Transport of macromolecules in porous media

Abstract

Three models of flow and diffusion of macromolecules in a porous medium are developed. The first model is fully deterministic and is, for given pore space and molecular configurations, exact. It can take into account the effect of both the convection and diffusion of the macromolecules, is valid for both steady and transient transport, and can yield all the important quantities characterizing the transport process. The second model is stochastic in which the macromolecules execute a random walk in the pore space, the transition probability of which takes into account the effect of molecular and pore sizes, and the flow field in the medium. The third model is based on an effective-medium approximation and can be used for both steady and transient diffusion of the molecules in the pore space. The porous medium is represented by a two- or three-dimensional network of interconnected cylindrical pores, in which the effective pore sizes are selected from an experimentally measured pore size distribution. The macromolecules are represented by hard spheres of a given hydrodynamic radius. Detailed calculations are carried out with the three models, and the advantages and disadvantages of each model are discussed. The predictions are compared with the experimental data on polymer diffusion in a porous catalyst, and in silica glasses. Good agreement between the predictions and the data is found in both cases. The extension of the models to more complex molecular and pore shapes is also discussed.