Influence of pore length non-uniformity on transport properties of random nanopore networks

Abstract

The modeling of fluid transport in nanoporous materials has long attracted attention because of the numerous industrial applications of such materials, particularly in membrane-based separations, and others such as adsorptive gas separation and storage, catalysis, and the emerging area of nanofluidics. While effective medium theory has been widely used in modelling this transport, a critical approximation that all pores have the same length is commonly made, whose adequacy is unknown. Here we apply effective medium theory to a randomly overlapping capillary model having an inherent pore length distribution related to the pore radius distribution, and compare the network transport properties with those of the commonly used uniform pore length random network. We find that the consideration of nonuniform pore length distribution leads to significantly higher effective diffusivity and lower associated apparent tortuosity, mediated by the lower mean pore length of large pores due to their higher probability of overlap. The decrease in pore length with an increase in pore radius and the competing effects of adsorption and diffusion, lead to more complex behaviour of the transport properties with variation in temperature and relative standard deviation of the pore radius distribution. Our results clearly demonstrate the importance of considering nonuniformity of pore length, as the conventional uniform pore length approximation leads to significantly different and therefore misleading results.