【摘要】 粗糙界面上浸润现象在工业生产和日常生活中有很多应用.刻画粗糙界面上宏观接触角大小的经典Wenzel和Cassie公式被广泛使用,但关于其正确性有很多争议.本文主要介绍作者近几年对该问题所做的一些数学分析.从数学上讲,粗糙界面上浸润现象是一个具有多尺度边条件的自由界面问题.通过对该问题的不同模型做均匀化,本文显示经典公式在考虑系统全局极小时是成立的,而考虑局部极小点时,宏观接触角应由新的公式描述.本文还分析了实际应用中比较感兴趣的接触角滞后现象,推导出某些条件下接触角变化的方程.更多还原

【Abstract】 Wetting on rough surface is a common phenomenon in nature and our daily life. It has many applications in some industry processes, such as painting, printing, etc. Nevertheless, the theoretical understanding for wetting on rough surface is not complete. There are some controversies on some well-known formulae, such as the Wenzel and Cassie equations. In this paper, we review some mathematical analysis for this problem, including homogenization for wetting problem on rough surface and analysis for contact angle hysteresis. We show how mathematics helps us to understand the complicated wetting phenomenon.更多还原