本論文針對矩形微管道內懸浮粒子，利用時變電滲微渦流產生之混沌對流來建構微混合器，其設計原理是透過空間與時間地調整埋設於液固界面下電極片之電壓，以在壁面形成特定時變且非均勻介達電位分布，進而在外加平行電場作用下產生所需微渦流。
文中提出封閉矩形區域內電滲流的二維半解析解，以準確且快速計算流體的運動速度。此半解析解結合文獻上半圓區域電滲流解析解以及矩形底部半圓弧之數值解，推導出四種微渦流類型，分別為環繞整個管道截面的單一渦流、同等大小反向旋轉的四個渦流、上下反向旋轉的雙渦流、以及左右反向旋轉的雙渦流。模擬研究顯示週期性地變換前兩種微渦流場類型，可以產生混沌對流以混合粒子，而最佳混合效率可藉由選擇適當的週期大小和管壁滑移速度來達成。

This thesis investigates the construction of a micromixer using chaotic advection created by time-dependent electroosmotic microvortex flows for suspended particles in a rectangular conduit. The design principle is to modulate spatially and temporally the voltages of the electrodes embedded beneath the liquid-solid interface. Such modulation would form a specific time-dependent and nonuniform distribution of zeta potentials at the conduit’s walls and subsequently creates the required microvortex flows when subjected to external parallel electric fields.
A two-dimensional semianalytical solution is proposed to compute accurately and rapidly the fluid velocities of electroosmotic flows in a confined rectangular cell. This solution combines an analytical solution for semicircular electroosmotic flows in the literature and the numerical solution along the semicircular arc on the bottom of the rectangular cell to derive four microvortex patterns. The four patterns consist of, respectively, a single vortex circulating across the entire cell, four counter-rotating vortices of equal size, two counter-rotating vortices on the upper and lower sides, and two counter-rotating vortices on the left and right sides. Simulation studies show that chaotic advection for particle mixing can be induced by periodically alternating between the first two flow patterns, while the best mixing efficiency can be achieved by properly selecting the period and the slip velocities at the conduit’s walls.

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