Modelling Binary, Knudsen and Transition Regime Diffusion Inside Complex Porous Media

Abstract

The problem of gaseous diffusion inside complex porous media arises in the modeling of many chemical processes (e.g. Chemical Vapor Infiltration (CVI), heterogeneous catalysis in porous catalysts, filtration, etc...). A program computing effective diffusivities in the bulk, Knudsen and transition regimes has been designed and tested, which uses a Monte-Carlo mean-square-displacement algorithm. The porous medium has been represented from a special interpretation of a computer 3D discretized image. Simulations were carried out in a typical case of complex structured porous medium: a stacking of tissues (e. g. 2D woven fiber preform for CVI-densified composite materials). The results are presented as tortuosity factors, i.e. deviations from an equivalent medium made of straight cylindrical pores. The evolution of the diffusivities with the geometrical parameters of the tissues, and with the stacking mode has also been studied. It appears that the perpendicular diffusivity is closely related to the proportion of matching holes between different layers of tissue. The intermediate regime appears for Knudsen numbers lying between 100 and 10 -1 . In this domain, the Bosanquet formula only gives a good description if the Knudsen number is multiplied by a factor γ = 1/4. This phenomenon had been reported, to a lesser extent, for unidirectional random fiber packings.