General Quantitative Description of Pore Diffusion

In an actual solid, with its complicated pore structure, the concept of an effective diffusivity is defined by the equation  

The definition of tortuosity factor in Eq. 3.5.b-2 includes both the effect of altered diffusion path length as well as changing cross-sectional areas in constrictions for some applications, especially with two-phase fluids in porous media, it may be better to keep the two separate (e.g., Van Brakel and Heertjes [39]). This tortuosity factor should have a value of approximately 3 for loose random pore structures, but measured values of 1.5 up to 10 or more have been reported. Satterfield [40] states that many common catalyst materials have a t 2 3 to 4 he also gives further data. 

the effective diffusivity would have the form 

Turning to a general description of pore diffusion, the dusty gas theory of Mason et al. [41,42] utilizes the results from the formal kinetic theory of gases, with one species, the dust, having a very large molecular wei t. Their final results can be clearly visualized in the form utilized by Feng and Stewart [43]. 

Equations 3.S.b-4 to 6 can also be combined to give a single equation containing only the total flux resulting from both diffusive and viscous flow mechanisms  

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