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Journal of Porous Media
SIMPLE FORMULAS FOR POROSITY AND SPECIFIC SURFACE OF THE CHERRY-PIT MODEL
Institute of Stochastics, TU Bergakademie Freiberg, D-09596 Freiberg, Germany
Institute for Solid State and Materials Research, IFW Dresden, P.O. Box 270116, D-01171
Sächsische Landesbibliothek – Staats- und Universitätsbibliothek Dresden (SLUB), D-01054
The cherry-pit or penetrable concentric-shell model is an important, very successful stochastic model for random porous media with open pores. It is based on a random system of hard spheres (the "pits"), which are dilated in order to
get open pores. The exact determination of porosity φ and specific surface s is a problem obviously too difficult for contemporary mathematics. In the 1980s approximations were found which are presented in the book by Torquato
(Random Heterogeneous Materials: Microstructure and Macroscopic Properties, New York: Springer-Verlag, 2002).
Since 2009 these formulas have been refined by the authors through a combination of simulation and ideas of stochastic
geometry. This includes the study of the polydispersed case of pits with random radii, which was mastered by means of
correction factors. In the present paper the true nature of these factors is explained, which leads to simple and elegant formulas in which only the first three moments of the radius distribution appear.
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