Compute the Tortuosity and the Effective Diffusivity
The DiffuDict module computes the tortuosity factor  and the effective diffusivity of porous media.
The porous media for the calculations with DiffuDict can be an imported structure from a file produced by a 3D imaging device (e.g. CT scanner or FIB/SEM) or an engineered media generated with GeoDict. Depending on the pore size, the diffusing fluid can be considered as a continuum or as single molecules, diffusing by reflections to the pore walls.
The Knudsen number (Kn), which describes the relationship between the pore diameter and the mean characteristic path length of the molecules in the fluid , determines which of both models is dominant.
The computation is parallelized for shared memory workstations or distributed memory clusters.
The Knudsen number (Kn), which describes the relationship between the pore diameter and the mean characteristic path length of the molecules in the fluid, determines which of both models is dominant.:
Small Knudsen numbers
For small Knudsen numbers, the fluid is considered as a continuum and the concentration distribution inside the porous media is governed by Laplace's equation. The effective diffusivity is then determined from the resulting concentration flux applying Fick's first law. The relative diffusivity and the tortuosity factor are then found by comparing the effective diffusivity through the porous material with the bulk diffusivity inside the fluid.
Large Knudsen numbers
For large Knudsen numbers, the reflection of single molecules at the pore walls is simulated to obtain the mean squared displacement of the molecules over time. The effective diffusivity can be computed from this value.
Intermediate Knudsen numbers
For intermediate Knudsen numbers, Bosanquet's approximation is used to find the effective diffusivity by averaging between those two cases.