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.
For small Knudsen numbers, the fluid is considered as a continuum and the concentration distribution inside the porous medium 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.
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.
For intermediate Knudsen numbers, Bosanquet's approximation is used to find the effective diffusivity by averaging between those two cases.
- DiffuDict module computes the tortuosity factor and the effective diffusivity of porous media
- The computation is parallelized for shared memory workstations or distributed memory clusters.
Examples of DiffuDict applications
- Determination of the tortuosity of pores.
- Estimation of the effective diffusivity of gas diffusion layers with or without micro-porous layers.
- Computation of the concentration distribution inside a catalyst layer.
Additional modules needed?
- The GeoDict Base package is needed for basic functionality.
- DiffuDict works on 3D (micro-) structure models that can either be a segmented 3D image (microCT-scan, FIB-SEM) imported with ImportGeo-VOL, or a 3D structure model created with one of the GeoDict modules for Digital Material Design, e.g. FiberGeo for nonwovens, GrainGeo for granular or sintered structure models or sphere-packings, or FoamGeo for foams.