Mechanisms for overlimiting current and concentration polarization in electrodialysis (ED) with ion exchange membranes are not yet well understood despite its half century history. A first-principles model involving the Nernst-Planck-Poisson equations fully coupled to the Navier-Stokes equations and containing no adjustable parameters is proposed. The calculated current voltage (I-V) curve of an ED flow through cell shows a linear region, a sloped plateau surpassing "limiting" current and a rapidly rising region characterized by increasing current oscillations. This curve and concentration profiles are compared with experimental data and with "classical" models It is shown that the initial smooth region of the I-V plateau relates to a new electrokinetic mode, which is similar to the Dukhin-Mishchuk regime. The difference is in the fact that in the case of forced convection the tangential electric force producing stable electroconvection can appear at a homogeneous flat membrane due to nonuniformity in the lateral concentration distribution; membrane surface nonflatness or electric heterogeneity are not necessary. The oscillating region with a higher slope relates to the Rubinstein-Zaltzman unstable electrokinetic mode. I-V curves calculated with the no slip and the Navier slip conditions are compared. (c) 2013 Elsevier B.V. All rights reserved