Mixing enhancement in electro-osmotic flows via modulation of electric fields

The mixing of a passive tracer in a three-dimensional rectangular microchannel is studied numerically. A time-dependent electric field across a microchannel, filled with an electrolyte solution, is applied in order to realize a well-mixed state. Random perturbations to a time-periodic electric field are introduced in order to break the invariant tori of the system and to attain better mixing results. Two types of nonperiodic protocols are used to generate chaotic mixing by modulating the transverse electric field. In each case the quality of mixing is quantified with Lyapunov exponents for nondiffusive tracers and variance in concentration for diffusive tracers. The numerical results suggest that when the Lyapunov exponent is properly scaled, its probability density function measured over various numbers of periods has the same geometrical structure. It was also found that the variance in the concentration of the passive scalar exhibits an exponential decay. For the modulated and periodic systems considered in this investigation, its evolution curves exhibited self-similarity when plotted versus the product of the nondimensional time and the mean Lyapunov exponent of the flow. As the axial flow in this study varies only inside the Debye layer, and the tracers were introduced into the middle pluglike region of the flow, it was found that Taylor dispersion effects are more pronounced for flows (at least in their early stages) with effective mixing in the cross section.