A simplified solution–diffusion theory in pervaporation: the total solvent volume fraction model

A simplified solution–diffusion model called total solvent volume fraction model is developed for the description of the permeant transport through highly selective membranes in pervaporation. It is based on the assumption that the diffusion coefficient is the product of a limit diffusivity and an analytic function depending only on the total volume fraction of all the solvent species in the membrane. The equations developed for binary liquid mixtures in the particular case where the analytical functions are the same for both permeant species were checked with the experimental data obtained from the pervaporation of water–ethanol mixtures through a PVA-based membrane. The three computed parameters obtained by fitting were successfully used to predict the variations of the partial fluxes with the downstream pressure, particularly the maximum in the ethanol flux, and the inversion of the membrane selectivity. The model appears to be also valid for a moderately selective membrane, the cellulose acetate membrane, in the pervaporation of water–ethanol mixtures.