臺灣博碩士論文加值系統

　　本研究主要以數值模擬方式分析在微管道中電驅動流和壓力驅動流彼此交互作用下之流場問題。本研究中假設低雷諾數流場下電雙層厚度(<10奈米)遠小於管道之特徵長度(100微米)，運動方程式中描述電滲效應之電驅動力項可以Helmholtz-Smoluchowski滑動壁面速度取代之，因此本研究之數值模擬物理模式可簡化至（1）描述外加電場電位勢分佈之Laplace方程式（2）描述流場之Navier-Stokes方程式（3）描述電滲效應之Helmholtz-Smoluchowski方程式。研究問題主要分成下列兩項：
　　首先，以數值模擬之方式探討在一直微管道中壓力驅動流結合電滲效應下之流場，進而設計一局部微粒子操控裝置。其工作原理為: 在直微管道中鍍一對微電極，施以電場以產生一與壓力驅動流反向之電滲效應，由於此效應電極間管道壁面兩側將產生一對稱之迴流區，此迴流區域之大小將隨著電滲效應與壓力驅動之流速比增加而變大，而擠壓壓力驅動之流體而造成加速之效果，如同微噴嘴效應一般。進一步地，針對此效應應用於直微管道中微粒子分離之問題進行相關的探討，數值模擬結果顯示當微粒子通過電極間的迴流區域時，微粒子會被加速而造成微粒子彼此間之分離距離加大，並討論分離距離的大小和微粒子位置之間的關係。
　　最後，針對低雷諾數下直角彎管之流場問題進行探討，探討之問題分為：壓力驅動之流場、電驅動流場，以及結合壓力驅動與電驅動之流場。在數值模擬結果顯示壓力驅動下在管道轉角外側產生一微小之分離泡，而電驅動下則不會有分離泡的情形產生。在壓力驅動下，再外加一順向的電場以產生一與壓力驅動流同方向之電滲效應，由於壁面電滲效應之因素，微分離泡將不會形成，而施加一逆向電場，則會形成一較複雜之流場結構，本研究進而透過粒子追蹤的方式來觀察及分析此一流場。

This research focuses on analyzing the flow field that is counterbalanced by a pressure driven flow and electro-osmotic flow in a microchannel. In this text, we assumed that the Electrical Double Layer thickness（<10nm） is smaller than the characteristic length of microchannel（>100 nm）and the flow field is under low Renyold number. The body force term in the momentum equation describes the electro-osmotic effect which can be replaced by the Helmholtz-Smoluchowski equation. The physical models are based on（1）the Laplace equation for the externally applied electrostatic field distribution, （2）the Navier-Stokes equations describes the flow field in microchannel, and（3）the Helmholtz-Smoluchowski equation describes electro-osmotic effect. This study consists of following two parts：

Firstly, we utilized the numerical simulation method to analyze the flow field that is counterbalanced by a pressure driven flow and electro-osmotic flow in a straight microchannel. And then designed a localization microparticle manipulation device. The principle of the device is to plate with a pair of microelectrodes in a straight microchannel. We applied an adjustable electric field across a section of the mirochannel to generate electro-osmotic flow between two electrodes. The electro-osmotic flow between the two electrodes is counterbalanced by the pressure driven flow in this section of the mirochannel. The numerical simulation results show that the recirculation flow is the consequence of the counterbalancing hydrodynamic against electroosmotic flow between two electrodes. Therefore the accelerated flow near the electrodes inside the microchannel acts like the effect of micronozzle, the particles can be separated by the recirculation flow. The results show that when particles passed through electrodes, particles will be accelerated and the distance between two particles will be increased.

Secondly, we study the flow field in a L-shape microchannel, utilizing the pressure driven, electro-osmotic driven and combination of the two to discuss the flow field in each case. The computational results show that there is a separation bubble existed near the corner in microchannel under the pressure driven flow. There is no separation bubble under electric driven flow, but the flow velocity near the corner will be faster than other region in the microchannel. Therefore, we can applied an electrical field to generate electro-osmotic flow in the same direction as pressure driven flow. Through the electro-osmotic affect to avoid the existence of the separation bubble. If we applied a regression electrical field, the flow field becomes more complicated. In this study, we utilized the particle tracing method to observe and analyze this phenomenon.

摘　　要 i
Abstract ii
誌　　謝 iv
目　　錄 vi
圖 目 錄 viii
符號彙編 xii
第一章　緒論 1
1.1　前言 1
1.2　微流場介紹 2
1.3　電雙層的形成機制 4
1.4　電滲流理論歷史回顧 5
1.5　電滲流形成機制 7
1.6　研究動機 8
1.7　本文架構 9
第二章　電滲流統御方程式與數值方法 10
2.1　序論 10
2.2　基本假設 11
2.3　描述外加電場分佈之Laplace方程式 11
2.4　描述電滲流流場之Navier-Stokes方程式 12
2.5　粒子追蹤方程式 16
2.6　邊界條件 17
2.7　程式驗證 18
第三章　微管道迴流區效應討論 20
3.1　序論 20
3.2　解析推導 22
3.3　參數定義 31
3.4　計算之幾何與邊界條件 31
3.5　不同電場強度Ex時管道內流速分佈情形 33
3.6　不同電場強度Ex時管道內壓力分佈情形 35
3.7　調控電壓進行微粒流動操控 36
3.7.1　微粒位於管道中心之流動操控過程 36
3.7.2　微粒位於管道不同高度之流動操控過程 40
3.8　不同入口流量時管道內流速分佈情形 44
3.9　不同入口流量時管道內壓力分佈情形 46
3.10　調控入口流量進行微粒流動操控 47
3.10.1　微粒位於管道中心之流動操控過程 47
3.10.2　微粒位於管道不同高度之流動操控過程 51
3.11　結論 55
第四章　結合壓力和電驅動之直角彎管流場分析 56
4.1　序論 56
4.2　純壓力和電驅動於直角彎管流場討論 58
4.3　結合壓力和電驅動於直角彎管流場討論 63
4.3.1　壓力結合順向電驅動於直角彎管流場討論 63
4.3.2　壓力結合逆向電驅動於直角彎管流場討論 65
4.4　利用壓力結合電驅動應用於粒子操控 70
4.5　結論 73
第五章　總結與未來展望 74
5.1　總結 74
5.2　未來展望 75
參考文獻 76
附　　錄 81
自　　述 83

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