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As the classical Fickian theory has shown several shortcomings in describing mass transport in complex structured media, we here propose a new model that investigates the permeation behavior of a penetrant through a viscoelastic polymeric membrane. We choose the extra stress tensor as an additional structural state variable to track known the viscoelastic behavior of the polymer. We have modified the nonlinear Maxwell rheological model to incorporate mass transport. A set of two nonlinear coupled and partial differential equations are derived to describe the time evolution of the stress and concentration. Two dimensionless parameters, namely: a diffusion–Deborah number De and a diffusion–stress coupling constant emerge naturally in the dimensionless form of the governing equations. We have compared our theoretical predictions with experimental data taken from the literature and corresponding to the acetone/rubber mixture. A good agreement is observed.
