Viscous Fingering Patterns in Ferrofluids |
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Authors: | Michael Widom José A Miranda |
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Institution: | 1. Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213 2. Departamento de Fisica, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
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Abstract: | 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 fingerlike 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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