## 3 Results and Discussion
### Developing Microfluidic Pump and Mixer Driven by Bipolar Janus AC-FFET
#### 3.4.2 Effect of the Applied AC Voltage on the Integrated Device's Performance
With the optimal signal frequency f = 150 Hz and driving voltage V\({}_{\text{D}}\) = 2 V in the current device design, we examine the importance of bipolar AC field-effect flow control in generating controllable flow behaviors along the length and width of the channel. With the definition of absolute voltage bias \(\bigtriangleup\)V\({}_{\text{G}}\) = V\({}_{\text{G}}\) - 0.5V\({}_{\text{D}}\), a dimensionless number \(\beta\) = (V\({}_{\text{G}}\) - 0.5V\({}_{\text{D}}\))/0.5V\({}_{\text{D}}\) is extractable, and its specific value is bounded between \(-1\) and \(1\) in an actual situation, in which 0 \(\leq\) V\({}_{\text{G}}\)\(\leq\) V\({}_{\text{D}}\). When the bias ratio \(\beta\) of the gate voltage imposed on the metal phase of the Janus pillar becomes zero, although an electrokinetic flow component is induced along the channel axis due to non-uniform interfacial polarizability, all the units in the post array float in external AC fields with V\({}_{\text{G}}\) = 0.5V\({}_{\text{D}}\), and no symmetry breaking in the transversal ICEO-vortex flow pattern takes place, resulting in only active ICEO pumping without apparent sample stirring (Figure 11A). As the absolute value of \(\beta\) increases gradually from 0 to 0.9, the gate voltage varies from V\({}_{\text{D}}\)/2 to the peak magnitude with V\({}_{\text{G-odd}}\) = 0.95V\({}_{\text{D}}\) and V\({}_{\text{G-even}}\) = 0.05V\({}_{\text{D}}\), the swirling ICEO fluid motion even becomes asymmetric in the transversal direction, and it tends to behave as one large whirlpool around each pillar (Figure 13A-D)). At a larger gate-offset ratio, the biased ICEO eddies rotate in one specific direction along the width of the channel, which is upward and downward for the odd- and even-numbered pillars, respectively. For the current integrated device design with the bipolarly biased gate-voltage sequence of \(\beta_{\text{odd}}\) = \(-\beta_{\text{even}}\), asymmetric ICEO eddies whose rotating direction is constantly reversed between adjacent microvolinders are induced along the discrete Janus pillar via AC field-effect flow control, which is, therefore, more apt for analyte mixing. As the gate-voltage offset ratio \(\beta\) increases from 0.1 to 0.9, although the traveling wavelength of the diffusion-phase interface remains unchanged, the amplitude of lateral displacement enhances significantly (Figure 13A-D)), implying an improved mixing performance (see the Supplementary Movie). Due to an enhancement in the input electric energy, the horizontal pump motion u\({}_{\text{x}}\) originating in the ICEO rises as the gate-voltage bias increases (Figure 13F). Moreover, the transversal rotating perturbation u\({}_{\text{y}}\) responsible for the sample stirring is linearly proportional to \(\beta\) and vanishes when the gate offset is zero, with \(\beta\) = 0 (Figure 13G). Thus, in AC field-effect flow control, it is preferable to selectively control u\({}_{\text{y}}\) rather than u\({}_{\text{x}}\), resulting in a dramatic increase in \(\chi\) = u\({}_{\text{y}}\)/u\({}_{\text{x}}\) with the gate-voltage-offset ratio (Figure 13H). In this way, for the biased modes, lateral ICEO rotating convection dominates the dynamics of the mixing between the stratified liquid streams (Figure 13A-D)). As the gate-voltage offset increases, the mixing index grows rapidly and tends to attain a stable plateau value when \(\beta\) exceeds 0.5 (Figure 13E). Not only is the mixing performance improved (Figure 13E), but the axial pump's motion is also intensified to a certain extent (Figure 13F). Thus, the enhanced pump ability does not, in turn, have a direct negative effect on the device's mixing efficiency. Based upon the analysis above, a flexible adjustment of the gate-voltage offset imposed on the metal phase of each Janus micropillar enables the simultaneous improvement in sample throughput and mixing performance of the integrated microdevice, which serves as the most important physical essence of Janus AC-FFET.