Describing mixture permeation across polymeric membranes by a combination of Maxwell-Stefan and Flory-Huggins models

The primary objective of this article is to develop an analytic procedure for calculating the permeation fluxes of mixtures of penetrant molecules across polymeric membranes. The developed approach combines (1) the Flory-Huggins (F-H) description of phase equilibrium thermodynamics, and (2) the Maxwell-Stefan (M-S) diffusion formulation. For compatibility reasons, the M-S equations are re-formulated in terms of volume fractions, rather than the more commonly used mole fractions. Using matrix algebra, explicit expressions are derived for calculation of the trans-membrane fluxes and component permeabilities. The accuracy of the developed procedure is demonstrated by comparison with published experimental data on CO₂/C₂H₆ and water/ethanol mixture permeation.