On the derivation of the transport equation for swelling porous materials with finite deformation

Deriving a physically meaningful transport equation for porous swelling materials that undergo finite deformations depends largely on our ability to relate thermodynamically defined variables to physically interpretable quantities. This article presents a novel and judicious choice of independent variables for the solid phase that clarifies the relationship between thermodynamically defined pressure and actual physical stress. Furthermore, it elucidates and simplifies the derivation of the transport equation previously investigated by [P.P. Singh, J.H. Cushman, D.E. Maier, Multiscale fluid transport theory for swelling biopolymers, Chemical Engineering Science 58(11) (2003) 2409–2419], while continuing to capture the important features. With this choice of variables, the assumptions and derivation of the transport equation are clarified. It is then shown how this framework can be used to derive a transport equation used to model swelling polymers. The result is compared with another transport equation derived using the Flory–Huggins theory.