Viscous fingering patterns in ferrofluids

Details Viscous fingering patterns in ferrofluids Viscous fingering patterns in ferrofluids

1998-02-18

arxiv.org/abs/cond-mat/9802194v1

Physics

Condensed Matter

Soft Condensed Matter

29 pages, 5 figures, Latex

Scientific paper

10.1023/B:JOSS.0000033156.44251.

Viscous fingering occurs in the flow of two immiscible, viscous fluids between the plates of a Hele-Shaw cell. Due to pressure gradients or gravity, the initially planar interface separating the two fluids undergoes a Saffman-Taylor instability and develops finger-like structures. When one of the fluids is a ferrofluid and a perpendicular magnetic field is applied, the labyrinthine instability supplements the usual viscous fingering instability, resulting in visually striking, complex patterns. We consider this problem in a rectangular flow geometry using a perturbative mode-coupling analysis. We deduce two general results: viscosity contrast between the fluids drives interface asymmetry, with no contribution from magnetic forces; magnetic repulsion within the ferrofluid generates finger tip-splitting, which is absent in the rectangular geometry for ordinary fluids.

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