可互溶磁性流體在靜止及旋轉之Hele-Shaw Cell 中的不穩定現象研究

Abstract

In this thesis, the interfacial instabilities of miscible magnetic fluids and diesel in a Hele-Shaw cell are studied theoretically and experimentally. Two subjects are studied. In the first part, the labyrinthine fingering phenomena of the magnetic fluids on a perpendicular magnetic field is investigated. Experimental images clearly show unstable fingerings appearing on the interface of miscible magnetic fluids and diesel under a uniform perpendicular magnetic field. The growth of the interface length in the initial 20 seconds is analyzed from the experimental images, under different incremental rates of magnetic fields and different magnitudes of pre-magnetization. The experimental results are compared with the theoretical predictions. Experimental results show that the growth of the interface length is nonlinear with time and can be divided into two stages: the initial diffusion-dominating stage and the magnetic-force-dominating stage. The in initial growth rate of the interface length α is calculated at the ensuing time when fingers occur. The initial growth rate α is shown correlated linearly with (1) the dimensionless magnetic Peclect number, Pe’, considering the effects of different incremental rates of magnetic fields, and (2) the dimensionless magnetic field √((3μ_0)/ρχ) M in the pre-magnetization cases. Both Pe’ and √((3μ_0)/ρχ) M are derived from our theoretical analyses. The second subject of this thesis focuses on the stability analyses of the miscible magnetic fluid interface in a rotating Hele-Shaw cell. First, the dimensional analysis is performed to get the dimensionless groups of parameters, which help to understand the orders of magnitude between magnetic force, viscous force, centrifugal force, and Coriolis force, and design the experiments matrix. Experimental results show that the interface of miscible magnetic fluids and diesel appears more unstable when the rotating speed and the consequent centrifugal force increase. Contrarily, the experimental results show that the interface will be more stable when the magnitude of the perpendicular magnetic field increases, The theoretical analyses show that the slight non-uniformity of the magnetic field generated by the pair of Helmholtz coils at a certain distance from their centerline results in a negative magnetic field gradient which generates an opposite force to the centrifugal force, and therefore stabilizes the interface therefore.