臺灣博碩士論文加值系統

多孔物質與自由液體之間的邊界條件一直是學者們關注的難題，而近年來切應力不連續條件廣泛的使用於處理此一問題，因此，本研究以數值方法探討多孔膠體粒子在切應力不連續條件下的電泳運動現象。我們考慮電雙層極化效應，並且採用Brinkman所提出的多孔物質模型，以及於多孔物質界面引入應力不連續條件(stress-jump condition)。為了適當描述系統，我們使用球座標進行多區聯解，在外加弱電場的假設下，將相互耦合的電動力學方程組線性化，以Chebyshev擬譜方法求解線性化後的電動力學方程組。

我們針對電動力學的一些重要參數，如切應力不連續係數(stress-jump coefficient)、電雙層厚度、多孔粒子摩擦係數、懸浮液密集度、多孔粒子帶電量等對電泳動度所造成的影響加以研究，並且發現切應力不連續係數對於粒子電泳現象有非常大的影響。研究結果發現切應力不連續係數越大，粒子所受流體阻力越小，粒子泳動度越快，且切應力不連續係數能有效影響極化效應的強弱，這些特性會使整體粒子泳動趨勢變得更為複雜。我們的數值結果與相關實驗文獻有著非常良好的吻合，因此也確立我們理論的正確性以及切應力不連續的重要性。

The boundary condition for the flow field across a porous material-liquid interface has drawn the attention of many researchers. Stress-jump condition, proposed by Ochoa-Tapia and Whitaker, has been introduced to solve this type of problem. In this study, the electrophoretic behavior of a porous particle in stress-jump condition is investigated. The effect of double-layer polarization is taken into account. Brinkman model is adopted to simulate the porous structure, and stress-jump condition is introduced into porous material-liquid interface. We treat the problem by separating the physical region into two domains using spherical coordinates. The coupled electrokinetic equations are linearized assuming the applied electric field is weak. General electrokinetic equations are employed and solved with pseudo-spectral method based on Chebyshev polynomials and Newton-Raphson schemes.

Key parameters of electrokinetic interest such as stress-jump coefficient, double layer thickness, friction coefficient of the porous particle, volume fraction, and fixed charge density are examined for their respective effect on the particle motion. We found, among other things, the stress-jump coefficient is a crucial factor in determining the particle electrophoretic behavior. As stress-jump coefficient increases, the electrophoretic motion becomes quicker, due to the friction force decreases. In addition, stress-jump coefficient has a significant influence on the degree of double-layer polarization. These properties make electrophoretic behavior becomes more complicated. Comparison with experimental data available in the literature is excellent, indicating the reliability of this analysis, as well as the importance of using stree-jump condition.

摘要................................................................................................................ I
Abstract。.....................................................................................................III
目錄............................................................................................................. V
表目錄....................................................................................................... IX
圖目錄......................................................................................................... X
第一章 序論 1
1-1 膠體概述 1
1-2 多孔膠體粒子與聚電解質 4
1-3 電動力學現象及文獻回顧 7
1-3.1 電雙層理論 7
1-3.2 電雙層的極化效應 9
1-3.3 電泳理論文獻 10
1-3.4 多孔粒子電泳文獻回顧 13
1-4 多孔物質理論 14
1-5 多孔物質界面與stress jump理論 17
1-6 研究動機 21
第二章 理論分析 22
2-1 系統描述 22
2-2 基礎電動力學方程組 25
2-2.1 電位方程式 25
2-2.2 離子守恆式 25
2-2.3 流場方程式 26
2-3 平衡態與擾動態 29
2-3.1 平衡態 29
2-3.2 擾動態 30
2-4 邊界條件 33
2-4.1 平衡態邊界條件 34
2-4.2 擾動態邊界條件 35
2-5 系統一維化 38
2-6 無因次化分析 40
2-6.1 無因次一維化之主控方程式 42
2-6.2 無因次一維化之邊界條件 43
2-7 粒子受力計算 45
2-8 電泳動度之計算 46
第三章 數值方法 48
3-1 正交配位法 49
3-2 空間映射 53
3-3 兩區聯解 54
3-4 Newton Raphson迭代法 57
3-5 擾動態多變數聯解 60
3-6 數值積分 62
第四章 結果討論 65
4-1 收斂性測試 67
4-2 電雙層的影響及其極化效應 73
4-3 懸浮液密集度對電泳動度的影響 80
4-4 摩擦係數對電泳動度的影響 88
4-5 多孔粒子固定電荷密度對電泳動度的影響 92
4-6 場圖說明電動力學現象 96
4-7 實驗比對 106
第五章 結論 108
參考文獻................................................................................................... 110
符號說明................................................................................................... 121
附錄........................................................................................................... 124
A. 常見電解質水溶液參數值 124
B. 連續條件之推導 126
C. 球型膠體粒子受力推導 129

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