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研究生:陳冠宏
研究生(外文):Kuan-HongChen
論文名稱:利用半圓形流道內電滲微渦流解析解進行粒子捕捉之設計
論文名稱(外文):Design of Particle Trapping Using an Analytical Solution of Electroosmotic Microvortices in a Semicircular Conduit
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:2016
畢業學年度:104
語文別:中文
論文頁數:81
中文關鍵詞:電滲流微渦流解析解粒子捕捉滑移速度短距力
外文關鍵詞:Electroosmotic flowAnalytical solution for microvorticesParticle trappingSlip velocityShort-range force
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本論文首先探討在半無窮平面區域,由帶電細長片上電動滑移速度所引起的微流體電滲流現象。文中推導出簡單多項式滑移速度生成之二維電滲流閉合解,然後利用多段三次樣條插值法和線性加成性來近似任意滑移速度分布,以獲得半無窮平面電滲流之通用解析解。另一方面,電動滑移速度在半圓區域會產生電滲微渦流,本文結合文獻之微渦流解析解和前述平面解,發展出一完整的半圓區域微渦流數學模型,具備符合真實操作情況和計算精確且收斂快速的優點。
  本文接著討論在半圓區域,利用微渦流和底部短距吸引力來進行粒子定點捕捉的問題,目的為設計出最佳的微渦流結構和安排相應滑移速度。為此先在對稱微渦流結構內,根據粒子捕捉時間長短劃分出數個難易捕捉區域,然後針對不同粒子初始分布的捕捉需求,提出對應之滑移速度安排策略。粒子隨機分布的模擬研究證實,所提對應策略生成之微渦流結構能夠更有效地捕捉粒子於底部停滯點,相較於對稱微渦流結構,捕捉時間可減少百分之三十。

This thesis first investigates microfluidic electroosmotic flow set up by electrokinetic slip velocities over charged strips in a semi-infinite domain. A two-dimensional closed-form solution is derived for electroosmotic flow induced by a simple polynomial slip-velocity distribution over a surface. Using the cubic spline interpolation and superposition principle, an arbitrary slip-velocity distribution can be well approximated to provide a general analytical solution for electroosmotic flow in a semi-infinite plane. On the other hand, electrokinetic slip velocities would induce electroosmotic microvortices in a semicircular domain. The thesis combines an analytical solution for microvortices from the literature and the aforementioned planar solution to develop a complete mathematical model for microvortices in a semicircular area. This model not only satisfies practical operating conditions but also possesses accuracy and fast convergence in computation.
The thesis then addresses the problem of particle trapping at a specified point in a semicircular area using microvortices and short-range force from the bottom. The aim is to design the best microvortex structure and arrange the corresponding slip velocities. To this end, a symmetric microvortex structure is first analyzed to divide the semicircular area into several easy-to-trap and difficult-to-trap regions according to the duration of particle trapping time. Various arrangement strategies for slip velocities are then proposed to meet the requirements given by different initial distributions of particles. Simulation studies based on random particle distributions demonstrate that the microvortex structures caused by the proposed strategies can capture particles more efficiently at a stagnation point on the bottom. Compared to the symmetric microvortex structure, the trapping time can be reduced by 30%.

表目錄…………………………………………………………………….i
圖目錄……………………………………………………………………ii
符號表……………………………………………………………………iv
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧與研究動機 2
1.3 論文架構 6
第二章 電滲流之基本原理與流場方程式 8
2.1 電雙層形成機制 8
2.2 電滲流形成機制 10
2.3 半無窮平面之微渦流場方程式 13
2.4 有限半圓區域之微渦流場方程式 16
第三章 半無窮平面與有限半圓區域之微渦流模型 20
3.1 半無窮平面之微渦流結構 20
3.1.1 模型描述 20
3.1.2 多項式滑移速度形成之電滲流流場及其特性 22
3.1.3 底部片段非多項式滑移速度分布之電滲流場分析 24
3.2 有限半圓區域之微渦流結構 26
3.2.1模型描述 27
3.2.2 有限半圓區域微渦流之粒子捕捉應用 32
第四章 利用電滲微渦流結構設計應用於半圓區域內之粒子捕捉 33
4.1 粒子捕捉實驗分析微渦流中心難捕捉區域特性 34
4.2 以區域分割分析難易捕捉區域提出捕捉粒子之策略 44
4.2.1 粒子均勻分散於半圓全域的捕捉策略 44
4.2.2 粒子亂數均勻分布於全域的捕捉實驗並驗證其捕捉策略 56
4.2.3 粒子局部分散於半圓任意區域的捕捉策略 58
4.2.4 粒子亂數局部分散於半圓中的捕捉實驗並驗證其捕捉策略 62
4.2.5 半圓區域內粒子全域均勻分布及局部分散之捕捉策略與結論 67
第五章 結論與未來研究展望 69
附錄A 半無窮平面三階多項式的微渦流解推導 71
附錄B 半圓解析解高頻項修正的推導 75
參考文獻 78


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