Knudsen Diffusion in Porous Solids

For Knudsen diffusion at constant total pressure, it can be shown that there is a bootstrap condition given by (Do, 1998) 

This is known as Graham s law of effusion for Knudsen diffusion of a multicomponent system at constant total pressure. For binary gas mixtures, equation (1-105) simplifies to 

For Knudsen diffusion in porous solids of porosity e and tortuosity t, 

A mixture of Oz (A) and N2 (B) diffuses through the pores of a 2-mm-thick piece of unglazed porcelain at a total pressure of 0.1 atm and a temperature of 293 K. The average pore diameter is 0.1 pm, the porosity is 30.5%, and the tortuosity is 4.39. Estimate the diffusion fluxes of both components when the mole fractions of 02 are 80% and 20% on either side of the porcelain. 

Calculate the mean free path from equation (1-102). Using data from Appendix B for oxygen and nitrogen, and equation (1-45), aAB = 3.632 A. Then, from equation (1-102), X = 6,807 A. From equation (1-101), Kn = 6.807 5.0. Therefore, transport inside the pores is mainly by Knudsen diffusion. From equation (1-103), DKA - 0.147 cm2/s. From equation (1-107), DKAejj = 0.0102 cm2/s from equation (1-108), NA = 1.272 x 10-3 mol/m2-s. From equation (1-106), Ng = -NA (32/28)0 5 = -1.069Aa = -1.360 x 10-3 mol/m2-s. 

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