Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux
Abstract 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...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-12-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-26786-8 |
| _version_ | 1797973639796097024 |
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| author | Piotr Skrzypacz Bek Kabduali Alua Kadyrbek Sławomir Szafert Vsevolod Andreev Boris Golman |
| author_facet | Piotr Skrzypacz Bek Kabduali Alua Kadyrbek Sławomir Szafert Vsevolod Andreev Boris Golman |
| author_sort | Piotr Skrzypacz |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-04-11T04:07:28Z |
| format | Article |
| id | doaj.art-7f000ec2cb254d6e89e01e0dc8a32443 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-11T04:07:28Z |
| publishDate | 2022-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-7f000ec2cb254d6e89e01e0dc8a324432023-01-01T12:17:16ZengNature PortfolioScientific Reports2045-23222022-12-0112111110.1038/s41598-022-26786-8Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion fluxPiotr Skrzypacz0Bek Kabduali1Alua Kadyrbek2Sławomir Szafert3Vsevolod Andreev4Boris Golman5Department of Mathematics, School of Sciences and Humanities, Nazarbayev UniversityDepartment of Mathematics, School of Sciences and Humanities, Nazarbayev UniversityDepartment of Mathematics, School of Sciences and Humanities, Nazarbayev UniversityDepartment of Chemistry, University of WrocławDepartment of Heat Power Setups, Faculty of Energy and Electrical Engineering, Chuvash State UniversityDepartment of Chemical and Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev UniversityAbstract 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.https://doi.org/10.1038/s41598-022-26786-8 |
| spellingShingle | Piotr Skrzypacz Bek Kabduali Alua Kadyrbek Sławomir Szafert Vsevolod Andreev Boris Golman Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux Scientific Reports |
| title | Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux |
| title_full | Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux |
| title_fullStr | Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux |
| title_full_unstemmed | Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux |
| title_short | Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux |
| title_sort | analysis of dead core formation in catalytic reaction and diffusion processes with generalized diffusion flux |
| url | https://doi.org/10.1038/s41598-022-26786-8 |
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