可互溶磁性流體在不同間隔的Hele-Shaw Cell中改變外加磁場上升速率時不穩定現象研究

Abstract

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.