臺灣博碩士論文加值系統

摘 要
近年來奈米科技引起世人廣泛的注意，由於表面效應，小尺度效應以及量子效應的影響使的許多物理，化學性質在奈米尺度下呈現完全不同的特性，如加入奈米顆粒之液體會使此液體之傳導性成指數的增加等等。
故本研究採用分子動力學模擬方法 (Molecular Dynamics Simulation)針對奈米尺度下液體性質進行研究，其中包含液滴於固體表面之接觸角受其尺度的影響與液滴於固體表面動態擴散的情形以及流體在奈米管道下之流場特性探討。
本研究結果顯示於奈米尺度下液滴接觸角會受其尺度大小所影響，而不是如大尺度下所顯示之接觸角為一定值，於奈米尺度下當液滴越大時接觸角也隨之增加，而此效應於液滴越小時越明顯。
液滴在固體表面之擴散研究中，結果顯示在奈米尺度下液滴會有層狀結構形成於靠近固體表面部分，而且此層狀結構中屬不同層的液體會擁有不同的擴散速度，當壁面與液體間作用力較大時，此液滴以最接近壁面之第一層為主要擴散層，而當其作用力較小時，則為液滴整體向外擴散﹔液滴於表面之擴散會受溫度及固體表面特性影響，溫度越高以及親合力大的表面擁有較大的擴散速率。
奈米管流之流場並不同於大尺度下之管流特性，由於液體之平均自由徑相較於管徑已不可忽略，故此時一些對於連續流體的假設並不成立，亦即由Navier-Sokes equations 所得結果可能並不正確，故本研究採用分子動力學針對每一分子進行模擬，以了解奈米管流流場特性，在所得結果中顯示無因次化之速度，剪應力曲線圖會隨著管徑改變而改變，當管徑越大時，其速度與剪應力分布就越接近Navier-Sokes equations以及牛頓流體所得之結果，且速度分佈會隨液體種類不同而改變，結果顯示在相同外在條件下水的速度分佈較argon及乙烷流體更接近Navier-Sokes equations﹔另外在奈米尺度下，無滑移邊界條件成立與否取決於力平衡之結果，當壁面與液體間之作用力較小且外界驅動力較大時，則滑移邊界條件產生，反之則無滑移邊界條件成立，故在奈米尺度下無滑移邊界條件成立與否與表面特性以及流體種類相關。

CONTENTS
ABSTRACT (Chinese) …………………………………………………………i
ABSTRACT (English) ………………………………………………………iii
ACKNOWLEDGEMENT………………………………………………………………v
CONTENTS………………………………………………………………………vi
LIST OF FIGURES ……………………………………………………………ix
LIST OF TABLES ……………………………………………………………xii
NMOENCLATURE………………………………………………………………xiii
CHAPTER ONE INTRODUCTION…………………………………………………1
1.1 Motivation………………………………………………………………1
1.2 Literature Reviews……………………………………………………4
1.2.1 Liquid Droplet Contact with Solid Wall………………………4
1.2.2 Nano Channel Flow …………………………………………………5
1.3 Objectives of this Research ……………………………………9
CHAPTER TWO THEORETICAL MODEL …………………………………………11
2.1 Liquid Droplet on the Solid Wall…………………………………11
2.2 Nano Channel Flow ……………………………………………………14
CHAPTER THREE SIMULATION METHOD ………………………………………21
3.1 Liquid Droplet on the Solid Wall ………………………………21
3.1.1 Potential Functions ……………………………………………21
3.1.1 (a) The Potential between Vapor and Liquid Droplet ……21
3.1.1 (b) The Potential between Liquid Droplet and Solid Wall.22
3.1.2 Boundary Conditions ………………………………………………22
3.1.2. (a) Periodic Boundary Conditions ……………………………23
3.1.3 Initial Conditions…………………………………………………23
3.2 Nano Channel Flow ……………………………………………………24
3.2.1 The Potential between Fluid Molecules ………………………24
3.2.1 (a) SPC/E Model for Water Molecules …………………………25
3.2.1 (b) AMBER Potential Model for Organic Molecules …………25
3.2.2 The Potential between Wall molecules…………………………26
3.2.3 The Potential between Fluid and Wall molecules …………27
3.2.4 Boundary Conditions ………………………………………………28
3.2.4 (a) Constant Temperature Wall Boundary Condition…………29
3.2.5 Initial Conditions…………………………………………………29
3.3 Numerical Scheme in Simulation……………………………………30
3.3.1 Numerical Integration Method……………………………………30
3.3.1 (a) Euler’s Method ………………………………………………30
3.3.1 (b) Verlet Integration Method …………………………………30
3.3.2 Neighbor List Method in MD Simulation ………………………32
3.3.2 (a) Verlet Neighbor Lists ………………………………………32
3.3.2 (b) Cell Link Neighbor List ……………………………………33
3.4 Molecular dynamic simulation of
rigid non-spherical bodies……………………34
CHAPTER FOUR RESULTS AND DISCUSSION …………………………………44
4.1 The Liquid Droplet on Solid Wall…………………………………44
4.1.1 The Size Effect for Equilibrium Contact Angle ……………44
4.1.2 Dynamic Wetting Behavior Study by Molecular
Dynamic Simulation…………………………………………………………46
4.1.2.1 Results and Discussion…………………………………………47
4.1.3 Summary ………………………………………………………………48
4.1.3.1 The size effect on equilibrium property of the system 48
4.1.3.2 Dynamic spreading of liquid droplets………………………49
4.2 Nano Channel Flow ……………………………………………………50
4.2.1 Results and Discussion……………………………………………51
4.2.1.1 Wall Dragged Flow……………………………………51
(a) Velocity profiles………………………………………………52
(b) Density profiles ………………………………………………52
(c) Pressure profiles………………………………………………53
4.2.1.2 Pressure Driven Channel Flow…………………………………53
(a) Velocity profiles ……………………………………………………54
(b) Density profiles………………………………………………………55
(c) Pressure profiles ……………………………………………………55
(d) Shear stress profiles ………………………………………………56
(e) Accommodation coefficient …………………………………………56
(f) Velocity profiles of water fluid…………………………………57
(g) Velocity profiles of ethane fluid ………………………………58
4.2.1.3 Summary ……………………………………………………………59
CHAPTER FIVE SUMMARY AND CONCLUSION …………………………………79
5.1 Summary …………………………………………………………………79
5.2 Conclusions ……………………………………………………………80
5.2 Future Work ……………………………………………………………83

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