賴君亮臺灣大學：機械工程學研究所方意慬Fang, Yi-ChinYi-ChinFang2007-11-282018-06-282007-11-282018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/61230摘 要 隨著微機電技術日益地成熟，過去十年來微型化的趨勢與潛力受到科學家與工程師的重視，許多在傳統實驗室中需多個步驟分開的實驗，可以被濃縮在一微晶片中一次處理完成，因而可應用在化學反應實驗、不同物種的混合與分離、生物檢測、醫學臨床測試與環境控制等方面。架構在如此微小的尺寸上，本文探討在一注滿電解質與鈍性物種的微管中，當溶液受到一振盪式電滲透流驅動後，其鈍性物種的質傳與溶質分離的物理現象。 儘管過去五十年來，已經有許多研究探討微管表面的電雙層現象（EDL）、電滲透流的特性（EOF）以及泰勒傳遞現象（Taylor Dispersion）現象，然而本文所討論振盪式電滲透流與泰勒傳遞現象的結合則尚未有文獻發表，因此本研究不僅在晶片設計上具有參考價值，在學術上也具有相當地挑戰性與重要性。 文中複變函數被使用來計算出速度場、濃度場與質傳速率的解析解。結果顯示，質傳速率的增加會先隨無因次化頻率增加而後減少，這樣的變化與三個時間常數間的關係、以及統御方程式中的三個特徵值有關。此外，Schmidt數、電雙層的厚度、雷諾數（Reynolds Number）、微管表面的電位、與外加電場的強度對質傳速率增加的影響，也都在本文中有系統地加以探討。結果發現在頻率低的狀態下，兩種不同的鈍性物質其傳遞速度相差較多，因此在此範圍內，此流場可被用來分離不同種的物質。本研究因而可被應用在分離DNA或其他有機物質的生物晶片內。ABSTRACT Over the last decade, the potential of micro-miniaturization of analytical procedures has been explored with the maturity of MEMS technology. Several sequential experiments steps are integrated into a single automated process. These microfluid chips can be applied to perform chemical reactions, mixing and separations, biological detections, medical testing, and environmental monitoring, etc. The present study is aimed at investigatory theoretically the mass transfer and separation driven by an electroosmotic flow (EOF) in a micropipette. Many researches about electrical double layer (EDL), EOF and Taylor dispersion have been published over the past five decades. However, the combination of a time periodic EOF and the phenomenon of Taylor dispersion is first investigated systematically in the present study. A complex variable approach is used to solve analytically the solutions of the velocity profile, the concentration distribution, and the mass flow rate. The results show that the enhancement of mass transport rate, , arises first and then decendes with the increase of the frequency of the electrical field applied. Parametric studies uncovered that three time constants, , , and together with the three eiganvalues in the governing equations , , and play significant roles in the process of mass transfer. The effects of Schmidt number, , the thickness of EDL, , Reynolds number, , the electrical potential on the surface of the micropipette, , and the intensity of the applied electrical field, on are systematically analyzed and discussed. It is also shown that at low frequency the oscillating EOF is conducive to the separation of species.CONTENTS 致謝 i 摘要 ii Abstract iii Contents iv Captions of Figures vi Notations xi Chapter 1 Introduction 1 1-1 Fundamental Physics 1 1-2 Motivation and Objectives 5 1-3 Background and Literature Review 6 1-4 Physical Models 9 Chapter 2 Assumptions and Formulation 11 2-1 Assumptions 11 2-2 Flow Charts 12 2-3 The Electrical Field 18 2-4 The Velocity Field 19 2-5 The Concentration Field of a Neutral Species 20 2-6 Volume Flow Rate and Mass Flow Rate 21 Chapter 3 Dimensional Analysis and Analytical Solutions 22 3-1 Nondimensionalization 22 3-1.1 Governing Equations and Boundary Conditions 22 3-1.2 Volume Flow Rate and Mass Flow Rate 27 3-2 Some Definitions for Simplification 28 3-3 The Electrical Potential 32 3-4 The Velocity Profile 33 3-5 The Concentration Distribution 36 3-6 Solution of Volume Flow Rate 43 3-7 Solution of Mass Flux 44 3-8 Solution of Mass Flow Rate 50 Chapter 4 Results and Parametric Discussions 56 4-1 Variations of The Velocity Profiles and The Concentration Distributions 57 4-2 Schmidt Number and Separations 58 4-3 Effects due to , , , and 58 Chapter 5 Conclusions and Future Work 60 5-1 Conclusions 60 5-2 Future Work 60 Appendix A 61 A-1 Guoy-Chapman Theory 61 A-2 Guoy-Chapman-Stern Theory 62 A-3 Zeta Potential 64 A-4 Electrokinetic Effects 65 A-5 Helmholtz-Smoluchowski Equation 67 Appendix B 68 B-1 Nernst-Einstein Equation 68 B-2 Nernst-Planck Equation 69 B-3 Boltzmann Distribution 70 B-4 Poisson’s Equation 72 B-5 Poisson-Boltzmann Distribution 73 B-6 Debye-Hückle Approximation 74 B-7 Fick’s Law 76 Appendix C 78 C-1 Complex Variable Method 78 C-2 List of Some Formulae of Bessel Functions and Modified Bessel Functions 79 C-3 Some Definitions for Simplification 80 References 87 Figures 91en-US電雙層振盪式電滲透流質傳泰勒傳遞溶質分離oscillatingelectrical double layer(EDL)Taylor dispersionseparationtime periodicelectroosmotic flow(EOF)mass transferthesis