Simple Formulas for Porosity and Specific Surface of the Cherry-Pit Model

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 _phi_ and specific surface s is a problem obviously too difficult for the contemporary mathematics. Already in the 1980ies approximations were found which are presented in the book by Torquato (2002). Since 2009 these formulas have been refined by the authors, by combination of simulation and ideas of stochastic geometry. This includes the study of the poly-disperse 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.