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

Abstract

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.

Breakup of thin films of micro-magnetic drops in perpendicular fields

“…An intricately patterned instability (labyrinthine instability) is reported by Romankiw et al [5] if the fluid is contained between two closely spaced plates (Hele-Shaw cell) and subjected to a normal field. Since then, great efforts have been devoted to this branch of interfacial instability [6][7][8][9][10]. On the other hand, the interfacial instability on a free surface of a horizontal magnetic layer which is not confined on the top is first studied by Cowley and Rosensweig [4].…”

Fingering of Chemical Fronts in Porous Media

“…Because of the influence of such fingers on the physical and chemical processes, numerous studies have analyzed to what extent the fingering instability can be affected, for instance, by heterogeneities of the medium [7], the non-Newtonian character of flows [8], particle accretion [9], the presence of a magnetic field [10], etc.…”

Rotating Hele-Shaw cells with ferrofluids

“…As a result of the ferrofluid interaction with the external field, the usual viscous fingering instability is supplemented by a magnetic fluid instability [10], resulting in a variety of new interfacial behaviors [11][12][13][14][15][16].…”