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

Hasanov A., Hasanoglu S.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.42, no.4, pp.741-751, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.1007/s10910-006-9138-1
  • Journal Name: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.741-751
  • Kocaeli University Affiliated: No

Abstract

The mathematical models of the ion transport problem in a potential field are analyzed. 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 I-D = I-D(t) and the classical Gottrellian I-G = I-G( t) is given on the obtained explicit formulas. The approach is extended to find out the current response I-c = I-c(t) corresponding to the diffusion-convection model. The relationship between the current response I-c = I-c( t) and Gottrellian I-G = I-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.