Local volume fraction fluctuations in heterogeneous media

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Abstract
The volume fractions of multiphase heterogeneous media fluctuate on a spatially local level even for statistically homogeneous materials. A general formulation is given to represent the standard deviation associated with the local volume fraction of statistically homogeneous but anisotropic D‐dimensional two‐phase media for arbitrary‐shaped observation regions. The standard deviation divided by the macroscopic volume fraction, termed the coarseness, is computed for D‐dimensional distributions of penetrable as well as impenetrable spheres, for a wide range of densities and observation‐region sizes. The effect of impenetrability of the particles, for fixed observation‐region size, is to reduce the coarseness relative to that of the penetrable‐sphere model, especially at high densities. For either sphere model, increasing the dimensionality D decreases the coarseness.