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Multiple-species model for electrokinetic instability

In this paper we present a multiple-species electrokinetic instability (MSEKI) model. We consider a high aspect ratio flow geometry, a base state where the conductivity gradient is orthogonal to the applied electric field (i.e., a spanwise gradient configuration), and a four-species chemistry model. A linear stability analysis (LSA) of the depth-averaged governing equations is shown to have unstable eigenmodes for conductivity ratios as close to unity as 1.01. We present the experimental image data and full nonlinear simulations of the governing equations for a conductivity ratio of 1.05. Images of the disturbance dye field from the nonlinear simulations show good qualitative agreement with the experiment. Both the trend and absolute value of the temporal evolution of the critical wave number are captured by the MSEKI model. Growth rates extracted from the experimental data also compare favorably with those predicted by LSA. Species electromigration is shown to have a significant influence on the developm...