Generalizing the fractal model of soil structure: the pore—solid fractal approach

A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory

“…The PSF is also defined (Perrier et al, 1999) by an iterative process: dividing a square into n 2 subsquares; then generating constant proportions s, p and f of solids, pores and porous subparts within these subsquares; then continuing across an infinite range of scales by partitioning the f porous subsquares using the same proportions as for the whole. The fractal dimension D is D(0) = (log (n 2 f )/log n).…”

Analysis of the effective thermal conductivity of fractal porous media

“…Now, the fractal models of porous media are enjoying considerable popularity [1,9,18,3,5]. This is in part due to the relatively small number of parameters that can define a fractal porous of great complexity and rich structures.…”

Geometric and Hydrodynamic Characteristics of Three-dimensional Saturated Prefractal Porous Media Determined with Lattice Boltzmann Modeling

“…If the iterative phase is composed solely of solids (or pores), the result is a mass (or pore) prefractal. Pore-solid prefractals (PSF) are generated when the iterative phase is composed of both voids and solids (Perrier et al 1999). Mass prefractals consist of different-sized pores and small uniformly-sized solid particles, while pore prefractals are made up of different-sized solid particles separated by small uniformly-sized pores.…”

“…PSF contain both solid-and pore-size distributions, and thus are expected to be the most physically heterogeneous. All three types of fractals have been used as models of natural porous media (Katz and Thompson 1985;Garrison et al 1992;Perrier et al 1999).…”