可互溶磁性流體在旋轉Hele-Shaw Cell中的界面不穩定現象之研究

Abstract

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.