# DIFFUSION-MIGRATION TRANSPORT IN A SYSTEM
WITH BUTLER-VOLMER KINETICS, AN EXACT
SOLUTION

## Artjom V. SOKIRKO and Fritz H. Bark

### Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden

*(Received 22 March 1993; in reuised form 25 August 1994)*
## Abstract

Steady one~dimensional electrolysis of a metal salt in a system with a supporting electrolyte is considered. The electrolyte in the system investigated is made up of three ionic species, one of which takes part in the electrode reactions. Attention is restricted to the quite common cases where the transfer coefficient in the Butler-Volmer law for the electrode kinetics is 1/2. For reasons of algebraic simplicity, the main part of the paper deals with the special case with two species of cations of charge numbers 2 and 1, respectively, and one species of anions of charge number 1. However, all results are easily generalized to any set of charge numbers. In the special case of a binary electrotype, an exact explicit simple expression is computed for the polarizarion curve. Also the drops in ohmic potential, concentration overpotential in the electrolyte and the surface overpotentials. are computed as functions of the electric current density. In the general case with three ionic species, an exact expression for the polarization curve is given in implicit form. In the limiting case of the polarization curve and the aforementioned parts of the difference in potential between the electrodes. For the diffusion layer configuration, and explicit expression for the polarization curve is computed for a system with arbitrary charge numbers and a more general form of the Butler-Volmer law.

*Key words: *Butler-Volmer law, diffusion metal salt, migration.