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On Variability and Interdependence of Local Porosity and Local Tortuosity in Porous Materials: a Case Study for Sack Paper

Author

Listed:
  • Matthias Neumann

    (Ulm University)

  • Eduardo Machado Charry

    (Graz University of Technology
    Graz University of Technology)

  • Karin Zojer

    (Graz University of Technology
    Graz University of Technology)

  • Volker Schmidt

    (Ulm University)

Abstract

The variability and interdependence of local porosity and local mean geodesic tortuosity, which is a measure for the sinuosity of shortest transportation paths, is investigated at the example of the microstructure in sack paper. By means of statistical image analysis, these two morphological characteristics are computed for several cutouts of 3D image data obtained by X-ray microcomputed tomography. Considering cutouts of different sizes allows us to study the influence of the sample size on the local variability of the considered characteristics. Moreover, the interdependence between local porosity and local mean geodesic tortuosity is quantified by modeling their joint distribution parametrically using Archimedean copulas. It turns out that the family of Gumbel copulas is an appropriate model type, which is formally validated by a goodness of fit test. Besides mean geodesic tortuosity, we consider further related morphological characteristics, describing the sinuosity of those shortest transportation paths, whose minimum diameter exceeds a predefined threshold. Moreover, we show that the copula approach investigated in this paper can also be used to quantify the negative correlation between local porosity and these modified versions of local mean geodesic tortuosity. Our results elucidate the impact of local porosity on various kinds of morphological characteristics, which are not experimentally accessible and which are important for local air permeance – a key property of sack paper.

Suggested Citation

  • Matthias Neumann & Eduardo Machado Charry & Karin Zojer & Volker Schmidt, 2021. "On Variability and Interdependence of Local Porosity and Local Tortuosity in Porous Materials: a Case Study for Sack Paper," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 613-627, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09761-1
    DOI: 10.1007/s11009-019-09761-1
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    References listed on IDEAS

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    1. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    2. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2003. "Evaluating Kolmogorov's Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i18).
    3. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
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