臺灣博碩士論文加值系統

本論文主要的研究目的在於利用時空守恆法來模擬毛細管中電泳分離的行為，其中包含了移動邊界電泳法，區間電泳法以及等速電泳法。茲簡略說明如下，電泳分離操控技術是在加入電位勢後，想要觀察或量測的樣品間藉由彼此遷移率速率的不同，而達到離子分離的效果。移動邊界電泳法是最早被發展出來的技術，此方法在當時分離了血清，使得人們在往後的研究中有很大的突破。區間電泳法以移動邊界電泳法作為基礎的技術，其在系統環境充滿均勻的緩衝液進行分離。等速電泳法則是在系統環境中為不連續的緩衝液而進行分離的技術。
時空守恆法利用統御方程式滿足積分形式守恆定律的概念，為在時間空間上均具有二階準確度的一種新數值方法。在傳統的數值計算方法用來模擬電泳分離中，一階準確度的方法所得到的結果會產生數值耗散；而二階準確度方法得到的解會產生數值震盪，其原因是在於在移動邊界電泳法和等速電泳法中，在分離過程達到定常後，樣品區會形成濃度不連續的介面，由於傳統方法是利用差分的概念，所以在描述濃度變化劇烈往往會產生數值震盪，而時空守恆在處理此問題時，並沒有此一問題發生而且能得到更精確的答案，因此我們期望此方法在往後應用於電泳分離的數值預測中能提供更準確的模擬結果。

The space-time conservation element and solution element (CESE) method is applied to simulate the moving boundary electrophoresis (MBE), zone electrophoresis (ZE) and isotachophoresis (ITP) separation phenomena. The CESE method expresses the governing equation in the integral form of the conservation law, and has a second-order accuracy in both space and time. The current results show that the CESE solutions for the ITP and ZE phenomena are more accurate than those obtained using conventional first-order numerical schemes, which are characterized by serious numerical diffusion. Furthermore, the CESE method suppresses the numerical oscillations or peaks observed in the results obtained using second-order finite difference schemes. Finally, the results reveal that the CESE method accurately models the sharp boundaries between adjacent ITP samples under steady-state conditions. Overall, the results presented in this study demonstrate the numerical accuracy of the CESE method and confirm its applicability to the modeling of a range of electrophoretic phenomena.

摘要 I
致謝 III
目錄 IV
圖目錄 VI
表目錄 IX
符號表 X
英文符號 X
希臘符號 XI
第一章 前言 1
1.1背景及文獻回顧 1
1.2 研究內容 4
第二章 電泳分離行為模式 6
第三章 一維時空守恆法之介紹 10
3.1 序論 10
3.2 線性方程式 11
3.3 非線性方程式 15
3.4程式驗證 17
3.4.1 17
3.4.2 20
第四章 結果分析 29
4.1 序論 29
4.2 移動邊界電泳法 (Moving Boundary Electrophoresis, MBE) 29
4.3 區間電泳法 (Zone Electrophoresis, ZE) 31
4.4 等速電泳法 (Isotachophoresis, ITP) 34
4.5 數值穩定度 38
第五章 結論與建議 61
5.1 結論 61
5.2 建議與未來展望 62
參考文獻 66
自述 70

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