Relationship between current response and time in ion transport problem including diffusion and convection. 2. Numerical approach
| Autor: | Arzu Erdem, Şafak Hasanoglu |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Chemistry. 43:1458-1469 |
| ISSN: | 1572-8897 0259-9791 |
| DOI: | 10.1007/s10910-007-9274-2 |
| Popis: | The mathematical models of the ion transport problem in a potential field are anayzed. Ion transport is regarded as the superposition of diffusion and convection. In the case of pure diffusion model the classical Gottrell’s result is studied for a constant as well as for the time dependent Dirichlet data at the electrode. Comparative analysis of the current response \({\mathcal I}_{\rm D}={\mathcal I}_{\rm D}(t)\) and the classical Gottrellian \({\mathcal I}_{\rm G}={\mathcal I}_{\rm G}(t)\) is given on the obtained explicit formulas. The approach is extended to find out the current response \({\mathcal I}_c={\mathcal I}_c(t)\) corresponding to the diffusion-convection model. The relationship between the current response \({\mathcal I}_c={\mathcal I}_c(t)\) and Gottrellian \({\mathcal I}_{\rm G}={\mathcal I}_{\rm G}(t)\) is obtained in explicit form. This relationship permits one to compare pure diffusion and diffusion-convection models, including asymptotic behaviour of current response and an influence of the convection coefficient. The theoretical result are illustrated by numerical examples. |
| Databáze: | OpenAIRE |
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