Three scale thermomechanical theory for swelling biopolymeric systems

Abstract

A three-scale theory for the swelling polymeric/biopolymeric media is developed via the hybrid mixture theory. At the microscale, the solid polymeric matrix interacts with the solvent through surface contact. At the mesoscale, the homogeneous mixture of vicinal fluid and solid polymers exchanges thermodynamic properties with two bulk fluids, one of which is of the same type as the vicinal fluid. The relaxation processes within the polymeric matrix are incorporated by modeling the solid phase as viscoelastic and the solvent phases as viscous at the macroscale. We obtain novel equations for the total stress tensor, chemical potential of the solid phase, heat flux and Darcy's law all at the macroscale. Viscoelastic stress components in Darcy's law make it applicable for both Fickian and non-Fickian fluid transport. The form of the generalized Fick's law is similar to that obtained in earlier works involving colloids. Thermoviscoelastic and thermoviscous effects are incorporated by coupling thermal gradients with strain-rate tensors for the solid phase and the deformation-rate tensors for the liquid phases.