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研究生: 林克承
Lin, Ko-Chen
論文名稱: 分子動力學於微系統流場行為探討
Molecular Dynamics Simulation of Micro-System Flow Field
指導教授: 楊瑞珍
Yang, Reuy-Jen
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2005
畢業學年度: 93
語文別: 中文
論文頁數: 102
中文關鍵詞: 分子動力學孔穴流
外文關鍵詞: Molecular Dynamics, Cavity flow
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  •   近十年來微電子機械系統的加工與應用已有了巨大進展,已經能夠加工一些微裝置,如微型泵,微型閥,微感測器等,但由於尚缺乏充分理論的指導及支持,這些裝置的功能的並非全然理想,這促使人們反過來加強理論方面的研究。
      微機電系統常常會牽涉到微奈米尺度的流場問題。傳統的方法已不能有效分析微觀尺度的傳輸現象。這個問題的發生主因在於微觀尺寸或高應力作用下連續體或平衡假設已不能成立。為了處理這類微觀尺度問題我們使用分子動力學模擬以幫助了解微觀傳輸機制,流體-結構相互作用和在微觀下的尺度效應。
      本文採用分子動力學方法探討微系統中流場行為,採Lennard-Jones勢能函數模擬分子間勢能及作用力,流體分子以液態氬(Ar)模擬,固體分子則以銅分子(Cu)模擬,本文由兩種模型比較由固體及流體拖曳孔穴流之流場行為。模型一是長寬比為二比一的微孔穴模擬,以平板抽動當作驅動力。模型二則以壓力方式來驅動流體以拖動孔穴流,吾人著眼於暫態狀態之呈現並探討其速度、密度分布情形,並提出日後在於生醫及工程方面之可能應用。

     Recently, the applications of micro-fluidic devices or nano-fluidic devices in various fields (such as bio-chemical analysis, energy and biomedical engineering) have been greatly developed. Particularly, the fluid transports play a crucial role in these systems, for example, the bio-samples or regents are transported by the motion of fluid in the micro-bio-chemical analysis systems. However, the order of the characteristic length scales in these systems is micro or nano, the Knudsen number may be very large compared to macro-scale and hence the assumption of continuum breaking down here; in other words, the traditional Navier-Stokes equations and analysis approaches may not be applicable to describe the motion of fluid in these systems.
     Accordingly, this study adopts Molecular Dynamic (MD) simulation to investigate the motion of fluid in nano-scale channels. The interaction of liquid-liquid molecules, liquid-solid molecules and solid-solid molecules are all modeled by a simple “Lennard-Jones potential” theory. Here the liquid is composed of Argon (Ar) atoms and the solid is composed of copper (Cu) atoms. There are two main issues studied in this work: (1) cavity flows in nano-scale (the ratio of the length to the width of cavity is 2), (2) pressure-driven flows in a nano-channel with a cavity. The transient processes of the motion of fluid and the properties of fluid in the two issues are simulated and then discussed.
     Finally, we think the results of this work are useful to the applications of nano-devices in bio-chemical analysis, biomedical and energy engineering.

    摘要 Ⅰ Abstract Ⅱ 誌謝 Ⅳ 目錄 Ⅴ 表目錄 Ⅷ 圖目錄 Ⅸ 符號說明 Ⅶ 第一章 緒論 1 1-1前言 11 1-2分子動力學之歷史背景 22 1-3分子動力學應用在流體力學模擬之文獻回顧 33 1-4研究動機與方向 55 1-5本文架構 77 第二章 分子動力學基礎理論 89 2-1數學模型 99 2-1-1牛頓力學 99 2-1-2 漢彌頓力學 10 2-2分子動力學模擬理論 13 2-3分子間作用力與勢能函數 16 2-3-1二體勢能函數 17 2-3-2多體勢能函數 21 2-4 起始位置和速度 24 2-4-1起始位置 24 2-4-2初始速度給定 26 2-5週期型邊界條件與最小映像法則 27 2-5-1週期型邊界條件 27 2-5-2最小映像法則 30 2-6截斷半徑與鄰近表列法 32 2-6-1截斷半徑 32 2-6-2鄰近表列法 33 2-7基本計算原理與數值積分方法 36 2-7-1計算原理 36 2-7-2數值積分方法 37 2-8 速度修正法 40 第三章 模型建構與計算 43 3-1計算流程 43 3-2勢能模式選定 46 3-3物理參數設定與無因次化 48 3-4計算參數設定與模型的建構 51 第四章 模擬結果分析與討論 57 4-1網格的建構與統計平均方法 57 4-2溫度平衡之確認 60 4-3溫度修正速度(Rescalling Method)對系統能影響 62 4-4模型一之流場分析與討論 65 4-5模型二之流場分析與討論 89 第五章 結論與未來展望 96 參考文獻 98 自述 102

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