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Fractal viscous fingering: Experiments and models

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  • Nittmann, Johann

Abstract

Highly ramified fingering structures occur when water is forced under pressure to displace a high viscosity shear-thinning fluid in a Hele Shaw cell. We found that water fingers grow by splitting of the leading finger tips giving rise to arborescent structures which obey fractal scaling. Their Hausdorff dimension df is 1.70 for a wide range of experimental conditions. We show that diffusion limited growth models can accurately simulate the growth of these fractal patterns.

Suggested Citation

  • Nittmann, Johann, 1986. "Fractal viscous fingering: Experiments and models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 124-133.
  • Handle: RePEc:eee:phsmap:v:140:y:1986:i:1:p:124-133
    DOI: 10.1016/0378-4371(86)90212-8
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    Cited by:

    1. Lenormand, Roland, 1986. "Pattern growth and fluid displacements through porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 114-123.

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