本文選題：浸潤(rùn)現(xiàn)象 + 均勻化��； 參考：《中國(guó)科學(xué):數(shù)學(xué)》2017年12期

【摘要】：粗糙界面上浸潤(rùn)現(xiàn)象在工業(yè)生產(chǎn)和日常生活中有很多應(yīng)用.刻畫粗糙界面上宏觀接觸角大小的經(jīng)典Wenzel和Cassie公式被廣泛使用,但關(guān)于其正確性有很多爭(zhēng)議.本文主要介紹作者近幾年對(duì)該問題所做的一些數(shù)學(xué)分析.從數(shù)學(xué)上講,粗糙界面上浸潤(rùn)現(xiàn)象是一個(gè)具有多尺度邊條件的自由界面問題.通過對(duì)該問題的不同模型做均勻化,本文顯示經(jīng)典公式在考慮系統(tǒng)全局極小時(shí)是成立的,而考慮局部極小點(diǎn)時(shí),宏觀接觸角應(yīng)由新的公式描述.本文還分析了實(shí)際應(yīng)用中比較感興趣的接觸角滯后現(xiàn)象,推導(dǎo)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(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院計(jì)算數(shù)學(xué)研究所;中國(guó)科學(xué)院大學(xué)數(shù)學(xué)科學(xué)學(xué)院;香港科技大學(xué)數(shù)學(xué)系;
【基金】：科學(xué)與工程計(jì)算國(guó)家重點(diǎn)實(shí)驗(yàn)室(LSEC) 中國(guó)科學(xué)院國(guó)家數(shù)學(xué)與交叉科學(xué)中心(NCMIS) 國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):11571354,16302715和16324416) 香港研究資助局(批準(zhǔn)號(hào):N-HKUST620/15)資助項(xiàng)目
【分類號(hào)】：O647.1
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本文編號(hào)：1831512