Electroconvection in electrodeposition: Electrokinetic regularization mechanisms of shortwave instabilities

We discuss the mechanism of electrokinetic regularization of the shortwave catastrophe in electrodeposition. Without suitable regularizations, both morphological and nonequilibrium electroosmotic instabilities occurring in electrodeposition are singular for shortwave perturbations in the following sense. In morphological instability the infinitesimal wavelength perturbation grows the fastest. In the electroosmotic instability in terms of the local electroneutrality approximation, the quiescent state is least stable for infinitesimal wavelength perturbations. Regularization of electroosmotic instability requires considering the finite width of the electric double layer. It was recently shown that in electrodeposition too, taking into account the finite width of the electric double layer combined with the finite electrode reaction rate constant, yields selection of a finite critical perturbation wavelength for instability, thus providing a regularization mechanism alternative to surface tension. We discuss the physical mechanism of this length selection, along with the effect exerted by the nonequilibrium electroosmotic flow which emerges in the limiting-overlimiting current regime.