Binglin Lu

Local volume fraction fluctuations in heterogeneous media

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.

Chord‐length and free‐path distribution functions for many‐body systems

We study fundamental morphological descriptors of disordered media (e.g., heterogeneous materials, liquids, and amorphous solids): the chord‐length distribution function p(z) and the free‐path distribution function p(z,a). For concreteness, we will speak in the language of heterogeneous materials composed of two different materials or ‘‘phases.’’ The probability density function p(z) describes the distribution of chord lengths in the sample and is of great interest in stereology. For example, the first moment of p(z) is the ‘‘mean intercept length’’ or ‘‘mean chord length.’’ The chord‐length distribution function is of importance in transport phenomena and problems involving ‘‘discrete free paths’’ of point particles (e.g., Knudsen diffusion and radiative transport). The free‐path distribution function p(z,a) takes into account the finite size of a simple particle of radius a undergoing discrete free‐path motion in the heterogeneous material and we show that it is actually the chord‐length distribution fu...

Rigorous bounds on the fluid permeability: Effect of polydispersivity in grain size

Rigorous bounds on the fluid permeability (on resistance) of porous media composed of spherical grains with a continuous size distribution are computed. For any finite degree of polydispersivity, scaling the resistance bound by the square of the specific surface (relative to the monodisperse case) yields effectively universal behavior at a fixed sphere volume fraction. A new proposition regarding an exact relationship between the permeability and another effective parameter, the trapping constant associated with diffusion‐controlled reactions among traps, is employed to assess the accuracy of the rigorous bound.

Nearest-neighbour distribution function for systems on interacting particles

One of the basic quantities characterising a system of interacting particles is the nearest-neighbour distribution function H(r). The authors give a general expression for H(r) for a distribution of D-dimensional spheres which interact with an arbitrary potential. Specific results for H(r) are obtained, for the first time, for D-dimensional hard spheres with D=1, 2 and 3. Their results for D=3 are shown to be in excellent agreement with Monte Carlo computer-simulation data for a wide range of densities. From H(r), one can determine other quantities of fundamental interest such as the mean nearest-neighbour distance and the random close-packing density.