Chaotic mixing in electro-osmotic flows driven by spatiotemporal surface charge modulation

This paper presents an investigation into chaotic mixing in an electro-osmotic flow through a microchannel. In the mixing system, the continuous throughput flow has the form of a pluglike electro-osmotic flow induced by a permanent surface charge on the wall surface, while electro-osmotic flows contributed by spatiotemporal surface charge variations act as a perturbed flow. The spatiotemporal surface charge variations are achieved using the field-effect control method. The analyses consider two different spatiotemporal surface charge modulation schemes, designated as "MS I" and "MS II," respectively. It is shown that both modulation schemes prompt the crossing of the flow streamlines at different instances in time and produce a chaotic mixing effect. Utilizing the thin double layer assumption, the study commences by solving the biharmonic equation for the electro-osmotic flow fields analytically. The mixing phenomena induced by the two modulation schemes are then analyzed using the Lagrangian particle tracing method. Finally, the mixing performances of the two schemes are evaluated analytically using the Poincaré section method, the finite-time Lyapunov exponent (FTLE) technique, and a stretching value distribution analysis method, respectively. It is found that the mean FTLE combined with the coefficient of variance of the FTLE distribution provides the most suitable criterion for obtaining quantitative estimates of the mixing performance and therefore provides a feasible means of estimating the amplitude and time-switching period of the perturbed flows which optimize the mixing performance. The validity of the analytical results is confirmed via a comparison with the results obtained from the back-trace imaging method and direct numerical simulations based on a species convection-diffusion equation, respectively. In addition, the direct numerical simulation results show that the dimensionless mixing length and dimensionless mixing time required to achieve a 90% mixing both vary as a logarithmic function of the Péclet number when the mixing system is in a nearly fully chaotic state.