含有表面活性剂的多相流液滴浸润问题近年来成为众多领域的一个热门研究问题。它在材料科学，尤其是纳米材料科学研究和制造中起着至关重要的作用。移动接触线是液滴浸润问题中的一个重点和难点，它的数学模型和计算逐渐成为这个领域的核心问题。本项目针对含有可溶性表面活性剂的一类液滴浸润问题，从能量原理的角度进行数学建模，拟提出扩散界面和尖锐界面两类数学模型，并从数学上分析两类模型之间的关系，提供模型的理论依据。对于模型计算，项目拟采取自由边界问题的经典数值方法，应用于此问题并进行改进，把水平集法与界面追踪方法复合应用，建立快速且稳定的数值计算方法并推广至并行计算版本，实现模型的仿真结果和实验的精细对比，从而保证模型的实用性和可靠性，为该交叉领域的研究提供数学基础。

Wetting problem in multiphase flow with surfactant has been a hot topic in many research areas recently. It plays an important role in nano science and technology. Moving contact line problem is an essential and difficult part of the wetting problem. Its modeling and computation have been a key problem in the research. This project aims to propose two types of models for the wetting problem with soluble surfactant from the consideration of energy principle: diffuse interface and sharp interface models. Their relation is mathematically analyzed. Numerically, the classical methods for free boundary problems are used and implemented for this kind of wetting problem. A hybrid method combining level-set and front tracking methods shall be proposed. The project will propose fast, efficient and stable numerical schemes for simulations and do parallel computation for comparison of the models and experiments. Mathematically the reliability of the model shall be established.