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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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References

Alavyoon, F. 1994 Double diffusive natural convection in a slender enclosure - cooperative solutal and thermal buoyancy forces. Proc. 3rd JSME-KSME Fluids Engng Conf. July 1994, Sendai, pp. 230–235.
Alavyoon, F. & Bark, F. H. 1993 Numerical computations of natural convection in a small copper electrolysis cell. Extended Abstr. Electrochem. Soc. 93, 1887–1888.Google Scholar
Alavyoon, F., Eklund, A., Bark, F. H., Karlsson, R. I. & Simonsson, D. 1991 Theoretical and experimental studies of free convection and stratification of electrolyte in a lead acid cell during recharge. Electrochim. Acta 36, 2153–2164.Google Scholar
Awakura, Y., Ebata, A. & Kondo, Y. 1979 Distribution of local current densities during electrodeposition on a plane vertical cathode. J. Electrochem. Soc. 126, 23–30.Google Scholar
Bard, A. J. 1978 Encyclopedia of Electrochemistry of the Elements, vol. 8. Marcel Dekker.
Bark, F. H., Alavyoon, F. & Dahlkild, A. A. 1992 On unsteady free convection in vertical slots due to prescribed fluxes of heat or mass at the vertical walls. J. Fluid Mech. 235, 665–689.Google Scholar
Eklund, A., Alavyoon, F., Simonsson, D., Karlsson, R. I. & Bark, F. H. 1991 Theoretical and experimental studies of free convection and stratification of electrolyte in a copper refining cell. Electrochim. Acta 36, 1345–1354.Google Scholar
Fukunaka, Y. & Kondo, Y. 1988 Electrolyte circulation in electrorefining process. Metall. Rev. MMIJ 5(1), 9–23.Google Scholar
Greenspan, H. P. 1991 The Theory of Rotating Fluids. Breukelen Press.
Hine, F. 1985 Electrode Processes and Electrochemical Engineering. Plenum Press.
Karlsson, R. I., Alavyoon, F. & Eklund, A. 1990 LDV measurements of free convection in electrochemical systems. Laser Anemometry - Proc. 3rd. Intl. Conf. pp. 329–337. BHRA/- Springer.
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.
Landolt-Börnstein, B. 1967 Numerical Data and Functional Relationships in Science and Technology, New Series 5(II). Springer.
Lobo, V. M. M. 1989 Handbook of Electrolyte Solutions, Part A. Elsevier.
Newman, J. S. 1991 Electrochemical Systems. Prentice-Hall.
Sokirko, A. V. & Bark, F. H. 1993 Diffusion-migration transport in a system with Butler-Volmer kinetics, an exact solution. Electrochim. Acta (submitted).
Tanaka, N. & Tamamushi, R. 1964 Kinetic parameters of electrode reactions. Electrochim. Acta 9, 963–989.Google Scholar
Veronis, G. 1970 Analogy between rotating and stratified flows. Ann. Rev. Fluid Mech. 2, 37–66.Google Scholar
Walin, G. 1971 Contained non-homogeneous flow under gravity or how to stratify a fluid in the laboratory. J. Fluid Mech. 48, 647–672.Google Scholar
Ziegler, D. & Evans, J. W. 1986 Mathematical modeling of electrolyte circulation in cells with planar vertical electrodes. J. Electrochem. Soc. 133, 559–566.Google Scholar