Diffusion in Mixtures of Reacting Thermoelastic Solids

A chemically reacting mixture of elastic solids is considered. As a constitutive assumption, the peculiar functions (such as the free energy, the entropy, and the stress) of a constituent are taken to be functions of a set of variables pertaining to that constituent. The interaction terms, namely the growth of mass, linear momentum, and energy, are allowed to depend on the set of variables pertaining to all of the constituents. While the dependence on the mass density is usually disregarded, the paper accounts also for such a dependence, which seems to be in order especially in connection with reacting mixtures where the mass densities change also in the reference configuration. The thermodynamic restrictions are derived by starting from the non-negative value of the sum of entropy growths and involving the properties of the peculiar functions. The results so obtained for stresses and chemical potentials are examined in connection with similar schemes (swelling solids). While the correct relations for the mass diffusion flux arise from balance equations, an analysis is given of whether and how Fick-type models are acceptable possibly depending on the fluid or solid character of the mixture