Diffusion of a fluid through an anisotropically chemically reacting thermoelastic body within the context of mixture theory
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abstract
A mixture theory approach is used to analyze the change in response characteristics of an anisotropic, non-linear viscoelastic fluid diffusing through a finitely deforming thermoelastic body of arbitrary symmetry wherein the fluid chemically reacts with the solid. It is assumed for simplicity that it is possible to characterize the reaction as having a single step and as one in which the reaction products remain within the body, thereby modifying the solid constituent. The effects of the reaction on the solid that render it anisotropic are quantified by means of a tensorial parameter that tracks the extent of the reaction in different directions. Both diffusion-dominated (diffusion of the reactants is far more rapid than the reaction) and reaction-dominated (the reaction is far more rapid than the diffusion of the reactants) processes are considered. Constitutive equations are derived from the requirement that the rate of entropy production be maximized, which makes it possible to characterize the behavior of the body through the specification of three scalar functions: the rate of entropy production function for the mixture, and the Helmholtz free energies of each of the constituents. It is noted that the model may be applied to regions of bodies with locally homogeneous damage, that is, regions damaged at a small enough scale to mimic an anisotropically porous continuum. Macroscale damage may also be modeled via the boundary conditions described in Section 5.
