Working Models of Flow and Diffusion in Isotropic Media

3 Working Models of Flow and Diffusion in Isotropic Media 

If the main pore network is isotropic and has a uniform pore size r, then Eq. (3.4-12) takes the form 

This result includes Eq. 10 of Johnson and Stewart (1965) and Eq. 2 of Satterfield and Cadle (1968) as special cases. Equation (3.4-11) predicts K = 1/3 for isotropic pore systems with no dead-end branches this value is accurate within a factor of 2 for many pelleted catalysts (Johnson and Stewart 1965 Brown et al. 1969 Horak and Schneider 1971). 

If the integral in Eq. (3.4-12) is approximated by an m-term summation, then for isotropic media we obtain 

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