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We present a comprehensive analysis of transport processes associated with electrohydrodynamic chaos in electrokinetic systems containing an ion-selective surface. The system considered is an aqueous symmetric binary electrolyte between an ion-selective surface and a stationary reservoir. Transport is driven by an external electric field. Using direct numerical simulations (DNS) of the coupled Poisson–Nernst–Planck and Navier–Stokes equations in 2D we show significant transitions in flow behavior from coherent vortex pairs to fully chaotic multi-layer vortex structures with a broadband energy spectrum. Additionally, we demonstrate that these vortices can eject both positive and negative free charge density into the bulk of the domain and completely disrupt the structure of the traditionally described extended space charge region. The resulting dynamical behavior poses a challenge for traditional asymptotic modeling that relies on the quasi-electroneutral bulk assumption. Furthermore, we quantify for the first time the relative importance of energy dissipation due to viscous effects in various transport regimes. Finally, we present a framework for the development of ensemble-averaged models (similar to Reynolds Averaged Navier–Stokes equations) and assess the importance of the unclosed terms based on our DNS data.
Druzgalski et al. (Wed,) studied this question.