Relationship between current response and time in ion transport problem including diffusion and convection. 1. An analytical approach期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Relationship between current response and time in ion transport problem including diffusion and convection. 1. An analytical approach

Authors:	Alemdar Hasanov Şafak Hasanoglu

Institution:	1.Applied Mathematical Sciences Research Center,Kocaeli University,Izmit-Kocaeli,Turkey;2.Chemical-Engineering Division, K?sek?y High School,Kocaeli University,Kocaeli,Turkey

Abstract:	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.

Keywords:	ion transport parabolic problem current response Gottrellian
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