Diffusion in Heterogenous Media and Sorption—Desorption Processes
We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/183 |
| _version_ | 1797504522866655232 |
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| author | Ana Paula S. Koltun Ervin Kaminski Lenzi Marcelo Kaminski Lenzi Rafael Soares Zola |
| author_facet | Ana Paula S. Koltun Ervin Kaminski Lenzi Marcelo Kaminski Lenzi Rafael Soares Zola |
| author_sort | Ana Paula S. Koltun |
| collection | DOAJ |
| description | We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., <i>K</i>(<i>x</i>) = <i>D</i>|<i>x</i>|<sup>−<i>η</i></sup>, with −1 < <i>η</i> and <i>D</i> = <i>const</i>, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells. |
| first_indexed | 2024-03-10T04:05:47Z |
| format | Article |
| id | doaj.art-eb7bd68ad26447038d99983e25be15ae |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:47Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-eb7bd68ad26447038d99983e25be15ae2023-11-23T08:23:27ZengMDPI AGFractal and Fractional2504-31102021-10-015418310.3390/fractalfract5040183Diffusion in Heterogenous Media and Sorption—Desorption ProcessesAna Paula S. Koltun0Ervin Kaminski Lenzi1Marcelo Kaminski Lenzi2Rafael Soares Zola3Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, BrazilDepartamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, BrazilDepartamento de Engenharia Química, Universidade Federal do Paraná, Av. Cel. Francisco H. dos Santos, 210-Jardim das Americas, Curitiba 81531-990, PR, BrazilDepartamento de Física, Universidade Tecnológica Federal do Paraná, Avenida Marcilio Dias 635, Apucarana 86812-460, PR, BrazilWe investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., <i>K</i>(<i>x</i>) = <i>D</i>|<i>x</i>|<sup>−<i>η</i></sup>, with −1 < <i>η</i> and <i>D</i> = <i>const</i>, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.https://www.mdpi.com/2504-3110/5/4/183fractional diffusion equationmemory effectanomalous diffusion |
| spellingShingle | Ana Paula S. Koltun Ervin Kaminski Lenzi Marcelo Kaminski Lenzi Rafael Soares Zola Diffusion in Heterogenous Media and Sorption—Desorption Processes Fractal and Fractional fractional diffusion equation memory effect anomalous diffusion |
| title | Diffusion in Heterogenous Media and Sorption—Desorption Processes |
| title_full | Diffusion in Heterogenous Media and Sorption—Desorption Processes |
| title_fullStr | Diffusion in Heterogenous Media and Sorption—Desorption Processes |
| title_full_unstemmed | Diffusion in Heterogenous Media and Sorption—Desorption Processes |
| title_short | Diffusion in Heterogenous Media and Sorption—Desorption Processes |
| title_sort | diffusion in heterogenous media and sorption desorption processes |
| topic | fractional diffusion equation memory effect anomalous diffusion |
| url | https://www.mdpi.com/2504-3110/5/4/183 |
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