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

摘要

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.