Mixture Diffusion in Nanoporous Adsorbents: Equivalence of Fickian and Maxwell−Stefan Approaches

Nanopore diffusion in multicomponent adsorption is described using different macroscopic theories: Onsager irreversible thermodynamics, Maxwell−Stefan, and Fickian approaches. A new equivalence between Fickian and Maxwell−Stefan formulations is described by [D] = [n s][B]−1[Γ][n s ]−1. The elements of D and B are explicitly related to the Fickian and Maxwell−Stefan diffusivities, respectively. Only when the saturation loadings n i s for different components are the same can the matrix be reduced to the generally accepted equation [D] = [B]−1[Γ]. On the basis of the relationship between the irreversible thermodynamics and Maxwell−Stefan approaches, an equation is derived for a binary system with the symmetric form (1/Ð 1 + θ2/Ð 12)(1/Ð 2 + θ1/Ð 21) = (L 11 L 22)/(L 12 L 21)(θ1θ2)/(Ð 12 Ð 21) The Maxwell−Stefan binary exchange coefficients Ð i j are shown to depend not only on the Maxwell−Stefan diffusivities, Ð i , but also on the Onsager coefficients. For a strong molecular interaction, that is, Ð i ≫ Ð i j , the ratio of Onsager coefficients will approach unity, giving the commonly used relation L 12 = L 11 L 22 . In addition, the Maxwell−Stefan diffusivities, Ð i , are shown to depend on the interaction effects in mixtures, and Ð i in mixtures will not generally be equal to pure component values evaluated at the same total fractional loading.