From pore network prediction based on the constructal law to macroscopic properties of porous media

Transfers through porous materials where the driving force is a concentration difference or a pressure difference are useful characteristics of a pore network arrangement. Two schools of thought are prevalent in this area-first, macroscopic characteristics are not too difficult to obtain experimentally and parameters like diffusion coefficients or permeability serve as input data for models describing transfers through porous media. Such parameters are helpful in describing the transfers but they are of no value for predicting transfers because they are very poorly related to pore network topology. Secondly, theoretical descriptions at the level of the material microstructure fail to represent the actual material, even when they are coupled with up-to-date visualization techniques (e.g. three-dimensional tomography). This work documents a tentative link between the pore network geometry and the diffusion coefficient, a macroscopic parameter. We apply the constructal law of design to determine the most probable pore path configurations that minimize the diffusion transfer resistance and determine the macroscopic diffusion coefficient. The predicted diffusion coefficients are compared to experimental results from aqueous and gaseous diffusion paths through two porous materials.