本研究主要以理論分析與實驗方法來探討Hele-Shaw Cell中磁性流體與柴油間可互溶界面的不穩性問題。
本研究中理論與實驗皆分為兩部分，第一部分為垂直磁場下磁性流體的複雜指狀化現象，實驗中觀察到磁性流體與柴油間所形成的可互溶界面，在通以垂直磁場的情況下會有指狀化不穩定現象發生，而本研究中針對不同上升速率的磁場強度以及不同磁場強度的預磁情況下觀察磁性流體界面周長在20秒內的成長並與理論作結合，實驗結果顯示磁性流體界面周長的成長並非線性而是分作兩階段，第一個階段為不穩定現象發生前因界面擴散現象造成的線性成長，第二階段為磁性流體指狀化不穩定現象發生後其界面周長呈現exponential rise to max的成長，在此階段磁性流體可互溶界面周長一開始會因為指狀物的產生而快速成長，但隨著界面濃度越來越低其成長速度會趨於平緩。而我們取指狀物生成後初期時其界面周長隨時間的變化為初始成長率α，並與我們定義之無因次參數magnetic Peclect number, Pe’關係作圖，其結果為兩者呈線性關係，而在預磁情況下α會與我們所定義之無因次磁場√((3μ_0)/ρχ) M呈線性關係。
第二部分為旋轉Hele-Shaw Cell實驗，我們首先以因次分析方法得到了磁力、黏滯力、離心力、科氏力間的大小量級關係，並依此為基準設計實驗。而實驗結果發現當轉速越快離心力越大時，磁性流體與柴油間的的可互溶界面越不穩定，但是實驗結果發現在垂直磁場越大時其界面反而越穩定越不容易甩出，針對這個現象我們利用理論分析與實驗結果做比對，歸納出其主要原因為：實驗所使用赫姆霍茲線圈並非完全均勻磁場，其磁場在r方向的梯度變化產生了與離心力相反的力，進而導致磁性流體的界面在磁場越大時越穩定。

In this thesis, the interfacial instabilities of miscible magnetic fluids and diesel in a Hele-Shaw cell are studied theoretically and experimentally.
Two subjects are studied. In the first part, the labyrinthine fingering phenomena of the magnetic fluids on a perpendicular magnetic field is investigated. Experimental images clearly show unstable fingerings appearing on the interface of miscible magnetic fluids and diesel under a uniform perpendicular magnetic field. The growth of the interface length in the initial 20 seconds is analyzed from the experimental images, under different incremental rates of magnetic fields and different magnitudes of pre-magnetization. The experimental results are compared with the theoretical predictions. Experimental results show that the growth of the interface length is nonlinear with time and can be divided into two stages: the initial diffusion-dominating stage and the magnetic-force-dominating stage. The in initial growth rate of the interface length α is calculated at the ensuing time when fingers occur. The initial growth rate α is shown correlated linearly with (1) the dimensionless magnetic Peclect number, Pe’, considering the effects of different incremental rates of magnetic fields, and (2) the dimensionless magnetic field √((3μ_0)/ρχ) M in the pre-magnetization cases. Both Pe’ and √((3μ_0)/ρχ) M are derived from our theoretical analyses.
The second subject of this thesis focuses on the stability analyses of the miscible magnetic fluid interface in a rotating Hele-Shaw cell. First, the dimensional analysis is performed to get the dimensionless groups of parameters, which help to understand the orders of magnitude between magnetic force, viscous force, centrifugal force, and Coriolis force, and design the experiments matrix. Experimental results show that the interface of miscible magnetic fluids and diesel appears more unstable when the rotating speed and the consequent centrifugal force increase. Contrarily, the experimental results show that the interface will be more stable when the magnitude of the perpendicular magnetic field increases, The theoretical analyses show that the slight non-uniformity of the magnetic field generated by the pair of Helmholtz coils at a certain distance from their centerline results in a negative magnetic field gradient which generates an opposite force to the centrifugal force, and therefore stabilizes the interface therefore.

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