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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.
Bargiel, M. and Moscinski, J.,
C-Language Program for the Irregular Close Packing of Hard Spheres, Computer Phys. Comm., vol. 64, pp. 183–192, 1991.
Bezrukov, A., Bargiel, M., and Stoyan, D.,
Statistical Analysis of Simulated Random Packings of Spheres, Part. Part. Syst. Char., vol. 19, pp. 111–118, 2002.
Chiew, Y.C. and Glandt, E.D.,
Interfacial Surface Area in Dispersions and Porous Media, J. Colloid Interface Sci., vol. 99, pp. 86–96, 1984.
Chiu, S.N., Stoyan, D., Kendall, W.S., and Mecke, J.,
Stochastic Geometry and its Applications, 3rd ed., Chichester: Wiley & Sons, 2013.
Devasena, M. and Indumathi, M.N.,
Distribution of Elemental Mercury in Saturated Porous Media, J. Porous Media, vol. 18, pp. 1221–1229, 2015.
Elsner, A.,Wagner, A., Aste, T., Hermann, H., and Stoyan, D.,
Specific Surface Area and Volume Fraction of the Cherry-Pit Model with Packed Pits, J. Phys. Chem. B, vol. 113, pp. 7780–7784, 2009.
Goetze, P., Mendes, M.A.A., Asad, A., Jorschick, H.,Werzner, E.,Wulf, R., Trimis, D., Gross, U., and Ray, S.,
Sensitivity Analysis of Effective Thermal Conductivity of Open-Cell Ceramic Foams using a Simplified Model based on Detailed Structure, Spec. Top. Rev. Porous Media, vol. 6, pp. 1–10, 2015.
Gotoh, K., Nakagawa, M., Furuuchi, M., and Yoshigi, A.,
Pore Size Distributions in Random Assemblies of Equal Spheres, J. Chem. Phys., vol. 85, pp. 3078–3080, 1986.
Advanced Theories of Two-Phase Flow in Porous Media, in Handbook of Porous Media, K. Vafai, Ed., Boca Raton: CRC Press, pp. 47–59, 2015.
Hermann, H., Elsner, A., and Stoyan, D.,
Surface Area and Volume Fraction of Random Open-Pore Systems, Modell. Simul. Mater. Sci. Eng., vol. 21, no. 8, Article ID 085005, 2013.
Hermann, H. and Elsner, A.,
Geometric Models for Isotropic Random Porous Media: A Review, Adv. Mater. Sci. Eng., vol. 2014, Article ID 562874, 2014.
Jodrey, W.S. and Tory, E.M.,
Computer Simulation of Close Random Packing of Equal Spheres, Phys. Rev. A, vol. 32, pp. 2347– 2351, 1985.
Kansal, A.R., Torquato, S., and Stillinger, F.H.,
Computer Generation of Dense Polydisperse Sphere Packings, J. Chem. Phys., vol. 117, pp. 8212–8218, 2002.
Kumar, P. and Topin, F.,
Impact of Anisotropy on Geometrical and Thermal Conductivity of Metallic Foam Structures, J. Porous Media, vol. 18, pp. 949–970, 2015.
Kumar, P., Topin, F., and Tadrist, L.,
Geometrical Characterization of Kelvin-Like Metal Foams for Different Strut Shapes and Porosity, J. Porous Media, vol. 18, pp. 637–652, 2015.
Lee, S.B. and Torquato, S.,
Porosity for the Penetrable-Concentric-Shell Model of Two-Phase Disordered Media: Computer Simulation Results, J. Chem. Phys., vol. 89, pp. 3258–3263, 1988.
Panda, M.N. and Lake, L.W.,
Estimation of Single-Phase Permeability from Parameters of Particle-Size Distribution, AAPG Bull., vol. 78, no. 7, pp. 1028–1039, 1994.
Rikvold, P.A. and Stell, G.,
Porosity and Specific Surface for Interpenetrable-Sphere Models of Random Two-Phase Media, J. Chem. Phys., vol. 82, no. 2, pp. 1014–1020, 1985.
Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches,Weinheim: Wiley-VCH, 1995.
Random Sets: Models and Statistics, Int. Stat. Rev., vol. 66, pp. 1–27, 1998.
Stoyan, D., Wagner, A., Hermann, H., and Elsner, A.,
Statistical Characterization of the Pore Space of Random Systems of Hard Spheres, J. Non-Cryst. Solids, vol. 357, pp. 1508–1515, 2011.
Bulk Properties of Two-Phase Disordered Media – I. Cluster Expansion for the Effective Dielectric Constant of Dispersions of Penetrable Spheres, J. Chem. Phys., vol. 81, pp. 5079–5088, 1984.
Random Heterogeneous Materials: Microstructure and Macroscopic Properties, New York: Springer-Verlag, 2002.
Torquato, S. and Stell, G.,
Microstructure of Two-Phase Random Media. IV. Expected Surface Area of a Dispersion of Penetrable Spheres and its Characteristic Function, J. Chem. Phys., vol. 80, pp. 878–880, 1984.
Vafai, K., Ed.,
Handbook of Porous Media, 3rd ed., Boca Raton: CRC Press, 2015.
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