第一篇:
本文之目的在於發展一套無因次的三維微氣泡通用相圖與其升力圖。由此，我們將能針對靜態液面下平板上或孔洞上的微氣泡(或懸掛型液滴)進行分析。微氣泡動力學是相當重要的一項研究，因為它在微米及奈米科技中，同時支配著質量、動量、能量以及濃度的傳輸率。在本文中，我們將利用O’Brien(1991)所發展的氣泡外型方程式，來求取無因次的微氣泡相圖與力學圖，而方程式將取至二階微小Bo(Bond number)的精度。以Bo和接觸角(或底部半徑)兩個獨立參數來求取靜態以及動態的微氣泡之無因次相圖與受力圖。相圖依微氣泡的外形而分為三個區域，氣泡頂端到反曲點為第一區，反曲點至頸部為第二區，頸部至氣泡底部為第三區，微氣泡的成長、瓦解、脫離與塌陷包埋都能在相圖中獲得描述。升力包含有浮力、氣泡底部氣體與靜壓的壓差、毛細壓力以及因圓周變化所造成的表面張力所組成。因圓周變化所造成的表面張力效應是將微氣泡附著於固體表面的主因，而此項效應對微氣泡的影響則尚未被相關文獻所提出。調整底部半徑來控制微氣泡靜態與動態的行為，將比調整Bo來得更有效率。

第二篇:
本文之目的在於提出一套能控制靜態液體中位於平面上微氣泡(或微液滴)狀態以及成長的一般相圖(general phase diagrams)。微氣泡ㄧ直以來常被用於觀察在微米與奈米技術中對於傳輸現象的影響。在本文中，我們將利用Young-Laplace方程式的微擾解求得氣泡形狀方程式，並配合截斷誤差取至二階微擾解而得到一廣泛的三維氣泡相圖，此三維相圖由距離氣泡頂端的無因次曲率半徑R(0)、氣泡接觸角 及氣泡底部半徑 所組成，且在一特定Bo之下為唯一。我們可以在相圖上任意選擇起始與終止的狀態點(state)，兩狀態間可有多條路徑稱為過程(process)，藉由在相圖上選擇不同的路徑而能達到控制氣泡成長、衰敗或者脫離表面的目的。此外，我們更引進一套能適用於所有Bo下的通用相圖(universal phase diagram)。

Part I:
The present work is to calculate dimensionless three-dimensional universal phase and lift force diagrams for a microbubble or pendant drop in a static liquid on a solid surface or orifice. Studying microbubble dynamics is important due to its controlling mass, momentum, energy and concentration transfer rates encountered in micro- and nano-sciences and technologies. In this work, dimensionless phase and force diagrams are presented by applying an equation for microbubble shape to accuracy of the second order of small Bond number provided by O’Brien (1991). Two dimensionless independent parameters, Bond number and contact angle (or base radius), are required to determine dimensionless phase and force diagrams governing static and dynamic states of a microbubble. The phase diagram divides the microbubble surface into three regions, the apex to inflection, inflection to neck, and neck to the edge of microbubble. The growth, collapse, departure and entrapment of a microbubble on a surface thus can be described. The lift forces include hydrostatic buoyancy, difference in gas and hydrostatic pressures at the microbubble base, capillary pressure and surface tension resulted from variation of circumference. The force to attach the microbubble to solid surface is the surface tension resulted from variation of circumference, which is not accounted for in literature. Adjusting the base radius to control static and dynamic behaviors of a microbubble is more effective than Bond number.

Part II:
Controlling states and growth of a microscale bubble (or pendant drop) in a static liquid on a surface by introducing general phase diagrams is proposed. Microbubbles are often used to affect transport phenomena in micro- and nano-technologies. In this work, a general phase diagram is provided by applying a perturbation solution of Young-Laplace equation for bubble shape with truncation errors of the second power of small Bond number. The three-dimensional phase diagram for a given Bond number is uniquely described by the dimensionless radius of curvature at the apex, contact angle and base radius of the microbubble. Provided that initial and end states are chosen, adjusting two of them gives the desired states and growth, decay and departure of the bubble described by path lines in the phase diagram. A universal three-dimensional phase diagram for a microbubble is also introduced.

第一篇:
中文摘要…………………………………………………Ⅰ
英文摘要…………………………………………………Ⅱ
謝誌………………………………………………………Ⅲ
目錄………………………………………………………Ⅴ
圖目錄……………………………………………………Ⅶ
符號說明…………………………………………………Ⅸ

第一章　緒論……………………………………………1
1.1　前言…………………………………………………1
1.2　本文架構……………………………………………7

第二章　理論模型之假設與分析………………………8
2.1 系統模型與假設…………………………………8
2.2 氣泡力平衡分析…………………………………9
2.2.1 氣泡表面力平衡………………………………10
2.2.2 氣泡內部之動量方程式………………………12
2.2.3 氣泡體積式……………………………………15
2.2.4無因次化………………………………………17
2.3 微氣泡分析………………………………………22
2.3.1 微氣泡在不同Bo下的各方向曲率……………22
2.3.2 通用微氣泡相圖………………………………24
2.3.3 微氣泡的頸部半徑 與頸部高度 ………………24
2.3.4 微氣泡力學與體積相圖………………………25
2.4 印證文獻數據………………………………………25

