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)[Gamma][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 ni(s) for different components are the same can the matrix be reduced to the generally accepted equation [D]=[B](-1)[Gamma]. 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/Eth1 + theta2/Eth12)(1/Eth2 + theta1/ Eth21)=(L11L22)/(L12L21)(theta1theta2)/(Eth12Eth21) The Maxwell-Stefan binary exchange coefficients Ethij are shown to depend not only on the Maxwell-Stefan diffusivities, Ethi, but also on the Onsager coefficients. For a strong molecular interaction, that is, Ethi>>Ethij , the ratio of Onsager coefficients will approach unity, giving the commonly used relation L12=square root L11L22 . In addition, the Maxwell-Stefan diffusivities, Ethi, are shown to depend on the interaction effects in mixtures, and Ethi in mixtures will not generally be equal to pure component values evaluated at the same total fractional loading.