Models to predict effective diffusivities in porous media with pores of nonuniform cross section
Wheeler, Michael Lewis
Master of Science
In this study, several new models were developed for diffusion in porous media. These models all use a simple unit pore which consists of a single large spherical cavity connected to smaller neck pores. A single pore model was developed to compare predicted diffusivities with measured effective diffusivities in beds of glass spheres. These comparisons show that the unit pore can be used to accurately model diffusion in porous media where the pores vary in cross section. Several different network models were developed using the unit pore. The simplest of these approximates the porous media as a regular network of unit pores. To find the effective diffusivity, a mass balance was performed at a node in the network. The concentration terms in the mass balance were then expanded in Taylor series about the node. This yielded a differential form of the mass balance i.e. the equation of continuity. The effective diffusivity is extracted from this differential form of the mass balance. Three dimensional networks were used to find a relationship between the effective diffusivity and macroscopic properties e.g. porosity and surface area. An electrical network model is developed to study networks of nonidentical pores. The simple technique of extracting the effective diffusivity from the mass balance at a single node does not work for networks of nonidentical unit pores. The electrical network model allows the prediction of effective diffusivities by solving the analogous electrical network problem. This technique is used to model effective diffusivities in porous media where the pore geometry varies considerably. Finally, the network pore model is used to predict the rate of drug release from a polymer-drug composite as the drug dissolves in water. To be released, the drug must first dissolve and then diffuse through the polyrcer matrix. A simple network model was used to predict the effective diffusivity in the polymer matrix. The prediction of release also involves the solution of a Stephan problem. The predicted results are compared with experimentally measured rates of drug release.