Numerical Analysis of Some Active and Passive Electro-Kinetic Micro-Mixers by Applying Poisson-Nernst-Planck and Navier–Stokes (PNP-NSE) Equations

Micro-mixers are vital components of “Lab-on-a-Chip” devices. Their main functionality is the mixing of two streams with desired quality and at minimum mixing time. In this work, numerical modelings of some active and passive micro-mixers with innovative designs are reported. Increasing mixing quality and decreasing mixing time are the design objectives. Our numerical model features solving the set of non-linear and inter-coupled Poisson-Nernst-Planck-Naiver-Stokes equations (PNP-NSE) instead of using simplified models like Poisson-Boltzmann (PB). These equations describe a more realistic model of the physics involved at continuum level by incorporating diffusion, electro-migration, and convection, which are the dominant phenomena in electro-kinetic micro-mixers especially those using AC voltage electrodes. The computations are carried out using Rayan (in-house code). The traditional Poisson-Boltzmann (PB) model relies on simplifying assumptions and is proven to lose its accuracy in complex geometries and near active electrodes. On the other hand, the PB model is much less sophisticated and therefore much less computationally expensive. One of the contributions of this research is to show that in passive micro-mixers making the obstacles smaller but more numerous increases the mixing quality (for the case studied by 13%). The other major contribution of this work is the introduction of the combination of the vertical and horizontal AC electrodes. This new design creates jets normal to the direction of the mainstream which is responsible for enhancing chaotic mixing. This results in a stable mixing quality of 99% at 2.7s.