Statistical geometry of porous media

Abstract

The geometrical characterization of porous media is an important task in problems occurring in hydrology. The usual geometrical quantities, such as porosity, specific surface, etc., are not sufficient to describe a given porous medium fully, and a different approach must therefore be sought. An attempt is made to characterize a porous medium from data which can be read off a photomicrograph. Four possibilities are considered: a correlation function, a spectral analysis in terms of harmonic functions, a spectral analysis in terms of other orthogonal functions, and a spectral analysis of a specially constructed characteristic function of the porous medium in terms of harmonic functions. The two types of harmonic analyses yield the most satisfactory descriptions of a porous medium. The method is applied to an actual example.