Viscous fingering in a magnetic fluid. I. Radial Hele-Shaw flow

Viscous fingering phenomena in a circular geometry are studied for a magnetic fluid submitted to a perpendicular magnetic field. Air is injected at the center of a Hele-Shaw cell filled with a viscous magnetic fluid. The instability of the interface between the air and the magnetic fluid is favored by the presence of a magnetic field. More precisely, the threshold of the instability is magnetic field dependent. The patterns obtained for high values of the magnetic field with a low injection rate are similar to those obtained in the absence of an external field and at high flow rates. We also give a linear analysis for the stability of radial flow under the influence of a magnetic field. This calculation provides us with an understanding of the magnetic field effect.