Theory of Dispersion in a Granular Medium

This report is a presentation of the theoretical aspects of the investigations and a few confirmatory laboratory studies of the dispersion process. The basic assumptions associated with the development of the dispersion equation, based on the applicability of a heuristic expression similar to Pick's law, are described. In general, these assumptions limit its application to a homogeneous medium in which the dispersion process is anisotropic. The present level of knowledge is made apparent through the presentation of several solutions for the differential equation that approximates the dispersion process. Adsorption and its effect on the fate of a contaminant is given only limited discussion because of the lack of formal studies, on a macroscopic scale, applicable to the hydrologic regimen. The equations approximating dispersion in a two-fluid system (salt-fresh water) are also presented.