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In the present work fournontrivial stages of electrokinetic instability areidentified by direct numerical simulation (DNS) of the fullNernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence ofthe initial conditions (milliseconds); ii) 1D self-similar evolution(milliseconds-seconds); iii) The primary instability of the self-similarsolution (seconds); iv) The nonlinear stage with secondary instabilities. Theself-similar character of evolution at intermediately large times is confirmed.Rubinstein and Zaltzman instability and noise-driven nonlinear evolution toover-limiting regimes in ion-exchange membranes are numerically simulated andcompared with theoretical and experimental predictions. The primary instabilitywhich happens during this stage is found to arrest self-similar growth of thediffusion layer and specifies its characteristic length as was firstexperimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). Anovel principle for the characteristic wave number selection from thebroadbanded initial noise is established.

Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability