臺灣博碩士論文加值系統

本論文首先針對半無窮區域內，置於非帶電表面上帶電細長片所產生的電滲流現象進行理論性研究。從單一細長片的問題開始，藉由簡單多項式之表面電荷或滑移速度分布來證明數個基本二維解可以組合成類似於理想流場解之閉合型式，由此提供了一個明晰方式來揭露流體流動特徵。這些解析解透露兩種流場拓樸型式：其一為對稱式表面電荷分布所產生之簡單吸入與噴出流，其二為非對稱式表面電荷分布所產生之一對微渦流。對於任意的表面電荷分布，更複雜之流場結構可由這些基本解的疊加來取得。
此分析被進一步延伸到兩個均勻帶電的細長片上，用來演示流體流動特徵如何隨著細長片的大小和表面介達電位而變化。以漸近方式鑑別出的遠場速度行為，指明了該流場之流力本質是典型遠距的。接著針對電滲微渦流的粒子捕捉應用進行理論分析，經由這些基本流場解的使用顯示，在收斂停滯點附近的對稱渦流可以結合短距吸引力的影響，有效率地捕捉粒子，而非對稱性渦流粒子捕捉效果則相當有限。
本論文也探討在受侷限微渦流裡粒子之捕捉和釋放，包括在固體表面附近由動電滑移速度驅動產生的微渦流以及在氣液介面由外部動量源所造成的微渦流。一具有通用性之二維解析解被推導出來描述半圓區域內之微渦流，適用於底表面滑移速度分布為多項式的情況。然而在實際應用上，底表面滑移速度分布常為階梯式，難以用多項式來近似。本解析解的一個明顯優點即為經簡單修改後，它亦可處理階梯式或其他型式之表面滑移速度分布。
最後，本論文考慮粒子受到各種流速場和力場的影響，應用分歧理論於粒子運動方程式來說明不同粒子操作機制的產生條件，包含渦流捕捉陷阱、點捕捉陷阱、極限環捕捉陷阱以及粒子於不同捕捉陷阱的選擇性分離。當懸浮粒子只受到零散度力作用時，發現對於已知滑移速度分布，僅需利用與Stokes阻力、重力和流動渦旋相關的兩個參數即可完成所有粒子捕捉拓樸結構的分類。亦可證明非零散度力，如非均勻排斥或吸引力，可捕捉懸浮粒子至某一陷阱或是將兩種不同性質的懸浮粒子選擇性地分離至不同陷阱中。

This dissertation theoretically investigates electro-osmotic flow set up by charged strips on an otherwise uncharged surface in a semi-infinite domain. Starting with a single-strip problem, it is demonstrated that for simple polynomial surface charge or slip velocity distributions, several basic two-dimensional solutions can be derived in closed forms constituted by the analogous idea-flow solutions, which provides a more lucid way for revealing the flow features. These analytical solutions reveal two types of the flow topology: simple draining-in/pumping-out streaming and a pair of microvortices for symmetric and anti-symmetric surface charge distributions, respectively. For an arbitrary surface charge distribution, more complicated flow structures can be found by the superposition of these basic solutions.
The analysis is further extended to two uniformly charged strips, showing how the flow characteristics vary with the strips’ dimensions and surface zeta potentials. The far-field velocity behavior is also asymptotically identified and indicates that the hydrodynamic nature of the flow is typically long-range. An application to particle trapping with electro-osmotic microvortices is then theoretically analyzed. The use of these basic solutions shows that in collaboration with short-range attraction effects, the trapping can be facilitated by symmetric vortices with a converging stagnation point, but not by asymmetric vortices.
This dissertation also examines particle trapping and release in confined microvortex flows, including those near a solid surface due to variations in the electrokinetic slip velocity and those at a liquid-gas interface due to an external momentum source. A general analytical solution is derived for a two-dimensional microvortex flow within a semicircular cap. This analytical solution is suited to describing a microvortex flow driven by a polynomial slip velocity on the bottom surface. However, stepwise slip velocity distributions are often encountered in practice, which are difficult to approximate by polynomials. One distinct advantage of the analytical solution is that via simple modification, it can still deal with stepwise or other slip velocity distributions.
Finally, the dissertation uses a bifurcation theory on the kinetic equation of particles under various velocity and force fields to delineate the conditions for a vortex trap, a point trap, a limit cycle trap, and the selective sorting of the particles into different traps. In the presence of only divergence-free forces on suspended particles, it is found that two parameters, such as those related to Stokes drag, gravity, and flow vorticity, are sufficient to classify all the trap topologies for a given slip velocity distribution. It is also shown that nondivergence-free forces like nonuniform repulsion or attraction can capture suspended particles in one trap and selectively sort a binary suspension into different traps.

目錄

圖目錄 i
第一章、 緒論 1
1.1 前言 1
1.2 基本原理 2
1.2.1 電雙層(electric double layer, EDL)形成機制 2
1.2.2 電滲流(electro-osmotic flow)形成機制 5
1.3 研究動機與文獻回顧 7
1.4 論文架構 14
第二章、 半無窮平面之微渦流生成及結構 17
2.1 單一帶電細長片上之電滲流生成及結構 17
2.1.1 模型描述 17
2.1.2 理想流動類比方法及其應用 20
2.1.3 電滲流流動場及其特性 22
2.1.4 對非均勻外加電場之電滲流的延伸應用 25
2.2 兩個不同帶電細長片之電滲流流動 28
2.2.1 模型描述 28
2.2.2 細長片帶電量、寬度和細長片間距對電滲流動結構的影響 30
2.2.3 幫浦淨流率 33
2.2.4 兩異性電細長片產生之封閉渦流 37
第三章、 有限半圓區域之微渦流生成及結構 41
3.1 半圓平面區域中Stokes流體流動之數學模型及其解 41
3.1.1 微渦流之解析解 42
3.1.2 有限邊界之微渦流解析解 45
3.2 半圓區域下表面有階梯狀滑移速度分布之微渦流解 50
第四章、 利用電滲微渦流結構在半無窮平面區域之粒子捕捉 52
4.1 粒子在微渦流中之運動行為 53
4.2 不同電滲微渦流架構下之粒子捕捉 55
第五章、 利用電滲微渦流結構在半圓區域之粒子操控，包括粒子捕捉、釋放和分選 63
5.1 單一粒子在電滲微渦流流場中之運動 63
5.2 粒子在微渦流中被捕捉和釋放之機制 66
5.2.1 粒子流的線性穩定分析 66
5.2.2 DF場之渦流捕捉陷阱 67
5.2.3 DF場存在情況下，粒子捕捉在底表面之收斂停滯點 68
5.2.4 NDF場存在情況下，粒子捕捉在底表面之收斂停滯點 75
5.2.5 旋轉渦流中之粒子點捕捉陷阱 79
5.2.6 旋轉渦流中粒子在極限環之捕捉和釋放行為 82
5.3 利用渦流中之點捕捉陷阱或極限環捕捉陷阱進行粒子分選 84
5.3.1 利用點捕捉陷阱進行粒子分選 85
5.3.2 利用極限環捕捉陷阱進行粒子分選 87
第六章、 結論和未來研究展望 91
附錄A 理想流動的遠場行為 95
附錄B 單一帶電細長片上電滲微渦流的遠場行為 95
附錄C 細長片上，任意整數次方電荷分布的電滲微渦流解 96
附錄D 微渦流之基本解析解推導 97
附錄E 半圓有限區域微渦流解析解之推導 99
附錄F NDF力場不存在情況下產生之渦流捕捉陷阱 101
附錄G 在微小慣性效應存在下固定點之特徵值 102
參考文獻 104

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