Modeling the diffusion of a fluid through viscoelastic polyimides

This paper is concerned with the diffusion of a fluid through viscoelastic polyimides undergoing large deformations. Using ideas from the classical theory of mixtures and a well established thermodynamic framework that uses the notion of maximization of the rate of entropy production, the constitutive relations for a mixture of a viscoelastic solid and a fluid (specifically Newtonian fluid) are derived. By prescribing forms for the specific Helmholtz potential and the rate of dissipation, the relations for the partial stress in the solid, the partial stress in the fluid and the interaction force between the solid and the fluid, are derived. Results from the developed model are shown to be in good agreement with the available experimental data for the diffusion of various solvents through polyimides. The deformation of the viscoelastic solid under simultaneous swelling and application of an external force is also studied.