在本論文中，主要探討微氣泡系統中的兩個題目：1) 固液界面間氣泡包之氣孔形成分析；2) 固體中的氣孔形成分析。
在第一項研究中，探討微小氣泡在固化過程中被固液界面捕捉形成氣孔之機制。固體內之氣孔為影響材料的特性，微觀結構，和應力分布最關鍵因素之一。為求簡化及不失一般性，本研究將微小氣泡固化界面以上之頭部假設為一球帽狀。幾何分析發現，微小氣泡的接觸角可以以第一類Abel’s方程式表示。氣孔的伸長、擴大、縮小和封閉以氣泡成長率與固化速率的相對變化決定。氣孔封閉可以由氣泡微小的成長率, 或氣泡成長率與固化速率的比值在 接觸角有最小氣泡半徑而產生。因此,文獻上指出氣孔的封閉是起因於固化速度大於氣泡成長速度是不正確的。控制固體中氣孔形成可以控制氣泡成長率,或是控制固化速率。
在第二項研究中，預測固化過程中氣泡之成長或衰減為界面吸收形成氣孔之形狀. 氣泡因固化界面前緣之液體過飽和氣體而產生。氣孔的形狀影響材料的特性、微觀結構, 及應力分布。本研究發現固體內氣孔形狀可依文獻中微小氣泡形狀統御程式, Young-Laplace方程式的微擾解以3D相圖描述。結果發現所預測微小氣孔的成長和埋入情況與實驗觀察相吻合。本研究提供了不同工作參數下,可以預測氣孔形狀的通式及真實的模型。

In this dissertation，two topics in microbubble systems are investigated：1) Pore Formation from Bubble Entrapment by a Solidification Front；2) Pore formation in Solid。
In the first study，mechanism of the pore shape in solid resulted from a tiny bubble captured by a solidification front is geometrically and generally investigated。Pore formation and its shape in solid are one of the most critical factors affecting properties，microstructure，and stresses in materials。For simplicity without loss of generality, the tiny bubble beyond the solidification front is considered to have a spherical cap in this work。Introducing a geometrical analysis it is found that the contact angle of the bubble cap can be governed by the Abel’s equation of the first kind in terms of displacement of the solidification front。The pore can be elongated, expanded，shrunk and closed，depending on relative variation of the bubble growth rate and solidification rate。The pore can be closed by imposing infinitesimal bubble growth rate-to-solidification rate ratio，and a finite bubble growth-to-solidification rate ratio in order to produce a minimal bubble radius at the contact angle of 。A criterion intuitively accepted in the literature，stating that closure of a pore is attributed to a greater solidification rate than bubble growth rate，is incorrect。The predicted pore shape and contact angle agree with experimental observations。Manipulating either bubble growth rate or solidification rate can control pore formation in solid。
In second study，the shapes of a growing or decaying bubble entrapped by a solidification front are predicted in this work。The bubble results from supersaturation of a dissolved gas in the liquid ahead of the solidification front。Pore formation and its shape in solid are one of the most critical factors affecting properties，microstructure, and stresses in materials。In this study，the bubble and pore shapes entrapped in solid can be described by a three-dimensional phase diagram，obtained from perturbation solutions of Young-Laplace equation governing the tiny bubble shape in the literature。The predicted growth and entrapment of a microbubble as a pore in solid are found to agree with experimental data。This work thus provides a realistic prediction of the general growth of the pore shape as a function of different working parameters。

TABLE OF CONTENTS
LIST OF FIGURE v
NOMENCLUATE vii
ABSTRACT x
中文摘要 xi
INTRODUCTION xii
CHAPTER 1 PORE FORMATION FROM BUBBLE ENTRAPMENT BY A SOLIDIFICATION FRONT 1
1.1 System model and analysis 1
1.2 Results and discussion 4
CHAPTER 2 PORE FORMATION IN SOLID 7
2.1 System Model and Analysis 7
2.2 Solution procedure. 9
2.3 Results and Discussion 12
CHAPTER 3 CONCLUSIONS 14
REFERENCES 16
Appendix Three-Dimensional Temperature Field in a Line-Heater Embedded by a Spiral Electrical Resistor 31

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