Mass transport with relaxation in polymers

The non‐Fickian mass transport behavior observed in polymeric materials is here analyzed through a viscoelastic constitutive equation for the diffusive flux, endowed with concentration‐dependent relaxation time and diffusivity. The present model thus overcomes the limitations shown by Neogi's model and by the Cattaneo equation used by Camera‐Roda and Sarti. In addition to the Fickian behaviors at both small and high Deborah numbers, the model accounts for case II behavior and anomalous diffusion at intermediate Deborah number, possibly with the presence of a shock wave in the concentration profile which moves at a concentration‐dependent velocity. Weight uptake accelerations and overshoots are also accounted for at intermediate Deborah numbers. The dimensionless problem has been numerically solved and the role of the relevant dimensionless parameters is discussed for both sorption and desorption.