Simulation and experiment of gas diffusion in a granular bed

Abstract: The diffusion of gas through porous material is important to understand the physical processes underlying cometary activity. We study the diffusion of a rarefied gas (Knudsen regime) through a packed bed of monodisperse spheres via experiments and numerical modelling, providing an absolute value of the diffusion coefficient and compare it to published analytical models. The experiments are designed to be directly comparable to numerical simulations, by using precision steel beads, simple geometries, and a trade-off of the sample size between small boundary effects and efficient computation. For direct comparison, the diffusion coefficient is determined in Direct Simulation Monte Carlo (DSMC) simulations, yielding a good match with experiments. This model is further-on used on a microscopic scale, which cannot be studied in experiments, to determine the mean path of gas molecules and its distribution, and compare it against an analytical model. Scaling with sample properties (particle size, porosity) and gas properties (molecular mass, temperature) is consistent with analytical models. As predicted by these, results are very sensitive on sample porosity and we find that a tortuosity $q(\varepsilon)$ depending linearly on the porosity $\varepsilon$ can well reconcile the analytical model with experiments and simulations. Mean paths of molecules are close to those described in the literature, but their distribution deviates from the expectation for small path lengths. The provided diffusion coefficients and scaling laws are directly applicable to thermophysical models of idealised cometary material.