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Free convection in an electrochemical system with nonlinear reaction kinetics

Published online by Cambridge University Press:  26 April 2006

Fritz H. Bark  and
Farid Alavyoon
Fritz H. Bark
Affiliation:
Department of Mechanics, Royal Institute of Technology, Stockholm, S-100 44 Sweden Government Industrial Research Institute, Tohoku Sendai, Nigatake, 4-2-1, Miyagino-ku, 983 Japan
Farid Alavyoon
Affiliation:
Department of Mechanics, Royal Institute of Technology, Stockholm, S-100 44 Sweden Government Industrial Research Institute, Tohoku Sendai, Nigatake, 4-2-1, Miyagino-ku, 983 Japan Present address: Vattenfall Utveckling AB, Älvkarleby, S-810 70 Sweden
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Abstract

Unsteady electrolysis of a dilute solution of a metal salt made up of two ions in a system with vertical electrodes is considered for large values of the Rayleigh and Schmidt numbers. The mass transfer at the electrodes is assumed to be related to the local charge transfer potential and concentration by a nonlinear Butler–Volmer law. Free convection of the electrolyte appears owing to the variation of the concentration field. After a short initial period, the electrolyte becomes strongly stratified and the motion takes place in boundary layers at the solid boundaries. An approximate model equation for the evolution of the stratification is derived by using perturbation theory. Predictions from the simplified model are found to be in good agreement with numerical solutions of the complete problem. Significant differences compared with earlier studies for linear kinetics, i.e. cases in which the electric current density at the electrodes is constant, are found. Among other things, for large values of the difference ΔV in electric potential between the electrodes, most of the dissolved salt eventually collects near the bottom of the cell. The concentration in the bulk of the electrolyte is, for large values of ΔV, approximately given by a ninth-order polynomial to be compared with a linear behaviour for linear kinetics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 290 , 10 May 1995 , pp. 1 - 28
Copyright
© 1995 Cambridge University Press

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