus can be used to describe the contact angle hysteresis phenomena. Then we introduce a volume preserving thresholding dynamics method for this problem. The method is simple, stable and very efficient. In each iteration, only one or two convolution operations for functions defined in a regular domain are needed. This can be done easily by fast algorithms. Finally, we will discuss recent work on simulations for two-phase flow with complex boundary conditions.