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The effective diffusion coefficient is 
, where 
is the binary diffusion coefficient. The definition of Ψ, as published in the original manuscript and in some cases in the community, is the ratio of the void volume to tortuosity 
and is corrected here to the proper definition of the ratio of the void volume to tortuosity factor (
, where 
). There is some confusion with how the tortuosity of a porous medium relates to the flow or diffusion. An excellent discussion on this is provided by Epstein1 and DeCaluwe et al. ,2 with an additional discussion in Ref. 3, 4. The formulation given in Ref. 1, which gives rise to the tortuosity factor, is summarized here for completeness. Consider a one-dimensional Fickian diffusion in a porous medium modeled as a bundle of parallel capillaries with a constant tortuosity. The superficial axial diffusion flux 
, given in Eq. 1, is related to the interstitial axial diffusion flux 
through the porosity 
. The residence time 
of component 
in the porous medium can be expressed with the thickness 
of the porous medium, the interstitial axial diffusion flux 
, and the mean concentration of 
. The residence time can also be expressed with the effective thickness 
, the average diffusion flux 
, and the mean concentration of 
, where the average diffusion flux is given in Eq. 2. The expressions for the residence time and the relation between the superficial and the interstitial axial diffusion flux are substituted into the expression for the average diffusion flux to give Eq. 3. Equating the right side of Eq. 1, 3, we obtain Ψ in the expression for the effective diffusion coefficient, as described with the updated definition of the ratio of the porosity to the tortuosity factor
Using this definition, the tortuosities were recalculated in the 
, 
, and 
directions for increasing cube size of the representative volume, as shown in Fig. 3c. The calculations with the new definition have the same trends; however, the values of the tortuosity are now 1.71, 1.81, and 1.77 for the 
, 
, and 
directions, respectively. These values compare well to the tortuosity of 1.77, measured using the pore size distribution curve obtained experimentally with mercury intrusion porosimetry.
Figure 1. Fluctuations in the tortuosity along 
, 
, and 
of the representative volume, calculated by increasing the size of the volume starting from the center voxel.