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本研究以理論推導及實驗分析來探討旋轉Hele-Shaw Cell中磁性流體與柴油間可互溶界面的不穩定現象。首先以因次分析方法得到了磁力、黏滯力、離心力、壓力和科氏力間的大小量級關係，並依此為基準設計實驗。在無磁場的旋轉Hele-Shaw Cell實驗中，可以觀察到在越高轉速下其可互溶界面呈現越不穩定現象，且產生之指狀物個數也越多。
接著，開放式的流場與封閉式流場中實驗結果幾近相同，首先可以觀察到在同種磁性流體且同磁場下，其越高轉速下其指狀化現象越加明顯，是為離心力作用；然而在同轉速之實驗下，可以觀察到前期在越高磁場下界面旋轉半徑之成長趨勢為最高，是為磁力作用，而後期低磁場實驗的旋轉半徑成長極速增強是為離心力作用，而高磁場實驗則由於不同磁場會造成其黏滯度增加程度不同，因而成長趨勢有所抑制，是為黏滯力作用。
而比較三種磁性流體之結果，可以觀察到磁性流體EMG905之成長趨勢為最快，EMG909和EMG911則排序次之，第一個因素為EMG905的初始磁化率和濃度為最高，故其擴散作用和磁力作用最為強烈；第二個因素為EMG905與柴油之密度差異最大，故在旋轉流場下由於其離心力會增加其Rayleigh-Taylor instability，故EMG905之成長趨勢為最快。
在封閉式流場之實驗中，可視為剛體運動故產生一逆向壓力梯度(無因次參數為 ∆ρ/ρ_0 )，會抑制指狀化不穩定現象之成長，故封閉式流場的旋轉半徑成長趨勢會較開放式流場之結果為慢。
最後，比較開放式流場中不同平板間距h之實驗結果，可以得到在較大之平板間距h下之旋轉半徑成長速率較快的結果，故可得到三維方向之平板間距h會對可互溶界面不穩定現象之成長造成一定的影響。

In this study, the interfacial instabilities of miscible magnetic fluids and diesel were theoretically and experimentally studied in a rotating Hele-Shaw cell. First, the dimensional analysis was used to understand the relation magnetic force, viscous force, centrifugal force, pressure force and Coriolis force. In addition, it could assist in experimental design.
Two kinds of the flow field were studied, the open Hele-Shaw cell and the closed Hele-Shaw cell. The labyrinthine fingering phenomena of the miscible magnetic fluid interface on a perpendicular magnetic field were investigated. First, the interface of miscible magnetic fluids and diesel became more unstable when the rotating speed and the consequent centrifugal force were increased without magnetic field applied.
Three ferrofluids were used in this study. To compare the results, the gyration radius will be grown fast with ferrofluid EMG905. The first reason was that the initial susceptibility and particle concentration for EMG905 were higher than that for the other two ferrofluids. So the diffusion and magnetic effects for EMG905 will be the most obvious one. The second reason was that the density difference between EMG905 and the diesel was the highest, so the Rayleigh-Taylor instability will increase for the centrifugal force.
In the first part, the subject focused on the labyrinthine fingering phenomena of the interface in an open Hele-Shaw cell. Experimental results showed that the gyration radius will be grown fast with increasing the rotating speed in the same magnetic field. Under the same rotating speed condition, the gyration radius will be grown fast with higher magnetic field in the first stage. And in the later stage, there will be some differences between the developments of gyration radius with different magnetic fields. For lower magnetic field, the growth will be demonstrated by the centrifugal force. For higher magnetic field, the viscosity will be increased because of the perpendicular magnetic field, and the viscous force will stabilize the interface.
The second part of this study focused on the experiment in a closed Hele-Shaw cell. For the closed flow field, it can be regard as a solid-body rotation and there will produce an opposite pressure force, which can help to stabilize the interface. Experimental results showed that the growth of gyration radius will be fast in an open Hele-Shaw cell. By doing so, the appearance of the opposite pressure force can be proved.
At last, the experimental results also showed that the growth of gyration radius will be fast in an open Hele-Shaw cell with higher gap. So, the three-dimensional effect played an important role in miscible magnetic fluids and diesel.

目錄
中文摘要 I
Abstract III
誌謝 V
目錄 VI
表目錄 VIII
圖目錄 IX
符號表 XIV
第一章 序論 1
1.1 磁性流體之介紹 1
1.2 Hele-Shaw Cell 之介紹 3
1.3 文獻參考 4
1.3.1磁流體特性影響研究 4
1.3.2指狀化不穩定現象(Fingering Instability) 7
1.3.3磁性流體指狀化不穩定現象 9
1.3.4可互溶磁流體不穩定界面與其成長率研究 15
1.3.5旋轉Hele-Shaw Cell 指狀化不穩定現象 16
1.4研究目的 22
第二章 研究方法 23
2.1無因次化理論分析 23
2.1.1旋轉Hele-Shaw Cell 23
2.1.2實驗矩陣 36
2.2實驗方法 37
2.2.1實驗流體之選用 37
2.2.2實驗流程─開放流場 41
2.2.3實驗流程─封閉流場 42
2.2.4實驗設備 43
第三章 結果與討論 50
3.1開放式旋轉Hele-Shaw Cell 實驗 50
3.1.1無磁場下旋轉Hele-Shaw Cell 中磁流體的不穩定現象 50
3.1.2外加垂直磁場下旋轉Hele-Shaw Cell 中磁性流體的不穩定現象 57
3.2封閉式旋轉Hele-Shaw Cell實驗 76
3.2.1定性比較 76
3.2.2定量分析 83
3.3封閉式與開放式流場之比較 95
3.4三維效應對界面不穩定性之影響 100
第四章 結論 107
參考文獻 109

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