Highlighting Thermodynamic Coupling Effects in Alcohol/Water Pervaporation across Polymeric Membranes

The pervaporation of binary alcohol/water mixtures across polymeric membranes is modeled by combining the Maxwell–Stefan (M-S) diffusion formulation with the Flory–Huggins (F-H) description of sorption equilibrium. The combined M-S/F-H model shows that the flux of each penetrant species is coupled to the driving force of its partner penetrant. Two types of coupling contributions can be distinguished: (i) coupling arising out of correlated motions of penetrants in the polymer matrix and (ii) thermodynamic coupling. The focus of this article is on the contribution of thermodynamic coupling, which is quantified by the set of coefficients Γij  = ϕi ∂ln ai / ϕj ∂ln ϕj where ai, the activity of species i, is dependent on the volume fractions ϕi,ϕj, of both penetrants in the polymeric membrane. Detailed analyses of published experimental data for pervaporation of ethanol/water feed mixtures of varying compositions in both hydrophobic (poly(dimethylsiloxane)) and hydrophilic (cellulose acetate, polyimide, and polyvinyl alcohol/polyacrylonitrile composite) membranes show that in all cases, the cross-coefficients Γij (i ≠ j) are negative and may attain large magnitudes in relation to the diagonal elements Γii. The net result is that the permeation fluxes of each penetrant are suppressed by its partner, resulting in mutual slowing down of permeation fluxes. If thermodynamic coupling effects are ignored, significantly higher fluxes are anticipated than those that are experimentally observed.