Effects of non-linear kinetics on free convection in an electrochemical cell with a porous separator |
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Authors: | K I Borg K E Birgersson F H Bark |
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Affiliation: | (1) Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan;(2) Present address: Norra Real, Roslagsgatan 1, SE-113 55 Stockholm, Sweden;(3) Engineering Science Programme, Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore, 117576, Singapore;(4) Department of Mechanics, Royal Institute of Technology, Stockholm, 100 44, Sweden |
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Abstract: | The spatial evolution of the ionic concentration of an electrolyte in an isothermal electrochemical cell with a porous separator
between the electrodes was investigated for large values of Rayleigh number. The reaction kinetics were described by the Butler–Volmer
equation. The full problem, involving the coupled partial differential equations describing the velocity field, the ionic
concentration, and the electric potential, was reduced by means of regular and singular perturbation theory, to a simplified
evolution equation, coupled with a transcendental function for the ionic concentration and electric potential; the solution
was found to agree well with the numerical solution of the full problem. In the limit of large and small cell voltages, closed
analytical solutions were secured for the concentration, potential, and overall current density. |
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Keywords: | Natural convection Reaction kinetics Porous separator |
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