本論文運用高精確之數值方法研究在非穩態間隙可互溶 Hele-Shaw 流場界面之不穩定性。我們將重點放在三個相關之控制參數的影響：Peclet number 、黏滯度比 、Korteweg stresses 參數 。其中 與 所扮演的作用，我們歸納出二個結果：較高的 值在沿著界面周圍附近會有較明顯的分枝，其導致有較長的界面長度；而較大的黏滯度比會產生顯著的指狀物滲透，其以量化可表示成有較大的迴轉直徑。而在Korteweg stresses 參數 上，我們也證實其如同一有效表面張力：它具有穩定化可互溶界面作用，與相似的不可互溶情況下所得的指狀物圖形有很大的相似性。最後我們發現到當在高的 值，大的 值及小的 值時，液滴外表會有明顯的發展現象：一些向外之指狀物被掐斷，及在最後可觀察到液滴的分離。我們證明此液滴分離過程可由較強之界面應力作用下而被抑制住。

Numerical simulations of interfacial instabilities on a miscible droplet in a time-dependent gap Hele-Shaw cell by means of high accurate numerical schemes are presented. We place the focal point on the influence of three relevant control parameters : Peclet number , viscosity contrast , Korteweg stresses .Concerning the role of and , we deduce two general results: higher Peclet number favors branching around a nearly circumferential region; while larger viscosity contrast results in more significant finger penetrations . We have also verified that the Korteweg stresses parameter does act as an effective interfacial tension: it stabilizes the miscible interface, leading to fingering patterns that present a greater resemblance with the structures obtained in similar immiscible situations. Finally, we have identified the development of a visually striking phenomena in the limit of high ,large , and relatively small : some outward fingers pinch, and subsequent droplet detachment is observed. We show that such a droplet detachment process can be prevented by the action of stronger interfacial stresses.

中文摘要 ---------------------------------------------------------------------I
英文摘要 --------------------------------------------------------------------II
誌謝 -------------------------------------------------------------------III
目錄 --------------------------------------------------------------------IV
圖目錄 ---------------------------------------------------------------------V
符號說明 --------------------------------------------------------------------VI

第一章 緒論-----------------------------------------------------------------1
1-1 研究背景-------------------------------------------------------------1
1-2 研究目的-------------------------------------------------------------2
1-3 本文架構-------------------------------------------------------------3

第二章 物理問題與統御方程式-------------------------------------------------4
2-1 物理問題-------------------------------------------------------------4
2-2 統御方程式-----------------------------------------------------------4
2-3 邊界條件-------------------------------------------------------------7

第三章 結果與討論-----------------------------------------------------------8
3-1 擴散、黏滯性、Korteweg stresses作用之影響----------------------------8
3-1.1 參考範例-------------------------------------------------------------9
3-1.2 控制參數 的影響------------------------------------------------------9
3-1.3 黏滯度比控制參數 的影響---------------------------------------------10
3-1.4 Korteweg stresses控制參數 的影響------------------------------------11
3-2 液滴再變回圓形及指狀物競長行為的定量分析----------------------------14
3-2.1 界面長度之定量分析--------------------------------------------------14
3-2.2 迴轉直徑之定量分析--------------------------------------------------15

第四章 結論與未來展望------------------------------------------------------18
4-1 結論----------------------------------------------------------------18
4-2 未來展望------------------------------------------------------------19

參考文獻 --------------------------------------------------------------------20
簡歷 --------------------------------------------------------------------52

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