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

Matthias Neumann*, Fabio Eduardo Machado Charry, Karin Zojer, Volker Schmidt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Number of pages15
JournalMethodology and Computing in Applied Probability
Early online date29 Jan 2020
Publication statusE-pub ahead of print - 29 Jan 2020


  • Parametric copula model
  • Porosity
  • Sack paper
  • Statistical microstructure analysis
  • Tortuosity
  • X-ray microcomputed tomography (μ-CT)

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Fields of Expertise

  • Advanced Materials Science


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