Unsaturated fluid transport in swelling poroviscoelastic biopolymers

• Continuum thermodynamics based theory yielded general unsaturated transport laws.
• Inclusion of poroviscoelasticity resulted in temporally non-local transport laws.
• The equations can describe both Darcian and non-Darcian modes of fluid transport.
• Transport and stress relations include hydrophilic and phobic interaction terms.

The hybrid mixture theory was used to obtain the two-scale unsaturated transport and thermomechanical equations for biopolymers. The two-scale laws of conservation of mass, momentum, energy and entropy were utilized, the constitutive theory was formulated and the entropy inequality was exploited to obtain various equilibrium, near-equilibrium and non-equilibrium relations. The system was treated as poroviscoelastic with the viscoelastic biopolymers interacting with the viscous water and oil phases at pore-scale via hydrophilic and hydrophobic forces. The gas phase exchanged mass with the liquid water due to evaporation/condensation away from equilibrium. The exploitation of entropy inequality resulted in temporally non-local generalized Darcy׳s laws for the liquid phases, near-equilibrium swelling and capillary pressure relations, generalized stress relations, near-equilibrium Gibbs free energy relation and the rate of evaporation relation. The generalized Darcy׳s law relations include novel integral terms with long-memory effects. These can describe the effect of biopolymer–fluid interaction on both Darcian and non-Darcian modes of fluid transport depending upon the state of the biopolymers (glassy, rubbery or glass-transition). The resulting transport laws for various phases include the cross-effect terms in the form of volume fraction gradients. The unsaturated generalized Darcy׳s law relations were validated by making comparison to the experimental data on moisture transport, heat penetration and pressure development during frying of potato cylinders.