Random dispersions are frequently encountered in the petro- chemical as well as the high technology industries. Transport and reaction rates in these systems may be characterized by effective properties; some examples are the effectve electrical conductivity of colloidal suspensions and microemulsions, the effective thermal conductivity of composite materials and packed beds, the effective diffusivity of porous media, the effective nutrient consumption or reaction rate in cell aggregates, and the effective ligand binding rate to receptors in biological systems. Estimation and correlation of these effective properties accurately will enhance the understanding and facilitate the design of many engineering operations involving these heterogeneous systems. The effective conductivity (or mass permeability) and the effective reaction rate of a species in a random dispersion of particles depend not only on the properties (physical and chemical) of the constituent phases but also on their geometries, structures and connectivity. Present theories are successful only in describing these effective properties at low to moderate particle densities, and therefore are not applicable to dense dispersions. The calculation of these quantities at high particle concentrations will require taking into account the interplay between the structure of the dispersion and the transport process involved simultaneously. The essential focus of this proposed research is to systematically explore the connection between certain representative "families of structures and their effective conductivity and effective reaction rate. The PI plans to determine these effective properties for dense dispersions. This is achieved by using: (1) methods borrowed from statisitical mechanics of dense fluids to describe the spatial arrangements and clustering behavior of particles, and (2) stochastic random walk theory to model diffusion on a microscopic level (and thus avoiding the solution of the differential equation for the many-particle random system).
