Simulation of vapor diffusion in anisotropic particulate deposits

Abstract

In this study we determine the effective diffusivity tensor of computer-generated, particulate, anisotropic deposits. Deposits of polydispersed, spherical particles were generated by several algorithmic models, which simulate different deposition conditions. Depending on the nature of the arriving particle trajectories (diffusive/deterministic), the angle of incidence and the subsequent motion after they establish contact with an already deposited particle, both the deposit anisotropy and final solid fraction can be varied. Monte Carlo simulations of vapor molecules diffusing through cubic samples extracted from the generated deposits provided accurate estimates of their effective diffusivity tensor and associated tortuosities. The effective diffusivities were directly determined over the entire Knudsen number range, assuming self-diffusion in a constant pressure pure gas that consists of hard-sphere elastic molecules with exponentially distributed free-paths. In the continuum limit the effective diffusivities of the porous solids considered here could be closely correlated with porosity alone. Archie's power law [eq. (17)] with an exponent m = 1.45 fitted our computational results accurately. In the Knudsen limit on the other hand the details of the local microstructure became important and so an accurate prediction/correlation of the effective diffusivity required higher order information. An interpolation based on the experimentally measured effective diffusivities in the two Knudsen limits (Scott and Dullien, 1962) was used to correlate the diffusivities in the transition regime. For the deposits analyzed here the diffusivity properties became anisotropic only in the high Knudsen regime, that is, when diffusing molecule/solid interactions dominate. In the Knudsen limit we have also found significant “rectification” effects. Specifically, the transmission probability as determined by the test-molecule method could be up to 25% higher when the molecules diffused away from the target than when they diffused towards the target. Such “rectification” effects are attributed to the tree-like microstructures of the deposits.