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Direct relations between morphology and transport in Boolean models

Scholz, C., Wirner, F., Klatt, M.A., Hirneise, D., Schröder-Turk, G.E., Mecke, K. and Bechinger, C. (2015) Direct relations between morphology and transport in Boolean models. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92 (4).

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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.

Publication Type: Journal Article
Murdoch Affiliation: School of Engineering and Information Technology
Publisher: American Physical Society
Copyright: © 2015 American Physical Society
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