## 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
Therefore, we have shifted our attention from basic physics to the desired device's dual functionality in concurrent on-chip active pumping and mixing via the bipolar Janus AC-FFET. As the radius of the Janus pillar R increases, the pump velocity u\({}_{x}\) for both the non-biased and the biased modes enhances due to the enlarged area of the ideally polarizable metal-phase surface, while the mixing velocity u\({}_{y}\) gradually decreases due to the transversal confinement effect from a finite channel span (Figure 8H). Considering the decreasing time t\({}_{\rm mix}\) = L\({}_{\rm C}\)/u\({}_{x}\) for the sample particles to pass through the flow channel, both the diffusion distance W\({}_{\rm d}\) = (D \(\times\) t)\({}^{0.5}\) and the electrokinetic mixing distance W\({}_{\rm ICEO}\) = (D \(\times\) t)\({}^{0.5}\) + L\({}_{\rm C}\)\(\times\) u\({}_{y}\)/u\({}_{x}\) decay with R. A direct consequence of this is that the mixing efficiency M under both powering conditions declines as the Janus cylinder increases in size, and the biased mode always performs much better in the mixing function than the unbiased mode in terms of a larger M\({}_{\rm FE}\) than M\({}_{\rm S}\) (Figure 8G), on account of the additional hydrodynamic rotations along the oppositely polarized Janus pillars subjected to bipolar AC field-effect flow control. Both the mixing enhancement and the absolute mixing index are quite unsatisfactory under the largest pillar radius, R = 15 \(\upmu\)m (Figure 8E,F). Moreover, the already high mixing performance of the unbiased mode leaves insufficient room for mixing elevation to occur under the smallest R = 2.5 \(\upmu\)m, due to the low pump motion \(\mathrm{u_{x}}\) (Figure 8G). Therefore, an intermediate pillar radius of R = 5 \(\upmu\)m was ensured by achieving a subtle trade-off between the opposing variation trends of \(\mathrm{u_{x}}\) and \(\triangle\)M for the subsequent analysis, so as to induce a sufficient axial throughput \(\mathrm{u_{x}}\) and mixing-performance improvement \(\triangle\)M = \(\mathrm{M_{FE}}-\mathrm{M_{S}}\) = 42% at the same time. * (b) Effect of inter-pillar separation Based upon the optimal pillar radius of R = 5 \(\upmu\)m, it is important for us to reveal the effect of the spatial separation between the neighboring pillars \(\mathrm{L_{G}}\) on the resulting device's dual functionality. As shown in Figure 9A-C, an increase in the inter-post distance \(\mathrm{L_{G}}\) directly leads to an increase in the traveling wavelength of the diffusion-phase interface \(\lambda\) = 2\(\mathrm{L_{G}}\). Figure 9: A simulation analysis of the influence of inter-pillar separation \(\mathrm{L_{G}}\) in the integrated device design on the resulting electrokinetic pumping and mixing performances driven by bipolar Janus AC-FFET, in which neighboring Janus pillars are sequentially subjected to two oppositely polarized gate terminals for given values of f = 200 Hz, \(\mathrm{V_{D}}\) = 2 V, \(\mathrm{\beta_{odd}}=-\mathrm{\beta_{even}}\) = 0.8, R = 5 \(\upmu\)m, and n = 6. (**A–C**) A surface plot of analyte-concentration field in the unbiased powering mode for different pillar separations: (**A**) \(\mathrm{L_{G}}\) = 20 \(\upmu\)m, (**B**) \(\mathrm{L_{G}}\) = 30 \(\upmu\)m, and (**C**) \(\mathrm{L_{G}}\) = 120 \(\upmu\)m. (**D**) Numerical characterization of the mixing efficiency in the unbiased and biased modes and the relative mixing enhancement as a function of the pillar separation. (**E**) A quantitative comparison of the ICEO’s flow velocity between unbiased and biased powering modes as a function of the pillar separation in terms of electrokinetic pumping and mixing. With the rise in pillar separation L\({}_{\text{G}}\) from 20 to 100 \(\upmu\)m, u\({}_{\text{x}}\) increases, but u\({}_{\text{y}}\) decreases monotonically. The L\({}_{\text{G}}\) has a positive (negative) effect on the horizontal pump motion u\({}_{\text{x}}\) (transversal rotating motion u\({}_{\text{y}}\)) (Figure 9E).