本論文提出一種混合有限元素及PIC法的數值模式，來模擬在十字型毛細管電泳系統中，不同帶電離子的遷移現象。毛細管電泳系統主要是藉由具有不同電荷質量比的離子遷移來分離分析物。不同於傳統的數值方法，這種方法可以用於模擬不同帶電離子，在毛細管電泳系統中的遷移現象，以及處理複雜的幾何形狀和不規則的邊界條件。
本論文的研究重點為，在不同的德拜長度和轉角圓弧半徑時，對於在注入和分離過程中，正離子和負離子遷移現象的影響。數值結果指出，這些效應明顯地影響不同電荷分析物的遷移現象，如下所示。
由於正離子和負離子於溶劑中受到相反電力作用。因此，正離子比負離子較快遷移至分離流道。而隨著德拜長度減少，正離子和負離子會較快進入分離流道。同時，使得較多的正離子往分離流道遷移，並遷移至離注入流道較遠處。而負離子則會遷移至比正離子更接近分離流道的上壁面處。研究結果指出較小的德拜長度可以減少注入過程時間，以及在分離過程中提供更多分析物。
在注入的過程中，隨著增加轉角圓弧半徑，使得正離子和負離子不僅更快遷移至分離流道，並遷移至分離流道中離注入流道較遠處。而在分離的過程中，隨著增加轉角圓弧半徑，使得正離子和負離子的分佈會比較寬，且需要較長的時間使正離子和負離子可以完全分離。因此，當轉角圓弧半徑較大時，則需要更多的時間來注入和分離不同帶電離子。
數值的結果指出在毛細管電泳系統中，電場對於不同帶電離子遷移現象的影響，具有重要的意涵。這些發現對於毛細管電泳系統的設計、控制及發展，提出有助益的見解。

The dissertation proposed a numerical model of hybrid finite-element and particle-in-cell method to simulate charged ion migration in the cross-channel capillary zone electrophoresis system. Analytes separated by capillary zone electrophoresis are governed by the ion migration with different charge-to-mass ratios. Different to the traditional numerical method, this method can be used to simulate the migration phenomenon of the differently charged ions for handling complex geometries and irregular boundary conditions in the capillary zone electrophoresis system.
This research focused on the effects of Debye length and corner arc radius on the migration phenomena of the positive and negative ions in the injection and separation process. The numerical results indicate that these effects can affect obviously the migration phenomena of differently charged analytes as expressed in the following.
The positive and negative ions are subject to opposite electric field force relative to the buffer solvent. Hence, the positive ions migrate into the separation channel faster than the negative ions. With decreasing the Debye length, the positive and negative ions are faster carried into the separation channel. Furthermore, more positive ions migrate into the separation channel and migrate more far away from the injection channel. Meanwhile, the negative ions migrate more close to the upper wall of the separation channel. The results indicate that the short Debye length can shorten time for the injection process and provide more analytes for the separation process.
In the injection process, the positive and negative ions migrate not only faster into the separation channel but also more far away from the injection channel with increasing the corner arc radius. In the separation process, the zones of positive and negative ions are wider and the time to completely separate is longer with increasing the corner arc radius. Consequently, as corner arc radius is larger, more time is needed to inject and separate charged ions.
The numerical results provide useful insights into the influences of the electric field on the migration of differently charged ions in capillary zone electrophoresis systems. These findings have significant implications for design and control of capillary zone electrophoresis systems.

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