臺灣博碩士論文加值系統

本研究主要以假性光譜法對密集帶電水銀液滴在懸浮液中之電動力學現象進行數值模擬。對於非線性之流場、電場與濃度耦合方程組，必須予以適當地線性化。水銀本身為導體，且球內部具有流場，故眾多現象會因其特殊之表面性質而凸顯。在考慮電雙層重疊的效應下，我們發現在電泳方面，移動率在液滴半徑與電雙層厚度比值（κa）小時高估Ohshima之實解而在κa大時低估之，並會隨著κa做單調遞增；反之，電導度則會單調遞減，兩者在κa很大時，皆會趨近一定值。定性上，水銀液滴之電泳移動率與電導度會比同狀況下之膠體粒子大。至於在沈降方面，沈降電位在
κa小時維持一定值，隨著κa漸大而單調遞減，在表面電位很高的情形下，尚可發現一局部極大值。沈降速度在κa小時亦保持定值，此後單調遞減，在κa為1∼5左右可觀察到一下降趨勢減緩的現象，在κa大於10後陡降。

The study is to simulate numerically the electrokinetic phenomena of charged mercury drops in a suspension based on the pseudo-spectral scheme. The coupled hydrodynamic, electrical potential and ion-conser-vation equations must be linearized properly. Mercury itself is electrically conductive and with flow field inside it. Due to these specific surface properties many phenomena are pronounced. With considering double layer overlapping, we found that in electrophoresis, mobility calculated overestimates Ohshima’s exact solution when the ratio of drop radius to the double layer thickness（κa）is small, and underestimates it when κa is large. And mobility increases monotonically with κa. Conversely, the electrical conductance decreases with it. Both will approach constant when κa is large. Mobility and conductance of mercury drops are larger than those of general colloid particles qualitatively. As for sedimentation, the sedimen-tation potential keeps a constant when κa is small and decreases monoto-nically with
κa; furthermore, a local maximum could be found under high
surface potential. The sedimentation velocity also keeps a constant under low κa value, and decreases with κa after-wards. The decreasing tendency was observed facilitated when
κa is about 1∼5. But velocity decreases sharply after κa larger than 10.

中文摘要 …………………………………………………………………I
英文摘要 …………………………………………………………………II
目錄 ………………………………………………………………………III
表目錄 ……………………………………………………………………VII
圖目錄 ……………………………………………………………………VIII
第一章 緒論………………………………………………………………1
1-1 引言……………………………………………………………1
1-2 文獻回顧………………………………………………………2
第二章 理論分析…………………………………………………………5
2-1 系統描述………………………………………………………5
2-2 主控方程式……………………………………………………6
2-3 邊界條件之給定………………………………………………13
2-4 主控方程式之無因次化………………………………………15
2-5 線性化方程式…………………………………………………19
2-6 線性化方程組之一維表示式…………………………………21
2-7 電泳移動率（electrophoretic mobility）之計算………24
2-8 沈降電位（sedimentation potential）之計算…………27
2-9 沈降速度（sedimentation velocity）之計算……………29
2-10 電導度（electrical conductivity）之計算……………31
第三章 數值方法…………………………………………………………34
3-1 假性光譜法……………………………………………………34
3-2 空間映射………………………………………………………36
3-3 牛頓-拉夫森疊代法（Newton-Raphson Iteration）……37
3-4 計算流程………………………………………………………39
第四章 結果與討論………………………………………………………48
第五章 結論………………………………………………………………49
符號說明 …………………………………………………………………88
參考文獻 …………………………………………………………………92
附錄 ………………………………………………………………………95
附錄A 水銀液滴表面邊界條件之推導…………………………96
附錄B 水銀液滴之內部流場示意圖……………………………99
附錄C 流場方程式之推導………………………………………100
附錄D 液滴受力之推導…………………………………………102

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