## 3 Results and Discussion
### ICEO around a Janus Micropillar Free from External Wiring
#### 3.2.1 Effect of Metal-Phase Angle \(\alpha\) on Horizontal Pumping by ICEO around a Janus Post
However, since the surface area of the ideally polarizable metal/liquid interface was appreciably enlarged for \(\alpha=180^{\circ}\), the actuating range of asymmetric ICEO whirlpools doubled (Figure 3C) compared to that in the case of \(\alpha=90^{\circ}\) (Figure 3B), while the typical flow speed stayed almost the same (Figure 3F). As predicted, this extension in the effective actuating range of ICEO has a propensity to increase the net pump-flow rate along the channel axis (Figure 3G). When \(\alpha\) exceeds \(180^{\circ}\) and reaches \(270^{\circ}\), the surface of the Janus cylinder, whose body is occupied more by the metal phase (Figure 3D), has four ICEO vortices with strong flow rates identical to those around a uniformly conducting cylinder (Figure 2A). Since the scope of action of the two large vortices flowing to the right on the right side is larger than that of the two smaller vortices flowing to the left on the left side, the flow-field profile of ICEO still presents global asymmetry perpendicular to the field lines (Figure 3D), in which the net electrokinetic pump-flow component is still directed forward from the conducting end downstream with a positive u\({}_{x}\) (Figure 3F). However, because the leftward flow on the left of the Janus cylinder compensates for part of the rightward flow on its right side, the unidirectional propulsion along the length of the channel decays to some extent for \(\alpha=270^{\circ}\) compared the case of a neutral metal phase angle \(\alpha=180^{\circ}\) (Figure 3G). Based on the analysis above, a horizontal downstream pump-flow rate can always be induced by ICEO near a metal-dielectric Janus cylinder, even when free from external wiring, as long as it is not entirely made of metal or dielectric material, with \(0^{\circ}<\alpha<360^{\circ}\). As vividly shown in Figure 3G, the enabling of the pump's capability by the ICEO reaches a maximum value for \(\alpha=180^{\circ}\) with symmetrically distributed metal and dielectric phases; any further deviations in \(\alpha\) in either direction from this key value tends to monotonically weaken the pump-flow rate, which vanishes when \(\alpha\) approaches either \(0^{\circ}\) or \(360^{\circ}\), with the target pillar composed of a uniform dielectric or metal phase. This can be quite easily understood based on the aforementioned \(\alpha\)-dependent ICEO flow profiles (Figure 3A-D). When \(\alpha\) is less than \(180^{\circ}\), all of the ICEO eddies on the conducting side eject fluid downstream in the same direction, so an increase in the volumetric fraction of the metal phase causes a direct increase in the actuating range of ICEO whirlpools, resulting in enhanced pump ability. Once \(\alpha\) is raised beyond \(180^{\circ}\), however, the metal phase begins to occupy more than half of the Janus post. Since the two ICEO eddies on the left side generally flow in opposite directions to the two on the right side, an increase in \(\alpha\) from \(180^{\circ}\) towards \(360^{\circ}\) reduces the driving of the pump efficiency by the ICEO. This peak pump-flow rate at \(\alpha=180^{\circ}\) suggests that employing a standard Janus micropillar with equal metal and dielectric phases, even without applying a biased gate voltage, is an optimal method to achieve unidirectional sample delivery. Moreover, it is worth mentioning that, as shown in Figure 3F, the change in \(\alpha\) has no obvious impact on the localized slip velocity, and its effect on the overall ICEO flow field is mainly achieved by altering the actuating range of ICEO slipping, which makes a substantial contribution to the precise appearance of the peak pump rate at \(\alpha=180^{\circ}\). Consequently, in all the subsequent investigations, we directly adopted symmetric metal-dielectric Janus cylinders with \(\alpha=180^{\circ}\), which have the greatest potential to enable the horizontal pumping of electrolytes by ICEO.