### Abstract

A general formalism is developed to statistically characterize the microstructure of porous and other composite media composed of inclusions (particles) distributed throughout a matrix phase (which, in the case of porous media, is the void phase). This is accomplished by introducing a new and general n-point distribution function H_{n} and by deriving two series representations of it in terms of the probability density functions that characterize the configuration of particles; quantities that, in principle, are known for the ensemble under consideration. In the special case of an equilibrium ensemble, these two equivalent but topologically different series for the H_{n} are generalizations of the Kirkwood-Salsburg and Mayer hierarchies of liquid-state theory for a special mixture of particles described in the text. This methodology provides a means of calculating any class of correlation functions that have arisen in rigorous bounds on transport properties (e.g., conductivity and fluid permeability) and mechanical properties (e.g., elastic moduli) for nontrivial models of two-phase disordered media. Asymptotic and bounding properties of the general function H_{n} are described. To illustrate the use of the formalism, some new results are presented for the H_{n} and it is shown how such information is employed to compute bounds on bulk properties for models of fully penetrable (i.e., randomly centered) spheres, totally impenetrable spheres, and spheres distributed with arbitrary degree of impenetrability. Among other results, bounds are computed on the fluid permeability, for assemblages of impenetrable as well as penetrable spheres, with heretofore unattained accuracy.

Original language | English (US) |
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Pages (from-to) | 843-873 |

Number of pages | 31 |

Journal | Journal of Statistical Physics |

Volume | 45 |

Issue number | 5-6 |

DOIs | |

State | Published - Dec 1 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- Disordered media
- Kirkwood-Salsburg equations
- Mayer equations
- composite and porous materials
- effective conductivity
- elastic moduli
- fluid permeability
- liquids
- microstructure
- n-point distribution functions
- scaled-particle theory