Direct relations between morphology and transport in Boolean models

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2015
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Scholz, Christian
Wirner, Frank
Klatt, Michael A.
Hirneise, Daniel
Schröder-Turk, Gerd E.
Mecke, Klaus
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Physical Review E. 2015, 92(4), 043023. ISSN 1539-3755. eISSN 1550-2376. Available under: doi: 10.1103/PhysRevE.92.043023
Zusammenfassung

We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.

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ISO 690SCHOLZ, Christian, Frank WIRNER, Michael A. KLATT, Daniel HIRNEISE, Gerd E. SCHRÖDER-TURK, Klaus MECKE, Clemens BECHINGER, 2015. Direct relations between morphology and transport in Boolean models. In: Physical Review E. 2015, 92(4), 043023. ISSN 1539-3755. eISSN 1550-2376. Available under: doi: 10.1103/PhysRevE.92.043023
BibTex
@article{Scholz2015-10-30Direc-39257,
  year={2015},
  doi={10.1103/PhysRevE.92.043023},
  title={Direct relations between morphology and transport in Boolean models},
  number={4},
  volume={92},
  issn={1539-3755},
  journal={Physical Review E},
  author={Scholz, Christian and Wirner, Frank and Klatt, Michael A. and Hirneise, Daniel and Schröder-Turk, Gerd E. and Mecke, Klaus and Bechinger, Clemens},
  note={Article Number: 043023}
}
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