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Fractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon


What happens when one attempts to push water through a fluid of higher viscosity? Under appropriate experimental conditions, the water breaks through in the form of highly branched patterns called viscous fingers. Water was used to push a more viscous but miscible, non-newtonian fluid in a Hele-Shaw cell. The resulting viscous finger instability was found to be a fractal growth phenomenon. Reproducible values of the fractal dimension df were found and were interpreted using a modification of the diffusion limited aggregation model.

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Nittmann, J., Daccord, G. & Stanley, H. Fractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon. Nature 314, 141–144 (1985).

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