## 3 Results and Discussion
### Developing Microfluidic Pump and Mixer Driven by Bipolar Janus AC-FFET
#### 3.4.1 Geometry Dependence of the Integrated Microfluidic Pump and Mixer
Figure 8: Simulation results of the influence of the radii of the discrete Janus pillars R in the integrated array on the device’s dual functionality in simultaneous electrokinetic pumping and mixing, namely, an advanced microfluidic pump and mixer driven by bipolar Janus AC-FFET with adjacent Janus posts  
posts sequentially subjected to two oppositely polarized gate terminals for given values of f = 200 Hz, V\({}_{\rm D}\) = 2 V, \(\beta_{\rm odd}\) = \(-\beta_{\rm even}\) = 0.8, L\({}_{\rm G}\) = 80 \(\mu\)m, and n = 6. **(A)** A surface and streamline plot of the ICEO-vortex flow field in the unbiased powering mode for a pillar radius R = 5 \(\mu\)m. **(B)** A surface plot of the sample concentration field in the unbiased mode for a pillar radius R = 5 \(\mu\)m. **(C,D)** Counterparts of **(A,B)** in the biased powering mode, respectively. **(E,F)** Counterparts of **(C,D)** for one larger pillar radius R = 15 \(\mu\)m. **(G)** Numerical characterization of the mixing performance in the unbiased and biased mode and the relative mixing enhancement as a function of the pillar radius. **(H)** A quantitative comparison of the ICEO-flow velocity between unbiased and biased powering modes as a function of the pillar radius in terms of electrokinetic pumping and mixing. Thus, although the symmetrically distributed ICEO streamlines can be exploited for the axial transport of analytes, they are ineffective in flexibly steering the lateral motion behavior of the two-phase diffusion interface for sample mixing (Figure 8A,B). In contrast, the utilization of the AC field-effect flow-control technique for metal-dielectric Janus pillars solves this puzzle well by adding additional flow-symmetry breaking in the transversal direction so as to achieve the goal of simultaneous active pumping and mixing driven by pure ICEO (Figure 8C,D). As displayed in Figure 8D, by imposing sufficiently large opposite gate-voltage-offset ratios \(\beta_{\rm G\text{-odd}}\) = \(-\beta_{\rm G\text{-even}}\) = 0.8 to the two gate terminals connected to the odd- and even-numbered Janus pillars, respectively, biased ICEO eddies swirling either anticlockwise or clockwise can be produced along the sequence of the pillar array. The asymmetric ICEO vortex flow in opposite rotating directions imparts a time-averaged hydrodynamic torque to the working fluid, making the two-phase contact interface rotate in line with the lateral convection u\({}_{y}\), alternating between the downward and upward flow directions (Figure 8D). The additional rotating behavior u\({}_{y}\) with controllable circulating directions twists and extends the phase interface more efficiently (Figure 8D) than the unbiased version without u\({}_{y}\) at an identical longitudinal propagating distance (Figure 8B). As a result, the dynamic swap of analytes between the two stratified buffer streams is accelerated by a careful choice of the gate-polarity sequence for the array of discrete Janus post, leading to an enhanced mixing index M\({}_{\rm FEC}\) = 77.5% (Figure 8D) in comparison to the unbiased powering condition of M\({}_{\rm FEC}\) = 35.5% (Figure 8B). The combined action of unipolar horizontal u\({}_{x}\) and bipolar transversal u\({}_{y}\) from the bipolar Janus AC-FFET effectively gives rise to zigzagged streamlines with traveling wavelengths equal to twice the inter-pillar separation \(\lambda\) = 2L\({}_{\rm G}\), which consistently roll forward along the discrete pillar arrangement, irrespective of the constantly reversed rotating direction of the asymmetric ICEO eddies (Figure 8D). Based on the analysis of the fundamental fluid mechanics, the up-down asymmetric ICEO eddies are more efficient in enabling simultaneous electrokinetic transport and stirring in terms of bipolarly biased circulating flows of Janus AC-FFET than the symmetric situation, in which the gate terminal of all the Janus pillars floats in potential.