本研究為探討磁性流體與周遭可互溶性液體在Hele-Shaw cell中及外加磁場的影響下的介面不穩定現象；磁性流體由初始的液滴直徑(D0)開始觀察，因為磁性流體受到磁場的影響下介面會有微小指狀物產生，而在一段時間後磁性流體介面又會演變成大波的形狀。本研究主要觀察Hele-Shaw cell中磁性流體與周遭可互溶性的柴油介面的不穩定性現象，探討其不同的Hele-Shaw cell間隔所產生的三維效應，對於其不穩定現象的影響。
本研究分成兩部分進行，第一部分為不同定值的外加磁場下，探討磁性流體在不同的Hele-Shaw cell間隔中的第三維效應關係，在結果中發現到當Hele-Shaw cell板間隔h與磁性流體的初始直徑D0的比值大於0.06並不會符合三維效應相關關係式λ=(7±1)h，其中也發現到大波效應不僅僅受到一種三維效應影響，也會因為其Hele-Shaw cell間隔的不同產生不同的影響。
第二部分為觀察垂直磁場值為線性上升時對磁性流體可互溶性介面的影響，並且改變參數不同的磁性流體、不同的Hele-Shaw cell間隔、不同的垂直磁場最大值及不同的垂直磁場直線性上升率；而在此又分為前期20秒的觀察與整體實驗的300秒觀察。前期20秒發現到磁性流體介面周長初始成長與外加磁場直線性上升率較相關，受Hele-Shaw cell間隔的三維效應影響較小；而在整體實驗300秒的觀察主要觀察磁性流體的大波波長λ、Hele-Shaw cell間隔h與所定義的Pe'之間的關係，當中結果發現到其一當Pe'大於19000時，其λ/h磁性流體介面才會有受到三維效應與外加磁場的影響產生大波的現象；其二發現而當Hele-Shaw cell間隔h減小時，其三維效應也逐漸減小，當 h=0.8mm磁性流體介面幾乎沒有大波的現象發生，從中也證實三維效應存在於Hele-Shaw cell中的不穩定現象；其三發現到以Pe'=19000為定界，如果Pe'小於19000其區間受到影響力為擴散影響較大定義為擴散影響區間，Pe'大於19000則開始受到較強力的磁場影響，定義為磁力影響區間。

In this study, we investigated the interfacial instability of magnetic fluid and miscible fluid in a Hele-Shaw cell. Initially, because the magnetic force induced, there are some fingering surrounding circular ferrofluid with on initial diameter of D0.After a period of time, the interface becomes a wavy shape. This syudy focuses on observing the three-dimension at effect due to the instability incurred by Hele-Shaw cell’s gap.
There are two ways to find out the three-dimensional effect. First, we conduct the experiment under a fixed value of magnetic field. The result implied that when the ratio of the Hele-Shaw cell’s gap to the ferrofluid’s initial diameter is less than 0.6.The result will conform with the λ=(7±1)h,where λis the wave length and h is the Hele-Shaw cell’s gap.
Second, we conduct the experiment under an environment of which is the magnetic field value rise linearly to a setting value from zero. In this case, two part were analyzed the early stage is considered when the magnetic field is low value, and the late stage is considered when the magnetic field is in fixed value. In the early stage, we observed the period from 0s to 20s. We found out that the three-dimensional effect is very small in the early stage, the main influencing parameter is the rise rate of magnetic field. In the later stage, we observed the interfacial instability of ferrodluid. We analyze the interrelation of the wave length (λ)、the Hele-Shaw cell’s gap (h) and the dimensionless parameter Pe'. It’s found that when the parameter Pe' is greater than 19000, the three-dimensional effect will induce the instability the induced a wave shape. Another result is when the Hele-Shaw cell’s gap is smaller the three-dimensional effect becomes smaller moreover there are a commit when the Hele-Shaw cell’s gap is smaller than 0.8mm,the three-dimension effect will disappear for the ferrofulid instability. Another result is that Pe'=19000 is a demarcation point in the relative diagram of λ/h & Pe' , the dissuasive regime occurs for Pe'<19000, and the magnetic regime occurs for Pe'>19000.

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