title: Direct relations between morphology and transport in Boolean models.
abstract: 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.
authors.affiliation: 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.|Institut für Multiskalensimulation, Nägelsbachstraße 49b, Friedrich-Alexander Universität Erlangen-Nürnberg, 91052 Erlangen, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Scholz
authors.affiliation: 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Wirner
authors.affiliation: Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7B, 91058 Erlangen, Germany.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Klatt
authors.affiliation: 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Hirneise
authors.affiliation: Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7B, 91058 Erlangen, Germany.|Murdoch University, School of Engineering & IT, Maths & Stats, 90 South Str., Murdoch WA 6150, Australia.
authors.forename: Gerd E
authors.initials: GE
authors.lastname: Schröder-Turk
authors.affiliation: Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7B, 91058 Erlangen, Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Mecke
authors.affiliation: 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.|Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Clemens
authors.initials: C
authors.lastname: Bechinger
mesh_terms: D008962:Models, Theoretical; D009010:Monte Carlo Method; D010539:Permeability; D016062:Porosity