## 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
Unlike the pillar size R governing the hydrodynamic interaction between the array unit and the channel sidewalls, the inter-pillar separation L\({}_{\text{G}}\) plays a more important role in adjusting the active interplay of the electrochemical polarization between the adjacent Janus pillars. A more closely packed discrete pillar array at a smaller L\({}_{\text{G}}\) tends to lower the pumping ability u\({}_{\text{x}}\), but it enhances the transversal flow rotation u\({}_{\text{y}}\) for mixing (Figure 9E) due to the sophisticated charging dynamics of the interfacial capacitance skin for the practical discrete arrangement of Janus pillars with finite inter-unit separation. This abstruse action mechanism of the inter-pillar gap on the two orthogonal ICEO velocity components results in quite stable mixing performances under different L\({}_{\text{G}}\) from both the biased and the unbiased AC powering schemes (Figure 9D). Nevertheless, the preferable option is to use a special inter-pillar separation of L\({}_{\text{G}}\) = 30 \(\upmu\)m to enable the maximum local improvement in the mixing performance of 44%, even without significantly sacrificing the horizontal pump-flow rate (Figure 9D). * (c) Effect of the number of discrete Janus pillars within the array Regarding the geometry configuration, the number of Janus units in the discrete pillar array \(n\) also exerts an appreciable impact on the chip's performance in active pumping and mixing, in addition to the R and the L\({}_{\text{G}}\). With the optimal pillar radius of R = 5 \(\upmu\)m and separation of L\({}_{\text{G}}\) = 30 \(\upmu\)m, the mixing efficiency, two ICEO flow components, and their velocity ratio are quantified in terms of a direct comparison between biased and non-biased powering modes in Figure 10.  
As the number of Janus posts n increases from n = 2 to n = 12, the pump-flow rate u\({}_{\text{x}}\) in both modes rises monotonically (Figure 10H). That is, placing more pillars within the device channel definitely has a positive effect on the ICEO's driving force for forward sample delivery, which arises from the larger surface area of the ideally polarizable metal phase from which the ICEO slipping stems (Figure 10A-D)). In contrast, the transversal rotating perturbation u\({}_{\text{y}}\) is quite insensitive to changes in n because it grows by no more than 10% as the n increases by six-fold (Figure 10G). This intuitionally results in a more severe suppression of the velocity ratio \(\chi\) = u\({}_{\text{y}}\)/u\({}_{\text{x}}\) at a larger n (Figure 10H). As expected, the mixing index M\({}_{\text{S}}\) for the non-biased mode decreases rapidly with n due to the enhanced pump-flow rate, leading to a reduction in the residence time of the particle species in the flow channel. Contrary to what would be expected from the variation trend of u\({}_{\text{y}}\)/u\({}_{\text{x}}\), the biased powering mode in the bipolar Janus AC-FFET exhibits a relatively stable mixing effect within a broad range of n (Figure 10E). In fact, the effective actuating range of the transversal flow rotation u\({}_{\text{y}}\) is linearly proportional to the number of Janus pillars in the discrete array, leading to a substantial enhancement in the kinematic energy of u\({}_{\text{y}}\) with n (Figure 10A-D). However, this effect is not included in the approximate scaling analysis, so it is essential to obtain an accurate prediction of the device's performance in active pumping and mixing by conducting simulations with our extended physical model of ICEO. The authentic u\({}_{\text{y}}\)/u\({}_{\text{x}}\) may increase rather than decrease with n, which compensates for the decrease in the sample residence time from a larger u\({}_{\text{x}}\) to enable a stable distribution of the mixing index as a function of n under bipolar AC field-effect flow control.