## 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
Thus, when the applied frequency is inappropriate, the advanced technique of bipolar Janus AC-FFET fails, in turn, to improve the device's mixing performance, even if the pumping ability can be enhanced. Therefore, the ideal working frequency of the given device architecture is f = 150 Hz, at which we can acquire the optimum enhancement in mixing performance, together with a moderate ICEO pump-flow rate. * (b) Effect of the amplitude of AC-driven voltage  
According to Equations (25) and (26), both the horizontal pump motion \(u_{\text{x}}\) and the transversal rotating perturbation \(u_{\text{y}}\) are linearly proportional to the squared AC-driven-voltage amplitude, implying that it may be possible to regulate the pumping and mixing behavior by simply raising the voltage magnitude applied to the two DE plates embedded in the channel sidewalls. As shown in Figure 12F,G, the simulation results indicate that both \(u_{\text{x}}\) and \(u_{\text{y}}\) grow quadratically with the AC-driven voltage \(V_{\text{D}}\) under the prescribed gate-voltage-offset ratio \(\beta_{\text{odd}}=-\beta_{\text{even}}=0.8\), in good agreement with the preliminary dimensional analysis. As a result, their ratio \(\chi=u_{\text{y}}/u_{\text{x}}\) almost remains the same as a function of \(V_{\text{D}}\) (Figure 12H). In this situation, diffusive mass transfer governs the trend of the variation in the mixing behavior in both biased and unbiased modes, which decreases as the AC-driven voltage increases due to the enhanced pump-flow rate causing a lower in-channel sample-residence time. On the one hand, under an extremely small driving voltage, since the pump motion \(u_{\text{x}}\) is excessively weak, the mixing index for the unbiased mode is already very good and close to 100%, leading to a finite enhancement in mixing performance of \(V_{\text{D}}\leq 1\) V (Figure 12A,B,E). On the other hand, under a relatively large driving voltage with \(V_{\text{D}}\geq 2\) V, since the difference in \(u_{\text{x}}\) between the unbiased and biased modes is amplified to a great extent, the molecular-diffusion effect of the biased mode decays faster with \(V_{\text{D}}\) (Figure 12F), which further inhibits the improvement in mixing behavior (Figure 12C-E). Accordingly, an optimal driving voltage of VD = 2 V enhances the mixing index by a maximum of 53.2% compared to the traditional unbiased mode by exploiting the bipolar Janus AC-FFET. Figure 12: A simulation analysis of the AC-driven-voltage effect on the resulting electrokinetic pumping and mixing performances of the advanced device design driven by bipolar Janus AC-FFET, for given values of \(\beta_{\text{odd}}=-\beta_{\text{even}}=0.8\), R = 5 \(\upmu\)m, L\({}_{\text{G}}\) = 30 \(\upmu\)m, n = 12, and f = 150 Hz. (**A**,**B**) A direct comparison of the analyte-concentration field in terms of a surface plot between the unbiased (**A**) and biased AC powering modes (**B**) at V\({}_{\text{D}}\) = 1 V. (**C**,**D**) Counterparts of (**A**,**B**) at V\({}_{\text{D}}\) = 3 V. (**E**) Numerical quantification of the mixing efficiency in the unbiased and biased modes and the relative mixing enhancement as a function of V\({}_{\text{D}}\). (**F**) A quantitative comparison of the horizontal ICEO pump-flow velocity between unbiased and biased powering modes as a function of AC-driven voltage. (**G**) A quantitative comparison of the transversal ICEO mixing-flow velocity between unbiased and biased powering modes as a function of V\({}_{\text{D}}\). (**H**) A quantitative comparison of the driving-voltage-dependent ICEO mixing/pumping velocity ratio between unbiased and biased powering modes. * (c) Effect of gate-voltage offset For realistic applications, it is indispensable to know how the magnitude of gate-voltage bias affects field-effect-adjustable ICEO pumping and mixing at a given AC-driven-voltage signal.