Effects of sweep rates of external magnetic fields on the labyrinthine instabilities of miscible magnetic fluids

The interfacial instability of miscible magnetic fluids in a Hele-Shaw Cell is studied experimentally, with different magnitudes and sweep rates of the external magnetic field. The initial circular oil-based magnetic fluid drop is surrounded by the miscible fluid, diesel. The external uniform magnetic fields induce small fingerings around the initial circular interface, so call labyrinthine fingering instability, and secondary waves. When the magnetic field is applied at a given sweep rate, the interfacial length grows significantly at the early stage. It then decreases when the magnetic field reaches the preset values, and finally approaches a certain asymptotic value. In addition, a dimensionless parameter, Pe, which includes the factors of diffusion and sweep rate of the external magnetic field, is found to correlate the experimental data. It is shown that the initial growth rate of the interfacial length is linearly proportional to Pe for the current experimental parameter range and is proportional to the square root of the sweep rate at the onset of labyrinthine instability.