Viscous fingering patterns in ferrofluids
نویسندگان
چکیده
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. PACS number(s): 47.20.Gv, 47.20.Ma, 47.20.ky, 03.40.Gc
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