本文選題：浸潤現象 + 均勻化　； 參考：《中國科學:數學》2017年12期

【摘要】：粗糙界面上浸潤現象在工業(yè)生產和日常生活中有很多應用.刻畫粗糙界面上宏觀接觸角大小的經典Wenzel和Cassie公式被廣泛使用,但關于其正確性有很多爭議.本文主要介紹作者近幾年對該問題所做的一些數學分析.從數學上講,粗糙界面上浸潤現象是一個具有多尺度邊條件的自由界面問題.通過對該問題的不同模型做均勻化,本文顯示經典公式在考慮系統(tǒng)全局極小時是成立的,而考慮局部極小點時,宏觀接觸角應由新的公式描述.本文還分析了實際應用中比較感興趣的接觸角滯后現象,推導出某些條件下接觸角變化的方程.
[Abstract]:The phenomenon of infiltration on the rough interface has many applications in industrial production and daily life. The classical Wenzel and Cassie formulae for describing the size of the macroscopic contact angle on the rough interface are widely used, but there are many disputes about its correctness. This paper mainly introduces some mathematical analysis on the problem in recent years. The phenomenon of surface infiltration is a free interface problem with multi-scale boundary conditions. By homogenizing the different models of the problem, this paper shows that the classical formula is established in the consideration of the system global extreme hours, and the macro contact angle should be described by the new formula when considering the local extreme small points. The contact angle hysteresis phenomenon is interesting, and the equation of contact angle variation under certain conditions is derived.

【作者單位】： 中國科學院數學與系統(tǒng)科學研究院計算數學研究所;中國科學院大學數學科學學院;香港科技大學數學系;
【基金】：科學與工程計算國家重點實驗室(LSEC) 中國科學院國家數學與交叉科學中心(NCMIS) 國家自然科學基金(批準號:11571354,16302715和16324416) 香港研究資助局(批準號:N-HKUST620/15)資助項目
【分類號】：O647.1
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本文編號：1831512