本研究首先以實驗及理論分析來探討Hele-Shaw Cell流場中，在不同磁場強度與不同磁場上升速率下，兩種可互溶磁流體(Miscible Magnetic Fluid) 間的介面不穩定性問題。起始為一個圓形的磁性流體液滴，外層緊鄰可互溶環境流體-柴油，再施以一個均勻向上的垂直磁場，所形成的磁力會造成液滴周圍產生微小的指狀物，稱為複雜指狀化的不穩定現象。
結果顯示當磁性流體磁化強度及導磁率愈低時，其可互溶介面放射性的大波波形越不明顯；而介面周長的成長趨勢在初期呈現快速爬升，但隨著磁場強度增加，在到達實驗所設定的最大磁場值後會慢慢變小，最終趨於一定值。另外，本研究定義一個時間無因次參數 為擴散作用與磁場影響流場的特徵時間比，當其值越大時，外加磁場作用力越強，介面的初始成長率會越大，實驗結果發現介面的初始成長率與 成線性關係，且當 大於1000時，可互溶流體介面會有大波現象的產生，而大波波長(λ)與Hele-Shaw Cell的寬度(h)會有一關係為 ，此大波乃三維不穩定現象。
其次在旋轉Hele-Shaw Cell的實驗中，觀察到了兩種指狀化的現象，第一個是向心力所造成大的指狀物，第二個是由於外加磁場的影響形成細小的指狀物，其細小的指狀物由於擴散作用的影響，造成濃度變低，磁化強度變小，指狀物因而受到柯氏力的影響而呈現順時針旋轉的形狀。

In the first part of this thesis, the interfacial instability of miscible magnetic fluids in a Hele-Shaw Cell is studied, experimentally and theoretically, with different magnitudes and incremental rates of magnetic field. The initial circular oil-based magnetic fluid drop is surrounded by the miscible fluid, diesel. The external uniform magnetic fields induce small fingerings around the initial circular interface, so called labyrinthine fingering instability caused by the magnetic dipolar forces.
It is shown that the lower magnetization and susceptibility of the magnetic fluid, the less the secondary waves around the interface that were dominated by the three-dimensional effects. At the beginning when the magnetic field is applied, the interfacial length grows fast. It then decreases when the magnetic fields reach the selected values, and finally approaches certain asympototic values. In addition, a dimensionless time parameter, , is defined as the ratio of the characteristic diffusion time to the characteristic magnetic time. The larger represents the stronger magnetic fields and the faster initial growth rate. The initial growth rate is directly proportional to . When is larger than 1000, the secondary wave appears. A correlation is found between the secondary wave length (λ) and the gap of the Hele-Shaw Cell (h): .
In the second part of this thesis, two fingering phenomena are observed in a rotating miscible Hele-Shaw cell flow: the large branching pattern which is caused by the centrifugal force and the small fingering pattern which is induced by the external magnetic field. Due to the diffusion, the concentration of the magnetic fluid around each small fingering is getting lower, and the magnetization is weaker, accordingly. Therefore, the Coriolis force becomes important and influences the small fingering pattern.

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