電滲泵內多孔介質微流場特性之數值模擬

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姓名

邱亦絜(Yi-Hsieh Chiu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

電滲泵內多孔介質微流場特性之數值模擬
(Numerical Study for the Micro Porous Media Flow in an Electroosmotic Pump)

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摘要(中)

由於電滲泵目前已廣泛用於生物醫葯分析技術驅動流體的功能上，近來更在微電子冷卻技術中流體推動佔相當的重要性。本文以數值模擬探討在電滲泵中多孔介質微流道的電滲流，使用的物理模式包括：1) 描述電雙層分佈的Poisson-Boltzmann方程式，2) 描述外加電場電位勢分佈之Laplace方程式，3) 描述多孔介質流道下的電滲流之包含電驅動力及微觀的黏滯剪應力及多孔介質微結構的幾何效應的修正型Navier-Stokes的方程式，幾何外形為二維軸對稱微毛細圓管。
本文除了驗証Rice和Whitehead的解析解，並與Yao和Santiago的實驗數據做比較。文中對主導電滲流在多孔介質的特性的壁面及多孔介質的介面電位勢比值做詳細探討，發現其比值為正的流速分佈和比例為負值時有明顯差異。若以圓毛細管塞入球形粒子仿多孔介質流道的數值模擬，可有效修正Yao和Santiago以多根圓毛細管捆束後類多孔介質流道之解析解對於流率及壓力高估的問題。從文中得知電解液離子濃度會影響電雙層厚度，離子濃度愈高，電滲流流速愈快；其它如多孔介質間之孔隙流道大小、外加電場強度、入口壓力、壁面及多孔介質間介面電位勢都會影響電滲流流速的增減。

摘要(英)

The electroosmotic (EO) pump has been widely used in driving and controlling microfluidics in the biomedical and biochemical applications, and it is being used for cooling liquid transportation in the micro cooler in electronics industry recently. The physical models of present numerical study are based on 1) the Poisson-Boltzmann equation for electrical double layer (EDL) potential, 2) the Laplace equation for the externally applied electrostatic field, and 3) the Navier-Stokes equation modified to account for the electro-kinetic body force and porous media effect. This study numerically analyzed various flow characteristics of porous media within the EO pump.
We first validated the EO flow in a micro circular capillary tube with theory, and then developed a model for embedded micro particles into a circular capillary tube to mimic the porous media channels in a realistic EO pump. We have thoroughly investigated the effect of the ratio of zeta potential at wall to zeta potential of particles, which is a dominant factor for affecting the characteristics EO flow within the porous media. Numerical solution agrees with analytical solutions and it also compare with available experiment data, this modified model can effectively correct overestimated values of flowrate and back pressure in previous analytical model. We found many factors affect the EO flow within the porous media; these factors are the ion concentration, the pore size of porous media channel, the applied electrical field and the zeta potential.

關鍵字(中)

★ 電滲泵
★ 電滲流
★ 多孔介質

關鍵字(英)

★ Porous media
★ Electroosmotic flow
★ Electroosmotic pump

論文目次

中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
圖、表目錄 VII
符號說明 X
第一章電滲泵的研究 1
1.1 微泵之簡介 1
1.1.1 微泵的分類及微泵技術的發展 1
1.1.2 電滲泵與其他微泵的比較 3
1.2 電雙層及電滲流的形成機制 4
1.2.1 電雙層 4
1.2.2 電滲流 5
1.3 電滲流及電滲泵研究文獻回顧 6
1.3.1 電滲流之理論與數值模擬 6
1.3.2 電位勢及濃度關係 8
1.3.3 電滲流實驗分析 8
1.3.4 多孔介質電滲泵之數值模擬 10
1.4 研究動機與方向 11
第二章電滲泵之數值分析 13
2.1 基本假設 14
2.2 描述電雙層分佈之Poisson-Boltzmann 方程式 14
2.3 描述外加電場電位勢分佈之Laplace方程式 15
2.4 描述電滲流流場之Navier-Stokes方程式 16
2.4.1 修正型Navier-Stokes方程式 16
2.4.2 多孔介質流：Carman-Kozeny理論 17
2.4.3 考慮帶電毛細管壁面及塞入的帶電球形粒子
之壁面效應 18
2.5 無因次方程式 20
2.6 邊界條件 22
2.7 FEMLAB簡介 24
第三章結果與討論 25
3.1 模擬參數及格點測試 25
3.1.1 模擬參數 25
3.1.2 格點測試 26
3.2 速度場及相關物理參數 28
3.2.1 電雙層靜電位勢 29
3.2.2 長直圓毛細管電滲流速度場 29
3.2.3 多孔介質流道電滲流速度場 30
3.2.4 影響速度分佈之參數討論 30
3.3 影響流量的相關參數 32
3.4 影響壓力的相關參數 35
3.5 影響電流的相關參數 36
第四章結論與建議 39
4.1 結論 39
4.2 建議 40
參考文獻 63
附錄A FEMLAB定義方程式的語法 66
附錄B 電流相關解析解 69

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指導教授

吳俊諆(Jiunn-Chi Wu)

審核日期

2005-7-19

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