Unified network model for adsorption–desorption in systems with hysteresis

Abstract

The problem of equilibrium and kinetics for adsorption–desorption of condensable vapors in porous media is studied experimentally and theoretically. For adsorption, the network model for diffusion based on pore blocking theory with percolation (in the network) added by effective medium approximation is further improved. A new predictive model based on properties of the Bethe lattices is proposed to account for the existence of liquid-filled “blind” pores that result in a decrease in the total diffusion rate. For desorption, a new “shell and core” (or shrinking core) representation of the network model is proposed. Information from adsorption–desorption equilibria is needed to compute the thickness of the shell in which desorption/evaporation occurs for concentrations higher than the percolation threshold. These models form a unified equilibrium-kinetics theory for gas-porous solid systems that exhibit hysteresis. The models are applied to the systems silica gel-water vapor and Vycor glass-nitrogen. Concentration-dependent Fickian diffusivities for these systems have been measured for both adsorption and desorption branches. The adsorption model successfully predicts the experimental data with a maximum in diffusivity. The desorption model correctly predicts the concentration dependence of diffusivity with a steep minimum at the percolation threshold.