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Rescaling relations between two-and three-dimensional local porosity distributions for natural and artificial porous media

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  • Virgin, B.
  • Haslund, E.
  • Hilfer, R.

Abstract

Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensionl plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite correlation lenghts, a good degree of correspondence between the two sets of local porosity distributions can be obtained by rescaling lengths, and the mapping associating corresponding distributions can be found from two-dimensional observations alone. The agreement between associated distributions is good as long as the linear extent of the measurement cells involved is somewhat larger than the correlation length, and it improves as the linear extent increases. A simple application of the central limit theorem shows that there must be a correspondence in the limit of very large measurement cells, because the distributions from both sets approach normal distributions. A normal distribution has two independent parameters: the mean and the variance. If the sample is large enough, local porosity distributions from both sets will have the same mean. Therefore corresponding distributions are found by matching variances of two- and three-dimensional local porosity distributions. The variance can be independently determined from correlation functions. Equating variances leads to a scaling relation for lengths in this limit. Three particular systems are examined in order to show that this scaling behavior persists at smaller length-scales.

Suggested Citation

  • Virgin, B. & Haslund, E. & Hilfer, R., 1996. "Rescaling relations between two-and three-dimensional local porosity distributions for natural and artificial porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 1-20.
  • Handle: RePEc:eee:phsmap:v:232:y:1996:i:1:p:1-20
    DOI: 10.1016/0378-4371(96)00131-8
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    References listed on IDEAS

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    1. Boger, F. & Feder, J. & Jøssang, T. & Hilfer, R., 1992. "Microstructural sensitivity of local porosity distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(1), pages 55-70.
    2. Hilfer, R. & Nøst, B. & Haslund, E. & Kautzsch, Th. & Virgin, B. & Hansen, B.D., 1994. "Local porosity theory for the frequency dependent dielectric function of porous rocks and polymer blends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(1), pages 19-27.
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    Cited by:

    1. Biswal, B. & Manwart, C. & Hilfer, R., 1998. "Three-dimensional local porosity analysis of porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(3), pages 221-241.
    2. Andraud, C. & Beghdadi, A. & Haslund, E. & Hilfer, R. & Lafait, J. & Virgin, B., 1997. "Local entropy characterization of correlated random microstructures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 307-318.

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