Off-lattice reconstruction of porous media: critical evaluation, geometrical confinement and molecular transport

Abstract

Disordered porous solids are examples of interfacial systems where an internal surface partitions and fills the space in a complex way. These media play an important role in industrial processes. One challenging problem deals with the ability to describe the morphology and the topology of disordered porous media. Quantitative knowledge of the three-dimensional pore (3D) network is important in order to understand the role of geometric confinement in adsorption, condensation, transport and reaction processes. In this paper, we first describe a simple way to build `off-lattice' reconstructed porous media with or without periodic boundaries, based on Gaussian random fields. The possibility of having a continuous and analytical description of the internal interface avoids finite size effects and is highly suitable for studying gas kinetics, molecular dynamics or adsorption process within the representative elementary volume. Critical evaluation of these computer models and comparison with experiments are performed for different types of geometrical disorder (cement pastes, soils, Vycor glass, symmetrical sponge phase, mass or surface fractals). In the second part of this work, we analyse one the most basic transport types in disordered porous media, i.e. the gas diffusion in the Knudsen or molecular regime. We first discuss how geometric confinement influences this transport through its self-diffusion propagator. Available experimental data, such as the tortuosity factor, and numerical simulations on 3D off-lattice reconstructed porous media are directly compared. Finally, we focus more especially on the Knudsen diffusion. We show that this transport process can be analysed in term of a continuous time random walk formalism (CTRW) and strongly depends on the analytical shape of the pore chord distribution function, f p( r). Different no Gaussian regimes are observed when f p( r) follows an algebraic law with an exponent μ*. For 1<μ*<3, the Knudsen diffusion is a Levy walk. Analytical properties of this Levy walk are given for 1<μ*<2 (mass or surface fractal). Comparison with numerical simulations conducted inside some 3D off-lattice reconstructions conclude this paper.