本論文主要探討微粒子混合器中的渾沌現象和混合效率。混合器的設計理念是透過調整微流道管壁內電極片的電壓來驅使相鄰電雙層內的流體流動，進而產生不同形態的全流體電滲流，再由兩種不同流動型態的週期性轉換來生成渾沌流，以提升微粒子的混合效率。本文將二維矩形微流道的電滲流解析解分出難收斂項與易收斂項兩部分，讓邊界附近的流體流速能夠準確地計算出，然後創造出單渦流、四渦流和複合式渦流三種流動型態。使用各半週期分別計算的演算法，可確保混合器中微粒子運動的預測準確性。
本論文從龐加萊映射發現微粒子在單渦流/四渦流模型和單渦流/複合式渦流模型兩種混合器內，皆出現屬於非渾沌區和屬於渾沌區的不同運動方式，初始位置在非渾沌區的微粒子會持續進行規律循環；在渾沌區的微粒子則發散式分布且無法進入非渾沌區內。本文進而發現側邊流速或轉換週期的增加對兩種混合器混合效率的提升皆具有正面的效果，並且據此提出兩階段式混合器的設計。一般而言，側邊流速和轉換週期的增加皆會使得微粒子運動的渾沌區域擴大，因而改善混合效率。兩階段式混合器，在混合前後期分別採用高低不同的側邊流速，可兼具快速混合和節約能源的優勢。模擬研究顯示，單渦流/四渦流模型的混合效率不如單渦流/複合式渦流模型，而根據微流道形狀與流體模型去選擇適合的側邊流速和轉換週期，能使混合效率獲得極大的改善。

The thesis mainly investigates the chaotic phenomenon and mixing efficiency in a microparticle mixer. In the design of the mixer, the voltages of the electrodes in the microchannel wall are adjusted to drive the fluid flow within the adjacent electric double layer, thus producing electroosmotic bulk flows of various patterns. To promote the mixing efficiency of microparticles, chaotic flow is generated by periodically switching two different flow patterns. The analytical solution for the electroosmotic flow in a rectangular microchannel is decomposed into a difficult-to-converge part and an easy-to-converge part in order to ensure the computation accuracy for the flow velocity near the wall. Such a solution can be employed to create three flow patterns: single, quadruple, and complex microvortexes. The algorithm of respective computation for each semi-period is proposed to guarantee the prediction accuracy of microparticle motion in the mixer.
From the Poincaré maps of the single/quadruple microvortexes model and single/complex microvortexes model, it is found that the rectangular area can be divided into non-chaotic and chaotic zones. A microparticle whose initial position in the non-chaotic zone will continue to circulate regularly; microparticles in the chaotic zone will distribute in a divergent manner and cannot enter the non-chaotic zone. Moreover, it is found that an increase in the side flow velocity or switching period has a positive effect on the mixing efficiency. Generally, such an increase would enlarge the chaotic zone, thus promoting the mixing efficiency. This leads to the design of a two-stage mixer, in which the side flow velocity is high during the early period and is reduced afterwards. The two-stage mixer would possess the advantages of fast mixing and energy saving. Simulation studies reveal that single/complex microvortexes model is superior to single/ quadruple microvortexes model in terms of mixing efficiency, and mixing efficiency can be greatly improved by selecting the appropriate side flow velocity and switching period according to the shape of the microchannel and the flow model.

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