Kinetics of the chemical reaction front in spherically symmetric problems of mechanochemistry

The establishment of relations between chemicalreactions and processes of deformation and destruction is of importance from the viewpoint of both fundamental science and engineering applications. Theeffect of mechanical stresses on the reaction rate isconventionally taken into account heuristically—bypostulating the dependences of the diffusion processand the reaction constant on certain characteristics ofthe stressed state. At the same time, Gibbs [1] and DeDonder [2] laid the foundation for the theory of chemical reactions based on the concept of chemical affinity, which is a linear combination of the chemicalpotentials of substances participating in the reaction.In the classical physical chemistry dealing with gasesand ideal liquids, the chemical potential and, consequently, the chemical affinity are scalar values dependent, in particular, on pressure. However, in studiesdevoted to investigation of phase transformations indeformable materials, it was shown that the chemicalpotential should be a tensor (see, for example, [3–7]).Recently in [8, 9] for the case of a reaction between gasand deformable solid components, the expression forthe chemicalaffinity tensor was obtained as a result ofthe analysis of balances of mass, momentum, energy,and the second principle of thermodynamics. In turn,this has made it possible to obtain in a natural way thedependence of the reaction rate on stresses.Previously, we investigated the propagation of reaction fronts in the axisymmetrical problems [10] and fora plane front [11]. In this study, we investigated thekinetics of the reaction front in spherically symmetricproblems for linearly elastic solid components of thereaction.BASIC RELATIONSWe consider the chemical reaction of the type ofwhere , and are the chemical formulas ofmaterials of reacting components, and are thesolid elastic components, and is the gas component. We assume that the reaction is localized at thefront separating the regions occupied with materials and and supported by the diffusion of the component through the formed material . We assumealso that the all the gas that came to the reaction frontis spent for the reaction. An example of such a reactionis the oxidation of silicon .We consider the solid component as a solidsceleton for the diffusing gas component assumingthat the gas component causes additional deformations of the frame. Also we disregard the effects ofinternal friction related to the relative motion of thegas and solid components, the thermal effect of thereaction considering the temperature