Quantitative description of gas permeation and separation

Under isothermal conditions it follows from irreversible thermodynamics [1-3] for the flux / in a mixture of k components  

So the real driving force is the sum of the gradients of the chemical potentials as is also implicit in the general Maxwell-Stefan formulation [87-89]. 

Here the term 31nP/31ruj is the so-called thermodynamic factor (hereafter called r), Do( ) is the corrected or intrinsic diffusion constant and x is a correction term (see notes below). With q = qsafQ, Eq. (9.40a) becomes  

Notes on Eqs. (9.40a,b) (1) When is expressed in mol/kg the density (kg/m ) enters the nominator of Eqs. (9.40a,b) and g == p. (2) If the zeolite is supported with a support having porosity e, the effective surface area of the zeolite available for transport is e m /m and the term e enters the nominator of Eqs. (9.40a,b). If the flux is measured on a supported system and one wants to calculate the intrinsic zeolite properties, e enters the denominator of Eqs. (9.40a,b). (3) The term Do(q) dlr /dlnq is identical to the Pick diffusion coefficient Dp, while the intrinsic diffusion coefficient Do(q) is identical to the Maxwell-Stefan diffusion coefficient D s. 

The thermodynamic factor T corrects for differences in activities (chemical potentials) of different gases which can exist with similar concentration gradients. It is similar to the factor that has been described in solid state diffusion by Darken and is sometimes named after him. 

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