We present an investigation of instabilities that occur in a class of electrolytes, called oscillating-electrolytes, which become unstable under the effect of electric field. We analyze the onset of instability by modeling growth of small perturbations in concentration field of a binary electrolyte. Our analysis is based on linearizing the nonlinear species transport equations, which include the effects of electromigration, diffusion, and acid - base equilibria on electrophoretic transport of ions. Our linear stability analysis shows that, the growth rate of low wavenumber concentration disturbances increases with increase in wavenumber. Whereas, the growth rate of high wavenumber disturbances decreases with increasing wavenumber due to stabilizing effect of molecular diffusion. Our analysis also yields scaling for growth rates and the wavenumber of most unstable mode with electric field. The growth rates and scaling predicted by our linearized model compare well with those predicted by fully nonlinear simulations. In addition, we show that the oscillatory behavior is exhibited only over a range of species concentrations. We also discuss the physical mechanism that causes concentration disturbances to grow in oscillating electrolytes. We show that oscillations result when the binary electrolyte consists of a multivalent species with unusually high electrophoretic mobility in higher ionization states. Presence of such species causes abnormal variations in electrical conductivity due to concentration disturbances, which in turn alter the electric field in a way that destabilizes the electrophoretic system.

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