系統識別號 U0026-0812200915175838
論文名稱(中文) 時空守恆法於電泳分離和聚焦之應用
論文名稱(英文) Application of the Space-Time Conservation Element and Solution Element Method to Electrophoresis Separation and Isoelectric Focusing
校院名稱 成功大學
系所名稱(中) 工程科學系碩博士班
系所名稱(英) Department of Engineering Science
學年度 97
學期 2
出版年 98
研究生(中文) 鄒穎
研究生(英文) Ying Chou
學號 n9894114
學位類別 博士
語文別 英文
論文頁數 96頁
口試委員 口試委員-吳宗信
中文關鍵字 區間電泳法  時空守恆法  等速電泳法  等電點聚焦電泳法  適應性網格 
英文關鍵字 Adaptive Mesh Redistribution.  Isoelectric focusing (IEF)  Isotachophoresis (ITP)  Space-Time CESE scheme  Zone Electrophoresis (ZE) 
中文摘要 時空守恆法(CESE method)為一能提供高解析度、有效減低數值耗散與震盪之嶄新數值方法,有別於傳統數值方法,時空守恆法將空間一階導數視為變數,並將時間及空間同等對待,強制物理通量於時間及空間上滿足局部和全域內均保持守恆,此等特點使得時空守恆法成為模擬具有不連續分布之物理現象問題理想的數值方法,已成功的應用於震波捕捉、象變化研究、熱波研究及淺水波模擬等。
除上述之應用方面研究,吾人亦發展非均勻網格時空守恆法以結合適應性網格重新分布技術應用於電擁分離、聚焦問題。由於時空守恆法受庫倫數之限制,並且於過小庫倫數(CFL number<0.1)狀態下會產生數值耗散現象,因此再輔以庫倫數非敏感性技術(CFL number insensitive scheme)更能增進計算準確度。經由驗證,適應性網格時空守恆法於等速電泳法及等電點聚焦電泳法顯示具有高計算效率及準確度。此研究,不但拓展時空守恆法的應用性,更提供一個有效準確之電泳模擬工具。
英文摘要 The space-time conservation element and solution element (CESE) method provides a powerful numerical tool for solving a diverse range of problems in the continuum mechanics domain. The CESE method suppresses the effects of numerical dissipation and oscillation, and is therefore more accurate and robust than traditional numerical schemes such as finite difference method. In the CESE method, both the independent variables and their derivatives are treated as unknowns and are solved simultaneously. Furthermore, the CESE scheme treats the space and time domains in a unified fashion and enforces both local and global flux conservation in the space-time domain. As a result, the CESE method is an ideal solver for wave problems characterized by discontinuous phenomena or sharp gradients, such as shock waves, phase change phenomena, thermal waves, and so on.
Electrophoresis plays a key role in biomedical science in fractionating mixtures of ionic solutes for analytical and preparative applications. Due to the miniature scale of electrophoretic systems, electrophoresis phenomena are generally investigated using some form of numerical simulation technique prior to experimental investigations. In this dissertation, the CESE method is used to investigate various electrophoresis separation phenomena, including zone electrophoresis (ZE), isotachophoresis (ITP) and isoelectric focusing (IEF). The solutions are compared with those obtained from traditional numerical schemes such as finite difference scheme and finite volume method. It is shown that the CESE method is not only more computationally efficient than traditional numerical schemes, but also yields more accurate results. In addition, a 1-D mass transport model is proposed to describe the electrophoresis transport behavior within a microchannel with a variable cross-sectional area. The validity of the proposed model is confirmed by comparing the solutions with those obtained from the 2-D finite volume method (FVM). It is shown that the modified mass transport model provides reliable results with a low computational cost for electrophoresis transport problems within simplified-geometry channels.
Finally, this dissertation proposes an adaptive mesh redistribution (AMR) CESE scheme for the solution of the species transport equation in electrophoresis preconcentration and separation problems. To prevent numerical dissipation at very small values of the CFL number (i.e. <0.1), the spatial differential component within the CESE formulation is treated using a CFL number insensitive scheme. The results obtained for various ITP and IEF problems show that the AMR-CESE scheme improves the solution quality relative to that achieved using a uniform fixed-mesh solver whilst incurring no more than a moderate increase in the computational cost. This dissertation not only extends the application of the conventional CESE method, but also develops a powerful simulation method for general electrophoresis problems.
論文目次 Abstract I
中文摘要 III
致 謝 IV
List of Tables VIII
List of Figures IX
Nomenclature XV
Chapter 1 Introduction 1
1.1. General Introduction 1
1.2. Introduce to One dimensional formulation of CESE method 4
Chapter 2 Application of the CESE method to ZE and ITP 9
2.1. Introduction 9
2.2. Mathematical model 11
2.2.1. The dissociation model for monovalent analytes 11
2.2.2. The mass transport model for monovalent analytes 12
2.3. Numerical method 14
2.3.1. The space-time CESE method 15
2.3.2. Upwind scheme 16
2.4. Results and Discussion 17
2.4.1. Isotachophoresis 17
2.4.2. Zone electrophoresis 23
2.4.3. Stability condition 26
Chapter 3 Application of the CESE method to Isoelectric focusing (IEF) 29
3.1. Introduction 29
3.2. Mathematical model 32
3.2.1. Generalized dissociation model for multivalent analytes 32
3.2.2. General transport model 33
3.2.3. Modified 1-D mass transport model for cross area change 35
3.3. Numerical implementation 37
3.3.1. Space-time CESE method 38
3.3.2. CFL number Insensitive CESE scheme 39
3.3.3. Finite Volume Method (FVM) 41
3.4. Results and discussion 42
3.4.1. IEF simulation in planner channel 43
3.4.2. IEF simulation in contraction-expansion channel 46
Chapter 4 Adaptive mesh redistribution CESE scheme 57
4.1. Introduction 57
4.2. Numerical implementation 59
4.2.1. Non-uniform mesh CESE scheme 60
4.2.2. CFL number insensitive CESE scheme 63
4.3. The adaptive moving mesh method 65
4.3.1. Adaptive mesh redistribution 66
4.3.2. Solution updating on the new mesh 68
4.3.3. Adaptive time interval of CESE method 68
4.4. Results and discussion 69
4.4.1. Isotachophoresis (ITP) separation 69
4.4.2. Isoelectric Focusing (IEF) by IPG 75
4.4.3. Isoelectric Focusing (IEF) within 10 background ampholytes 80
Chapter 5 Concluding Remarks and Future Direction 85
5.1. Electricphoresis separation of monovalent analytes 85
5.2. Electricphoresis separation of multivalent analytes 86
5.3. Adaptive mesh redistribution CESE method 87
Bibliography 89
Curriculum Vitae 95
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