Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux

Sci Rep. 2022 Dec 23;12(1):22439. doi: 10.1038/s41598-022-26786-8.


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.

PMID:36575293 | DOI:10.1038/s41598-022-26786-8


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