Local Volume Fraction Fluctuations

Abstract

One of the most important morphological descriptors of heterogeneous materials is the volume fraction of the phases or, in the case of porous media, the porosity (i.e., the volume fraction of the fluid phase). Although the volume fraction is constant for statistically homogeneous media, on a spatially local level it fluctuates. An interesting question is the following: How does the “local” volume fraction fluctuate about its average value? The answer to this query has relevance to a number of problems, including scattering by heterogeneous media (Debye et al. 1957), the study of noise and granularity of photographic images (O’Neill 1963, Bayer 1964, Lu and Torquato 1990c), transport through porous media (Hilfer 1991, Hilfer 1996), mechanical properties of composites (Ostoja-Starzewski 1993), the properties of organic coatings (Fishman, Kurtze and Bierwagen 1992), and the fracture of composites (Botsis, Beldica and Zhao 1994, Torquato 2000a). It is actually in the context of photographic science that this question of local volume fraction fluctuations was first probed, and here primarily for simple two-dimensional models of photographic emulsions that do not account for impenetrability of the grains (O’Neill 1963, Bayer 1964).