Mixture Diffusion in Nanoporous Adsorbents: Equivalence of Fickian and Maxwell-Stefan Approaches.
June 29th, 2008 | by admin |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 n i (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/ Eth 1 + theta 2/ Eth 12)(1/ Eth 2 + theta 1/ Eth 21) = ( L 11 L 22)/( L 12 L 21)(theta 1theta 2)/( Eth 12 Eth 21) The Maxwell-Stefan binary exchange coefficients Eth i j are shown to depend not only on the Maxwell-Stefan diffusivities, Eth i , but also on the Onsager coefficients. For a strong molecular interaction, that is, Eth i >> Eth 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, Eth i , are shown to depend on the interaction effects in mixtures, and Eth i in mixtures will not generally be equal to pure component values evaluated at the same total fractional loading.
Wang Y, Levan MD.
m.douglas.levan@vanderbilt.edu.