實驗室整合晶片設備需要高效率的微流體混合機制來完成指定工作，因此對於電滲微混合器的高效設計有極高需求，特別是易於生產製造的矩形微混合器。本論文旨在設計一種高效的矩形渾沌電滲微混合器，透過調整嵌入矩形管壁內電極條的電壓來形成合適的電滲流類型，並通過在兩種不同流動類型之間週期性切換來產生渾沌流，以實現快速的粒子混合。
本研究首先針對微混合器內矩形區域的混合現象進行分析，並發現一些有用結果。其一，切換週期對混合速度有顯著影響，增加切換週期可以增大渾沌混合區域並減小非渾沌誘捕區域。當粒子出現在誘捕區域時，它們會進行週期性運動並失去混合功能。其二，龐加萊截面可以模擬混合器設計的空白區域，其存在會降低穩態混合占比，但可由增加寬邊流速來改善此占比。其三，出現在渾沌空白區域的粒子可能會以慢速運動至渾沌混合區域，然而出現在非渾沌空白區域的粒子會被困住而無法離開。本研究接著提出了李亞普諾夫指數法來彌補龐加萊截面模擬耗時的缺點，可以快速識別各個區域的粒子運動行為，並評估混合器設計對粒子初始位置的敏感性。此外，還開發了基於龐加萊截面的二階時延模型來計算混合效率，為微混合器的最佳設計提供了有力工具。
最後，本研究針對1:1至4:1的四個整數長寬比，提出適用於渾沌混合器的多種對稱和非對稱電滲微渦流類型，並利用上述混合效率計算方法，透過選擇多個操作變數(切換週期、寬邊流速、渦流流動方向)來獲得最佳混合器設計。同時，鑑於長寬比常為非整數的實際情況，本研究進一步將四種整數長寬比的最佳設計延伸應用於長寬比介於1:1至4:1範圍內的微混合器。研究結果顯示，所設計的微混合器比現有的微混合器具有更廣泛的應用性和更佳性能。

Lab-on-a-chip devices require highly efficient microfluidic mixing mechanisms to complete specified tasks. Hence, there is a high demand for efficient designs of electroosmotic micromixers, especially rectangular micromixers that are easy to manufacture. This thesis aims to design an efficient rectangular chaotic electroosmotic micromixer. It forms suitable electroosmotic flow patterns by adjusting the voltages of the electrode strips embedded in the rectangular wall, and generates chaotic flow for rapid particle mixing by periodically switching between two different flow patterns.
This research first analyzes the mixing phenomena in the rectangular area within the micromixer and uncovers several useful results. First, the switching period has a significant impact on the mixing speed, and increasing the switching period can increase the chaotic mixing area and reduce the non-chaotic trapping area. When particles appear in the trapping area, they will undergo periodic motion and loss mixing capability. Second, the Poincaré sections can simulate the blank areas of the mixer design. Their existence will reduce the steady-state mixing percentage, but this percentage can be improved by increasing the wide-side flow rate. Third, particles that appear in a chaotic blank area may move to a chaotic mixing area at a slow speed, while particles that appear in a non-chaotic blank area will be trapped and unable to leave. This research then proposes the Lyapunov exponent method to remedy the time-consuming shortcoming of Poincaré section simulation, which can quickly identify the particle motion behavior in various areas and evaluate the sensitivity of the mixer design to the initial position of particles. In addition, a second-order plus time delay model based on the Poincaré sections is developed to calculate the mixing efficiency, which serves as a powerful tool for the optimal design of micromixers.
Finally, for four integer aspect ratios from 1:1 to 4:1, this research proposes a variety of symmetric and asymmetric electroosmotic micro-vortex flow patterns suitable for chaotic mixers, and uses the aforementioned mixing efficiency calculation method to obtain the optimal mixer designs by selecting multiple operating variables (switching period, wide-side flow rate, vortex flow direction). At the same time, in view of the practical situation where the aspect ratio is often a non-integer, this research further extends the optimal designs for the four integer aspect ratios to micromixers with aspect ratios ranging from 1:1 to 4:1. It is shown that the proposed designed micromixers have wider applicability and better performance than available micromixers.

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