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Direct Numerical Simulation of Electrohydrodynamic Chaos Near Ion-Selective Surfaces

Ali Mani (Stanford University), Mathias Andersen (), Clara Druzgalski (Stanford University)

Electrohydrodynamics and electrokinetics of fluid systems

Mon 9:00 - 10:30

Barus-Holley 161

We present a comprehensive analysis of electrohydrodynamic chaos for a binary electrolyte near an ion-selective surface sustaining electric current above diffusion limitation. Our investigation goes beyond the well-known Rubinstein-Zaltzmann instability and into the relatively unexplored regime of fully chaotic electrohydrodynamic flow. Our model system consists of an aqueous symmetric electrolyte adjacent to an ion-selective surface, with an external electric field driving transport. By implementing a direct numerical simulation (DNS) of the Poisson-Nernst-Planck and Navier-Stokes equations in a two-dimensional domain, we are able to visualize the onset of steady vortex pairs and the transition to fully chaotic multi-layer vortices. Notably, we demonstrate that in the fully chaotic regime positive and negative free charge density created adjacent to the membrane are both ejected into the bulk, invalidating the quasi-electroneutral bulk assumption (used in traditional asymptotic models). Our simulations also demonstrate a current-versus-voltage curve that predicts overlimiting current. Furthermore, we explore the role of viscous energy dissipation in this system. Finally, we present preliminary steps towards a reduced order model, inspired by the Reynolds-Averaged Navier-Stokes (RANS) equations in turbulence theory, and use our DNS data to quantify the relative importance of the unclosed terms in this ensemble-averaged model.