Coupled concentration-dependent diffusivities of ethanol/water mixtures through a polymeric membrane: Effect on pervaporative flux and diffusivity profiles

Abstract

The partial pervaporative (PV) fluxes of ethanol/water mixtures in polydimethylsiloxane (PDMS) were predicted using Fick's first law and modified Maxwell–Stefan equation. The sorption levels were predicted using UNIQUAV-HB and the experimental solvent diffusion coefficients of the mixtures were expressed in terms of their sorption concentrations according to Long's model. Both permeant diffusion coefficients were found to vary with the ethanol concentration alone. The predicted partial fluxes and the PV separation factor agreed well with the experimental data by integrating Fick's law over the ethanol concentration. The modified Maxwell–Stefan equation was employed to estimate the partial fluxes by taking into account both permeant concentration gradients. The modified Maxwell–Stefan equation rendered similar partial permeant flux and ethanol-over-water separation factor as in Fick's law. The agreement between the predicted PV performance and the experimental data indicates that the unsteady-state permeant diffusion coefficients reflect the diffusion behavior in the steady-state PV operation. The concentration and diffusivity profiles for the permeants in the PDMS were illustrated along the trans-membrane direction. These diffusivity profiles can be explained using the Vrentas–Duda free volume theory.