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, cilt.42, ss.741-751, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 4
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1007/s10910-006-9138-1
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Sayfa Sayıları: ss.741-751

Özet

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.