Labyrinthine instability of miscible magnetic fluids

We consider an inhomogeneous magnetic fluid (MF), modeling a miscible MF pair, in a Hele-Shaw cell under a normal field. A linear stability analysis for the sharp straight interface (analytically) and for the diffused one (numerically) is performed. For the former case, the neutral curves and the stability diagram are found along with the critical wavelength and parameter values. Oscillatory or monotonous instabilities are shown to occur. For the diffused interface, we recognize the importance of 2D flow viscous effects along with the conventional wall friction and observe that in strong fields the dominant wavelength scales as the cell gap