FREE-CONVECTION IN AN ELECTROCHEMICAL SYSTEM WITH NONLINEAR REACTION-KINETICS

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 e lectrodes is assumed to be related to the local charge transfer potent ial and concentration by a nonlinear Butler-Volmer law. Free convectio n of the electrolyte appears owing to the variation of the concentrati on field. After a short initial period, the electrolyte becomes strong ly stratified and the motion takes place in boundary layers at the sol id boundaries. An approximate model equation for the evolution of the stratification is derived by using perturbation theory. Predictions fr om the simplified model are found to be in good agreement with numeric al solutions of the complete problem. Significant differences compared with earlier studies for linear kinetics, i.e. cases in which the ele ctric current density at the electrodes is constant, are found. Among other things, for large values of the difference Delta V in electric p otential between the electrodes, most of the dissolved salt eventually collects near the bottom of the cell. The concentration in the bulk o f the electrolyte is, for large values of Delta V approximately given by a ninth-order polynomial to be compared with a linear behaviour for linear kinetics.