Numerical Modeling of Chaotic Mixing in Electroosmotically Stirred Continuous Flow Mixers

We present numerical studies of particle dispersion and species mixing in a $ζ$ potential patterned straight microchannel. A continuous flow is generated by superposition of a steady pressure-driven flow and time-periodic electroosmotic flow induced by a streamwise ac electric field. $ζ$ potential patterns are placed critically in the channel to achieve spatially asymmetric time-dependent flow fields that lead to chaotic stirring. Parametric studies are performed as a function of the Strouhal number (normalized ac frequency), while the mixer geometry, ratio of the Poiseuille flow and electroosmotic velocities, and the flow kinematics (Reynolds number) are kept constant. Lagrangian particle tracking is employed for observations of particle dispersion. Poincaré sections are constructed to identify the chaotic and regular zones in the mixer. Filament stretching and the probability density function of the stretching field are utilized to quantify the “locally optimum” stirring conditions and to demonstrate the statistical behavior of fully and partially chaotic flows. Numerical solutions of the species transport equation are performed as a function of the Peclet number (Pe) at fixed kinematic conditions. Mixing efficiency is quantified using the mixing index, based on standard deviation of the scalar species distribution. The mixing length $(lm)$ is characterized as a function of the Peclet number and $lm∝ln(Pe)$ scaling is observed for the fully chaotic flow case. Objectives of this study include the presentation and characterization of the new continuous flow mixer concept and the demonstration of the Lagrangian-based particle tracking tools for quantification of chaotic strength and stirring efficiency in continuous flow systems.