Validation of the dusty-gas model for binary diffusion in low aspect ratio capillaries via direct simulation Monte Carlo

The dusty-gas model is an empirical formulation commonly used to describe gas flows in porous media. While experiments have validated the model for pores with high aspect ratios, i.e. pores are long compared to their radii, a validation for near-unity aspect ratios is lacking. We used direct simulation Monte Carlo as a theoretical benchmark to evaluate the accuracy of the dusty-gas model for binary diffusion in low aspect ratio capillaries. We found that the dusty-gas model deviates by less than 7% for all cases that we considered, and our results suggest that the highest errors are due to breakdown of the binary diffusivity when the diffusion length is smaller than the mean free path. We characterized the risk of incurring significant error from this breakdown according to the Knudsen number, aspect ratio, and fluid properties, concluding that the risk is generally low for air/water mixtures. Further, practical limits of fabrication and operation typically require aspect ratios greater than 1, in these cases we calculated less than 3% error. Therefore, the dusty-gas model can be seen as a suitable phenomenological model for gas transport in nanoporous structures in a wide range of applications such as heat transfer, catalysis, and water purification.