Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux
Skrzypacz P. Kabduali B. Kadyrbek A. Szafert S. Andreev V. Golman B.
December 2022Nature Research
Scientific Reports
2022#12Issue 1
Dead-core and non-dead-core solutions to the nonlinear diffusion–reaction equation based on the generalized diffusion flux with gradient-dependent diffusivity and the power-law reaction kinetics in catalyst slabs are established. The formation of dead zones where the reactant concentration vanishes is characterized by the critical Thiele modulus that is derived as a function of reaction order and diffusion exponent in the generalized diffusion flux. The effects of reaction order and diffusion exponent on the reactant concentration distribution in the slab and dead-zone length are analyzed. It is particularly demonstrated that by contrast to the model based on the standard Fick’s diffusion, dead-core solutions exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fick’s diffusion fluxes is established.
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Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Chemistry, University of Wrocław, 14 F. Joliot-Curie, Wrocław, 50-383, Poland
Department of Heat Power Setups, Faculty of Energy and Electrical Engineering, Chuvash State University, Cheboksary, 428015, Russian Federation
Department of Chemical and Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Mathematics
Department of Chemistry
Department of Heat Power Setups
Department of Chemical and Materials Engineering
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