臺灣博碩士論文加值系統

　　本論文是以分子動力理論(Molecular dynamics MD)來研究平板上液膜及自由液膜的三維動態破裂行為，所模擬之破裂過程包含兩個階段(1)由起始之平衡狀態至破裂發生，(2)從破裂發生至最終的破裂狀態。採用分子動力法的理由在於此種方法論除了可以避免連體理論處理上的困難外，更可以提供許多破裂過程中無法從巨觀理論得知的微觀細節。此兩種液膜系統之勢能模式皆採用12-6之Lennard-Jones勢能模型，其分子間作用力遵循牛頓第二運動定律，當系統於初始平衡後，我們給予系統一微小擾動而使其進入非平衡狀態，藉由持續地對系統之總動能加以重新修正，使系統在設定的溫度下運動，在薄膜破裂後，我們仍繼續對系統加以計算直到形成最終之破裂狀態，所有過程中並同時量測破洞的擴散速率及平板上固一液間的動態接觸角。為了能與巨觀理論所預測之結果作比較，我們調整不同之勢能參數來探討其對於液膜破裂的影響。為了縮短計算時間，我們採取截斷勢能概念及Gear之五階數值方法來預測分子於任一時刻之位置及速度，並運用統計熱力學理論直接求得系統之巨觀物理量，如溫度、壓力、表面張力等。研究發現，加強液─液間的勢能會加快液膜系統的破裂速度，而對平板上之液膜而言，若其固─液間之勢能變得愈小，則不但會加快液膜破裂速度，而且破洞之擴散速率及其與固─液間之動態接觸角也隨之變大。就第一階段之破裂過程而言，本文所模擬之結果在定性上與巨觀破裂理論所預測之結果相似，但就第二階段破裂過程而言，本文所預測之內容則是釐清液膜破裂後及巨觀理論所難以處理之動態發展的過程。

　　The three-dimensional dynamic rupture behaviors of liquid film on plate and free liquid film are studied with molecular dynamics theory (MD) in this paper. Two stages in the simulated rupture process will be shown: (1) From the state of beginning equilibrium to the one of rupture occurred. (2) From the occurred to the latest state. The reason we use molecular dynamics is not only to avoid the difficulty that macroscopic theory cannot figure out but also to provide many microscopic details which we cannot get from macroscopic theory. The 12-6 Lennard-Jones potential model is adopted in the potential models of these two liquid-film system. The interactions among molecules obey Newton's 2nd law. When the system was in beginning equilibrium, we gave system a tiny perturbation and make it into nonequilibrium state. By continuously correcting total energy, we let the system move in the temperature which we previously set. After thin film being ruptured, this system was still calculated until formed the latest rupture state. At the same time we measured hole's diffusion rate and the dynamic contact angle between solid and liquid phase on the plate. For comparing with the result predicted by macroscopic theory, we adjusted various potential parameters to discuss the influence of those parameters on liquid-film rupture. In order to shorten calculation time, the conception of cutoff potential and the Gear's 5th order numerical method were used to predict every molecule's position and speed in any time. Statistical thermodynamic theory was also used to directly figure out the macroscopic physical values such as temperature, pressure and surface tension etc. It is found that strengthening the potential between liquid and liquid phase will quicken the rupture speed. On the other hand, if the liquid film potential between solid and liquid phase on plate was getting smaller, the rupture speed would not only be quicken but the hole's diffusion rate and the dynamic contact angle between the film and the interface of liquid and solid phase would be getting bigger. As the rupture process in first stage, the result which we simulated is similar to the one predicted by macroscopic rupture theory in qualitative analysis. But as the second stage, the contents predicted in our paper is to figure out the dynamic evolution process which is occurred after the rupture of liquid film but difficult to describe by macroscopic theory.