MICROSTRUCTURE, CONNECTIVITY AND EFFECTIVE CONDUCTIVITY OF DISPERSIONS AND HETEROGENEOUS MEDIA (PERCOLATION, GELATION)

Many processes of great engineering importance take place in heterogeneous and disordered materials such as colloidal despersions, porous media, composite materials, etc. The common aspect of these systems is that their bulk or macroscopic properties depend strongly on their microscopic structure. The techniques of equilibrium statistical mechanics developed for liquid state theory are used to model the microstructure of these materials. In this work, a dispersion, i.e. a two-phase medium consisting of spherical particles distributed in a continuous matrix, is used to model heterogeneous media.;The connectivity behavior and the percolation transitions of monodispersed and multisized dispersions are determined analytically for assemblies of fully-penetrable, permeable and sticky spheres. The pair-connectedness function (which expresses the probability of finding two particles displaced by r that are in the same connected cluster of particles) is computed for the first time, in the Percus Yevick approximation. This approach gives a model for reversible gelation which takes into account the effect of solvent and excluded-volume interactions which are neglected in the traditional Flory-Stockmayer theory. In addition, this method provides a tool for the study of other agglomerating phenomena such as equilibrium polymerization and solute association.;The effect of the structure on the effective thermal or electrical conductivity k(,e) of a dispersion is examined and, it is found that the structure has an important influence. Furthermore, the effect of skin resistance on the particle surfaces and of internal radiation within the particle phase on k(,e) are studied. The results obtained are found to agree with the reported experimental data in the literature over a wide range of conditions.;Various aspects of the microstructure of dispersions are studied. Exact expressions for the specific interfacial surface area of porous media and dispersions are obtained. They are evaluated for different models ranging from fully-penetrable to totally impenetrable spheres. These results are of use in the modeling of chemical reactions and fluid flow in porous materials.