Targeting Complete Chaotic Mixing by Destabilizing Key Periodic Orbits in an Electro-osmotic Mixer

The ability to generate complete, or at least well spread, chaotic mixing is of great interest in numerous applications, especially microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter values at which complete mixing occurs. The technique is applied to a time periodic, two-dimensional electro-osmotic flow with spatially and temporally varying Helmoltz-Smoluchowski slip conditions. The strategy consists of following the linear stability of some key periodic orbits in parameter space, particularly identifying bifurcation points at which such orbits become unstable. Poincar\'{e} maps, Lyapunov exponents and a box counting measure are all computed to validate the strategy.