Viscous fingering patterns in ferrofluids
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 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.
Cite
@article{arxiv.cond-mat/9802194,
title = {Viscous fingering patterns in ferrofluids},
author = {Michael Widom and Jose A. Miranda},
journal= {arXiv preprint arXiv:cond-mat/9802194},
year = {2009}
}
Comments
29 pages, 5 figures, Latex