Unified network model for diffusion of condensable vapors in porous media

A unified network model is formulated for predicting effective Fickian diffusivities of condensable vapors in porous media where capillary condensation and adsorption - desorption hysteresis occur. The model unifies the equilibrium theory based on the pore-blocking interpretation of hysteresis in the interconnected network of pores and the percolation model of mass transport in the network with randomly interspersed regions for capillary condensation and surface flow. The Bethe network is used to represent the porous medium, and the effective medium theory is employed to obtain the effective diffusivity. Using the information on the connectivity and the positions of the closure points of the hysteresis loop enclosed by the equilibrium primary adsorption and primary desorption isotherms, the concentration dependence of the effective diffusivity is predicted. The model is applied to the systems water vapor-silica gel, water vapor-activated alumina, and literature data. It successfully predicts the concentration dependence of the effective diffusivity in the whole range of relative pressures for systems both with and without a peak in the diffusivity.