Computation of transition and molecular diffusivities in fibrous media

Ordinary and transition regime diffusion in random fiber structures

“…Melkote and Jensen (1992) used an interior radiator mechanism [I-randomness in the terminology of Coleman (1969)l to generate finite samples of the fiber structures they used in their work. The same construction scheme was also employed in their study of Knudsen diffusion in fibrous beds (Melkote and Jensen, 1989).…”

“…This necessitates the use of an adjustable computational parameter, the thickness of a boundary layer around the walls of the porous medium that defines the limits of the area where the discrete random walk has to be followed. The minimum value of this parameter that does not introduce any bias in the simulation results has to be determined carefully on the basis of repetitive calculations (Tassopoulos and Rosner, 1992;Melkote and Jensen, 1992). When an adequately large value is assigned to this parameter, FPT-based procedures give results identical to those of a discrete random walk technique.…”

“…However, the computational cost of such an explicit approach is prohibitive, if a relatively large region of the parametric space of the problem (such as large porosity range) is to be investigated. Ordinary regime diffusion can also be simulated by employing random walks based on the first passage time (FPT) probability distribution (Brown, 1956;Siegel and Langer, 1986;Zheng and Chiew, 1988;Torquato and Kim, 1989;Tassopoulos and Rosner, 1992;Melkote and Jensen, 1992). Instead of moving the molecule step-by-step in the porous medium, such random walks advance it to a random point on the surface of a sphere centered at the current position of the walker and tangent to the closest solid surface.…”

“…A numerical study on transition and bulk diffusion in fibrous beds was presented by Melkote and Jensen (1992), who employed a random walk procedure based on the concept of the first passage time to compute the effective diffusivity. Melkote and Jensen worked on three-directional fiber structures, but, as we will explain in some more detail later, their results are not representative of random fiber structures and therefore cannot be compared with those predicted in this study.…”

Continuum random walk simulations of diffusion and reaction in catalyst particles

“…Another possible way of solving this problem is to use the hybrid method introduced by Reyes and Iglesia (1991) in their investigation of Knudsen and transitional diffusion in catalyst particles, and subsequently used by Melkote and Jensen (1992), Tassopoulos and Rosner (1992), and Tomadakis and Sotirchos (1993). The hybrid method makes use of ZC plus the discrete random walk method.…”