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研究生:蔡秉宸
研究生(外文):Ping-ChenTsai
論文名稱:快速收斂之電滲流解析解與其在微粒子混合之應用
論文名稱(外文):A Fast Converging Analytical Solution of Electroosmotic Flow and Its Applications in Microparticle Mixing
指導教授:黃世宏
指導教授(外文):Shyh-Hong Hwang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:化學工程學系
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:75
中文關鍵詞:電滲流難收斂解析解週期性
外文關鍵詞:Electroosmotic Flowdifficult-to-convergeanalytical solutionperiodicity
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本論文主要探討Stokes流體在矩形微管道橫截面上之電滲流,首先將管壁電雙層內電滲流移動速度視為總體流體的邊界滑移速度,接著利用二維Stokes偏微分方程式和重疊原理推導出各種管壁内嵌電極設計所引起的總體流動解析解。
所得電滲流解析解為一無窮級數展開式,此展開式之係數存在收斂緩慢的問題,進而使得流速的計算在矩形邊界附近會產生較大的誤差。為了解決此問題,本文將展開式係數分為易收斂與難收斂兩部分,難收斂部分可在邊界流速分布具有特定週期性的條件下計算其漸近值,易收斂部分即可利用該級數前面少數項準確求解。接著透過週期性的概念重組展開式之特徵函數,使得解析解能夠在整個矩形區域快速收斂。在内嵌電極上施加不同的電壓組合能導引多種滑移流速分布,進而產生多種流體流動型態。最後本文透過周期性交替使用這些流動型態來設計多元微粒子混合器,並探討混合效率及粒子運動軌跡,以充分解析微混合器的運作過程。

This thesis mainly investigates the electroosmotic flow of a Stokes fluid on the cross-sectional plane of a rectangular microchannel. First, the electroosmotic velocities in the electric double layers adjacent to the walls are deemed the boundary slip velocities of the bulk fluid. Subsequently, the two-dimensional Stokes partial differential equation together with the superposition principle is employed to derive the analytical solution of the bulk flows induced by various designs of electrodes embedded in the walls.
The derived analytical solution is in the form of infinite series expansions. The expansion coefficients suffer from the problem of slow convergence, causing larger errors in the computation of velocities near the rectangular boundary. To resolve this problem, the expansion coefficients are divided into an easy-to-converge part and a difficult –to-convergent part. The asymptotic values of the difficult-to-converge part can be found under the conditions that the boundary velocity distribution possesses the specified periodicity; the easy-to-converge part can then be accurately calculated using the first few terms in the series. Subsequently, the concept of periodicity is used to reassemble the eigenfunctions in the series, so that the resulting analytical solution converges very rapidly within the entire rectangular region. Applying different combinations of voltages to the embedded electrodes would induce various slip velocity distributions and furthermore result in various patterns of fluid flow. Finally, the thesis utilizes the periodic alternation of these flow patterns to design multiple microparticle mixers, and studies the mixing efficiencies and moving particle trajectories to analyze thoroughly the particle mixing.

摘要 III
Abstract IⅤ
誌謝 Χ
目錄 ΧI
圖目錄 ΧIⅤ


第一章 緒論 1
1.1 前言 2
1.2 文獻回顧及研究動機 3
1.3 章節及組織 4

第二章 電滲流之基本原理與流場方程式推導 5
2.1 電雙層的形成機制 5
2.2 電滲流(Electro-osmotic flow)形成機制 7
2.3 管道中工作流體的數學模型建立 8
2.4 基本方程式推導及建立 12

第三章 方形管道內的數學解析解的理論回顧 17
3.1 流體的數學解析解的理論回顧 17
3.2 二維微流體之解析解與處理難收斂展開式係數 23
3.3 藉由解析解計算實際流速 26

第四章 經過整理的展開式係數與具週期性之邊界速度 28
4.1 處理對應難收斂部份之展開式 28
4.2 計算各別週期的對應方程式 37
4.3 偶函數方程式之通式 43
4.4 奇函數方程式之通式 44

第五章 微渦流混合器之設計與效率探討 45
5.1 利用隨時間變化的電滲流產生混沌現象 45
5.2 比較有無週期性的速度分佈的混合情形 47
5.3 各種微渦流組合應用於微混合器 51
5.3.1 四個微渦流及一個微渦流組合 51
5.3.2 四個微渦流及兩個微渦流組合 55
5.3.3 兩個微渦流及兩個微渦流組合 61
5.3.4 四個微渦流及四個微渦流組合 66

第六章 結論與未來展望 72
6.1 結論 72
6.2 未來展望 73

參考文獻 74

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[19]與同實驗室的研究生林敏巧共同完成方程式推導。

[20]黃健銘,矩形管道內電滲微渦流之半解析解及其在微混合器設計之應用,國立成功大學化學工程系碩士論文(2012)。

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