The effects of reaction kinetics upon the instabilities in cathodic electrodeposition

This article deals with a linear stability analysis of electrodeposition. The surface energy is disregarded in order to focus on the possible effects of the finite width of the electric double layer and the finite electrode reaction rate upon the wavelength selection. It is found that in the absence of electroconvection the fastest growing perturbation mode is that with a wavelength equal to the geometric average of the Debye length and the reaction diffusion length, which is the ratio of diffusivity to the electrode reaction rate. This wavelength is one–two orders of magnitude greater than that selected by the capillarity mechanism based on the surface energy estimates. This shift of the selected wavelength towards long waves is enhanced by another order of magnitude by electroconvection in the regime of the nonequilibrium electroosmosis developing upon the emergence of the extended space charge.