Diffusion of Chemically Reacting Fluids through Nonlinear Elastic Solids and 1D Stabilized Solutions

This paper summarizes a 1D adaptation (Hall et al., Math Mech Solids, 2014) of the reactive fluid–solid mixture theory of Hall and Rajagopal (Math Mech Solids 17(2):131–164, 2012), which considers an anisotropic viscous fluid diffusing and chemically reacting with an anisotropic elastic solid. The present implementation introduces a stabilized mixed finite element method for advection–diffusion–reaction phenomena, which is applied to 1D isothermal problems involving Fickian diffusion, oxidation of PMR-15 polyimide resin, and slurry infiltration. The energy and entropy production relations are captured via a Lagrange multiplier that results from imposing the constraint of maximum rate of entropy production, reducing the primary PDEs to the balance equations of mass and linear momentum for the fluid and the solid, together with an equation for the Lagrange multiplier. The Fickian diffusion application considers a hyperbolic first order system with a boundary discontinuity and stable approach to the usual parabolic model. Results of the oxidation modeling of Tandon et al. (Polym Degrad Stab 91(8):1861–1869, 2006) are recovered by employing the reaction kinetics model and properties assumed there, while providing in addition the individual constituent kinematic and kinetic behaviors, thus adding rich interpretive detail in comparison to the original treatment (Tandon et al., Polym Degrad Stab 91 (8):1861–1869, 2006); two adjustable parameters describing coupled chemomechanical and purely chemical dissipation are added. The slurry infiltration application simulates the imposed mass deposition process and consequent effects on the kinematic and kinetic behaviors of the constituents.