A continuum theory of chemically reacting mixtures of fluids and solids

In this work, a continuum theory of a chemically reacting mixture composed of solids and fluids is presented. Following a different line of localization, a set of balance equations applicable to every component in the mixture is obtained. These are: conservation of mass, balance of momenta, conservation of energy and the principle of entropy which is also given for every species in the mixture. The localization is so applied that the individual energy equations are form invariant under time dependent motions of the spatial frame of reference and every state variables appearing explicitly in these equations can be considered as objective quantities. By use of the concept of reactive mass density for solid continuum and modifying the axiom of equipresence, originally developed for single bodies, a set of thermodynamically admissible constitutive relations is derived for a reacting mixture composed of a solid and a non-Newtonian fluid. Finally, utilizing the linearized field and constitutive equations, the propagation of simple harmonic waves in such a medium is studied and several particular cases are discussed.