LAUSR

When a fiber is subjected to flow and mass transport, it deforms and swells and thus its orientation and length change accordingly. As a starting point, a semi-kinetic equation is proposed to describe the time evolution of the length and orientation of extensible fibers. Then a mesoscopic model, explicitly incorporating the coupling arising among flow, mass transport, and fibers extensibility and orientation in a mixture composed of a solvent and a fiber-reinforced polymer (FRP), is formulated. The derived governing and constitutive equations possess the GENERIC structure and are parameterized by mobility coefficients and the Helmholtz free energy density. The latter takes into account the orientational ordering of the fibers, the fiber-fiber topological interactions, and the flexible nature of the fibers. The unidirectional flow-free mass transport is thoroughly discussed via scaling analysis, numerical solutions, and comparison with sorption data selected from literature. The dynamics of the boundaries is also examined.