Highlighting pitfalls in the Maxwell–Stefan modeling of water–alcohol mixture permeation across pervaporation membranes

Abstract

The Maxwell–Stefan (M–S) equations are widely used for modeling permeation of water–alcohol mixtures across microporous membranes in pervaporation and dehydration process applications. For binary mixtures, for example, the following set of assumptions is commonly invoked, either explicitly or implicitly. (1) The M–S diffusivities Ð 1, and Ð 2, that portray interactions of individual components with the pore-walls, can be identified with the corresponding values for pure component permeation. (2) The Ð i are independent of the adsorbed phase mole fractions x i of the permeating mixture within the pores. (3) The exchange coefficient, Ð 12, that signify correlations in diffusional jumps within the pores, can be estimated on the basis of the logarithmic interpolation formula Ð 12 = ( Ð 12 x 1 → 1 ) x 1 ( Ð 12 x 2 → 1 ) x 2 , suggested by Vignes [Diffusion in binary solutions, Ind. Eng. Chem. Fund. 5 (1966) 189–199] for diffusion in binary liquid mixtures. (4) For structures such as LTA and DDR that consist of cages separated by narrow windows of sizes in the 0.35–0.42 nm range, the exchange coefficient is often assumed to have a large value, Ð 12 → ∞ , leading to a set of un-coupled M–S equations. Molecular Dynamics (MDs) simulations of diffusion in binary mixtures containing water, methanol, and ethanol in FAU, and LTA have been carried out to test each of the foregoing set of assumptions. The break-down of all four assumptions when applied to diffusion of water–alcohol mixture permeation is highlighted. The root-cause of this break-down can be traced to the hydrogen bonding between water and alcohol molecules, which is much more predominant than for water–water, and alcohol–alcohol molecule-pairs.