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International Journal of Fluid Mechanics Research
ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v27.i2-4.100
pages 312-319

A Mathematical Model of Surface-Reaction Diffusion

Yu. A. Elfimov
Department of Mathematical Physics, Ural State University Ekaterinburg, Russia
A. O. Ivanov
Department of Mathematical Physics, Ural State University Ekaterinburg, Russia

ABSTRACT

Contact between two solid reagents, when the atoms of one of them exhibit high mobility over the surface of the other may result in a rapid surface diffusion penetration accompanied by a chemical reaction. In the case of reactions with participation of solid substances with low surface energy (tungsten, molybdenum and vanadium oxides) the diffusion was experimentally found to cease entirely when the visible boundary of the surface reaction moved through a certain, critical, not temperature dependent, distance. The article discusses a mathematical model of this phenomenon, constructed by subdividing the total reagent flux into the surface, intergranular and intragranular diffusion fluxes. The analytic solution was obtained on the assumption that the limiting factor of the process consists in slow motion of the front of chemical reaction into the grains of the substrate material. The model predicts stabilization of the surface concentration distribution of the reaction product. The analytic results were verified on the basis of experimental data for the CuO + MoO3 → CuMoO4 system. The temperature dependence of the characteristic time of stabilization of the length of the surface layer is described by the Arrhenius law, corresponding to the temperature variation of the chemical reaction constant.


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