A mass transfer model for pure alcoholic permeation through the PDMS membrane

Abstract

This work focuses on the modeling of mass transfer in the pure compound pervaporation through hydrophobic membranes. For this purpose, a mathematical predictive model was established based on the solution-diffusion mechanism. In the sorption step, the Flory–Huggins theory was applied to predict the amount of component absorbed into the membrane. In the diffusion step, the generalized Fick’s law with a constant diffusion coefficient and a concentration/temperature-dependent diffusion coefficient was employed to describe the component diffusion across the polydimethylsiloxane (PDMS) membrane. The concentration/temperature-dependent diffusion coefficient was determined using Duda’s free volume theory. In order to solve the resulting nonlinear transport equations, both finite difference (FD) and finite element (FE) methods were employed. The proposed model enables to predict the permeation flux as well as the concentration, temperature, and diffusion coefficient profiles inside the membrane. The model was then validated using the experimental data obtained from the pervaporative process of pure substance with the PDMS membrane. The results showed that although both FD and FE approaches were able to solve the dominant equations with appropriate accuracy. The modeling case II was capable of predicting the permeation flux for systems of pure ethanol and isobutanol, respectively. Finally, the effect of feed temperature on the permeation flux was investigated.

Keywords:

• Pervaporation
• Mass transfer modeling
• Finite element
• Free volume theory
• Solution-diffusion mechanism

Acknowledgments

The authors would like to thank Helmholtz-Zentrum Geesthacht Zentrum fur Material und Küstenforschung GmbH (Geesthacht, Germany) for supplying the PDMS membranes.