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 , 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.