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We study sorption and transport processes in dry and wet (preadsorbed with CH2Br2) Vycor glass by combining small angle scattering and three-dimensional (3D) stochastic reconstruction methods. Three-phase systems of solid, condensate, and void space, are generated for the first time, by the combination of the above methods. The resulting 3D images can visualize the evolution of the adsorption process and show how sorption alters the pore space characteristics of the material. Desorption is modeled in this system with the additional employment of an invasion percolation algorithm to account for the hysteresis effect caused by the inaccessible regions of the porous matrix. It is found that desorption is simulated very well provided that the main mechanism for hysteresis depends only on the topology of the pore space and not on thermodynamic effects. Based on a random-walk procedure, Knudsen transport properties of the reconstructed images are also determined for different degrees of saturation, providing very good agreement with experimental relative permeability data. Thus, relative permeability reflects purely the pore accessibility properties of the material and may assist in discerning their exact contribution to the equilibrium sorption hysteresis loop.

In the present study we examine the thermodynamic consistency of lattice Boltzmann equation (LBE) models that are based on the forcing method by comparing different numerical treatments of the LBE for van der Waals fluids. The different models are applied for the calculation of bulk and interfacial thermodynamic properties at various temperatures. The effect of the interface density gradient parameter, kappa , that controls surface tension, is related explicitly with the fluid characteristics, including temperature, molecular diameter, and lattice spacing, through the employment of a proper intermolecular interaction potential. A comprehensive analysis of the interfacial properties reveals some important shortcomings of the LBE methods when central finite difference schemes are employed in the directional derivative calculations and proposes a proper treatment that ensures thermodynamically consistent interfacial properties in accord with the van der Waals theory. The results are found to be in excellent quantitative agreement with exact results of the van der Waals theory preserving all the major features of the interfacial characteristics of vapor-liquid systems of different shapes and sizes.

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