第三章 結果與討論……………………………………39
第四章 結論……………………………………………45

參考文獻…………………………………………………47
附錄………………………………………………………53

第二篇:
中文摘要…………………………………………………Ⅰ
英文摘要…………………………………………………Ⅱ
目錄………………………………………………………Ⅲ
圖目錄……………………………………………………Ⅵ
符號說明…………………………………………………Ⅷ
第一章 緒論……………………………………………1
1.1 前言…………………………………………………1
1.2 本文架構……………………………………………8

第二章 基本理論介紹與推導…………………………9
2.1 氣泡成長之理論模型與假設……………………9
2.2 曲率與Young-Laplace 方程式 ………………10
2.3 Young-Laplace equation參數式……………13

第三章　氣泡外型之微擾解……………………18
3.1 微擾法…………………………………………18
3.2 統御方程式與邊界條件………………………19
3.3 外部解…………………………………………22
3.4 內部解…………………………………………27
3.5 頸部解…………………………………………29
3.6 底部邊界層解…………………………………30
3.7 接合漸進展開法………………………………32
3.7.1 接合外部與上邊界層解……………………33
3.7.2 接合下邊界層解與頸部解…………………34
3.7.3 接合頸部解與底部邊界層解………………35
3.8 組合解……………………………………………36
3.8.1 第一區之組合解……………………………36
3.8.2 第二區之組合解……………………………37
3.8.3 第三區之組合解……………………………37
3.9 氣泡三區之組合解………………………………38

第四章　氣泡相圖與分析………………………………44
4.1 定義參數…………………………………………44
4.2 R(0)與L的關係…………………………………46
4.3 微氣泡相圖………………………………………47
4.4 通用的微氣泡相圖………………………………48
4.5 微氣泡相圖的分析與應用………………………50
4.6 微氣泡的頸部半徑 與頸部高度 …………………53
4.7 氣泡各方向之曲率值………………………………54

第五章　結論與討論……………………………………67
第六章　結論……………………………………………71

參考文獻…………………………………………………73

Part I:
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Part II:
1. Thome, J. R., 2004, “Boiling in Microchannels: A Review of Experiment and Theory,” International J. Heat and Fluid Flow, Vol. 25, pp. 128-139.
2. Kantarci, N., Borak, F., and Ulgen, K. O., 2005, “Bubble column reactors,” Process Biochemistry, Vol. 40, pp. 2263-2283.
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6. Kodama, Y., Kakugawa, A., Takahashi, T., and Kawashima, H., 2000, “Experimental study on microbubbles and their applicability to ships for skin friction reduction,” International J. Heat and Fluid Flow, Vol. 21, pp. 582-588.
7. Crum, L. A., 1994, “Sonoluminescence,” Physics Today, Vol. 47, pp. 22-29.
8. Thompson, L. H., and Doraiswamy, L. K., 1999, “Sonochemistry: science and engineering,” Industrial and Engineering Chemistry Research, Vol. 38, pp. 1215-1249.
9. Ohl, C. D., Arora, M., Dijkink, R., Janve, V., and Lohse, D. 2006, “Surface cleaning from laser-induced cavitation bubbles,” Applied Physics Letters, Vol. 89, pp. 074102-1- 074102-3.
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17. Geng, X., Yuan, H., , H. N., and Prosperetti, A., 2001, “Bubble- based micropump for electrically conducting liquids,” J. Micromechanics and Microengineering, Vol. 11, pp. 270-276.
18. Lin, L., and Pisano, A. P., 1994, “Thermal bubble powered microactuators,” Microsystem Technologies, Vol. 1, pp. 51-58.
19. Papavasiliou, A. P., Liepmann, D., and Pisano, A. P., 1999, “Fabrication of free floating silicon gate valve,” Proceedings of the ASME-MEMS Int. Mech. Eng. Congr. Expo., Nov. 14-19, 1999, Nashville, Tennessee, Vol. 1, pp. 435-440.
20. Lin, L., 1998, “Microscale thermal bubble formation: thermophysical phenomena and applications,” Microscale Thermophysical Engineering, Vol. 2, pp. 71-85.
21. Postema, M., and Schmitz, G., 2006, “Bubble dynamics involved in ultrasonic imaging,” Expert Review of Molecular Diagnostics, Vol. 6 pp. 493-502.
22. Dijkmans P A, Juffermans L J M, Musters R J P, van Wamel A, ten Gate F J, van Gilst W, Visser C A, de Jong N and Kamp O 2004 Microbubbles and ultrasound: from diagnosis to therapy European J. Echocardiography 5 245-256.
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