Modeling of multicomponent mass transfer across polymer films using a thermodynamically consistent formulation of the Maxwell–Stefan equations in terms of volume fractions

Abstract

The advantages of the Maxwell–Stefan (MS) formulation over Fick’s law to describe multicomponent mass transfer are well recognized. However, in its original form, the MS equations are written in terms of mole fractions, which are ill-defined if one of the components is a polymer. To overcome this problem, a revised formulation of the MS equations written in terms of volume fractions is proposed. The resulting equations satisfy the Gibbs–Duhem restriction and are fully consistent with the multicomponent Flory–Huggins theory in the sense that we avoid any assumption regarding the size of the penetrants or of the polymer segments. This formulation is combined with the Flory–Huggins model to derive general expressions for modeling steady-state mass transfer across polymer films for both pure components and binary mixtures. The proposed MS formulation is used to analyze the separation of carbon dioxide/ethane mixtures by a cross-linked poly(ethylene oxide) membrane. For this particular system, at T≥25oC, mixed-gas permeability coefficients can be predicted with an average deviation of less than 5% without any input from multicomponent permeation data.