Monte Carlo simulation of gas diffusion in regular and randomized pore systems

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Abstract
The rate of rarefied gas transport in clusters of hollow spheres and cylinders is determined using Monte Carlo simulation methods. The spheres and the cylinders, representing large pore bodies and narrow pore throats in actual porous materials, are either placed at the nodes and the branches, respectively, of a cubic network or arranged randomly in space allowed to overlap freely. The Knudsen diffusion coefficient is computed by simulating molecular trajectories and calculating statistical averages of the mean-square displacement of a sample of molecules per unit of travel time. The accuracy of approximating the transport resistance of regular structures of spheres and cylinders by the resistance of a commonly used network of sinusoidal conduits is checked in this work for the first time. It is found that networks of sinusoidal conduits approximate fairly well systems of spheres and cylinders in the low density region when Knudsen diffusivity estimates are pursued. However, at moderate and high densities, pore overlap becomes significant and the sinusoidal conduit geometry fails to represent efficiently the actual geometry during gas diffusion owing to the development of considerable end effects and strong interaction between remote overlapping pores. Regular arrays of spheres and cylinders yield diffusivities that compare well with those in structureless systems with randomized pore positions for the same number density of pores. Sphere-to-sphere, sphere-to-cylinder, and combined size correlations are introduced to regular structures using properly devised algorithms. Comparison of correlated-to-uncorrelated systems for continuous and discrete sphere and cylinder radius distributions reveals that sphere-to-sphere size correlation considerably facilitates the gas transport for any value of the pore system density. On the contrary, sphere-to-cylinder size correlation has a relatively small impact on the diffusivity results, which becomes non-negligible in low-density systems only and for discrete size distributions.