Competition between Dukhin's and Rubinstein's electrokinetic modes

The combined effect of two modes of electroconvection, i.e., (a) the electro-osmotic flow of the second kind induced by a curved membrane surface and (b) electrokinetic instability, is studied numerically. Both physical mechanisms are responsible for electric current enhancement to the surface, and these modes are strongly nonlinearly coupled. For the limiting regimes, their resonant interaction near the threshold of instability with a corresponding resonantly amplified current enhancement is found. For the overlimiting regimes, inside the unstable region, their interaction becomes more complex with negative sideband and positive subharmonic resonant interactions. Wall corrugation can still be in resonance with the unstable modes. At some wave numbers of corrugation, these two mechanisms compete and electrokinetic instability can even be completely suppressed by the wall corrugation.