Stability of magnetic fluid penetration through a porous medium with uniform magnetic field oblique to the interface

Recent work has shown that the fingering instability, which develops when a more viscous fluid is pushed through the voids of a porous medium or through a Hele-Shaw cell by a less viscous fluid, can be prevented if a magnetic field is applied tangential to a flat fluid interface separating magnetizable and non-magnetizable fluids. This earlier work is extended here by considering equilibrium magnetic field components both perpendicular and parallel to the flat interface. The tangential field component stabilizes those waves traveling along the field lines while the normal field is destabilizing. The analysis is developed through a general set of relations for perturbation field and flow interfacial variables defined for a "prototype" magnetizable fluid layer which can be used to describe the small signal stability characteristics of layered fluid systems. In a uniform tangential magnetic field geometry, experimental results of the most unstable wavelength in a Hele-Shaw cell are shown to agree well with theory.