Stability of electrophoretic transport of ions

We present an investigation of instability during electrophoretic transport of ions in a class of electrolytes called oscillating electrolytes. We analyze the onset of instability in electrophoretic transport in a binary electrolyte by modeling growth of small concentration disturbances over a base state with uniform acid and base concentrations. Our linear stability analysis shows that the growth rate of low wave-number concentration disturbances increases with an increase in wave number. Whereas, the growth rate of high wave-number disturbances decreases with increasing wave number due to the stabilizing effect of molecular diffusion. Our analysis also yields the scaling for growth rates and the wave number of most unstable mode with electric field. In addition, we show that the electrophoretic system exhibits instability only for a certain range of species concentrations. We also discuss the physical mechanism underlying the instability of transport process. We show that the instability is exhibited by those binary electrolytes that consist of a multivalent species with unusually high electrophoretic mobility in higher ionization states. Throughout, we provide verification of our linear stability analysis with full nonlinear simulations.