## 3 Results and Discussion
### ICEO around a Janus Micropillar Free from External Wiring  
To induce a net pump motion in the horizontal direction, it is necessary to cause symmetry breaking in the ICEO flow profile perpendicular to the field axis. For this reason, we used a metal-dielectric Janus cylinder to replace the uniform metal post used previously. For a circular Janus micropillar fixed on the channel floor, a portion of its main body is composed of nonconducting dielectric material, while the remaining part consists of highly conducting metal material (Figure 1). This nonuniformity in interfacial polarizability gives the Janus post the ability to produce asymmetric ICEO fluid motion even under unbiased AC voltage excitation, facilitating unidirectional pump action along the channel length (Figures 3 and 4). Figure 2: A simulation validation of our proposed physical model against the standard benchmark, in which a uniform metal cylinder immersed in aqueous electrolyte solution is fixed in space in the presence of a uniform background AC electric field applied in the transversal direction. (**A**) Numerical prediction of the familiar quadrupolar ICEO-vortex flow field adjacent to an ideally polarizable conducting cylinder in terms of a surface and streamline plot of nonlinear electro-osmotic streaming. (**B–D**) A quantitative comparison between the analytical and numerical solutions of various field variables evaluated at the metal/electrolyte interface; (**B**) position-dependent tangential ICEO slipping velocity \(\upomega\) as a function of the polar angle under four distinct field frequencies at \(\text{V}_{\text{D}}=2\) V; (**C**) frequency-dependent surface-averaged \(\text{abs}(\upomega)\) at \(\text{V}_{\text{D}}=2\) V; and (**D**) driving-voltage-dependent surface-averaged \(\text{abs}(\upomega)\) at \(\text{f}=200\) Hz. Figure 3: A simulation analysis of the influence of the metal-phase angle \(\alpha\) of the Janus micropillar on symmetry breaking in the horizontal ICEO flow profile, which effectively gives rise to a net forward-pump-flow component responsible for unidirectional sample delivery towards channel exit, for given values of \(t=200\) Hz, V\({}_{\rm D}=2\) V, and R \(=5\)\(\upmu\)m, in the conventional unbiased AC powering mode. **(A–D)** A surface and streamline plot of the circulating ICEO flow field next to an individual metal-dielectric Janus cylinder of varying metal-phase angles \(\alpha\): **(A)**\(\alpha=0^{\circ}\), **(B)**\(\alpha=90^{\circ}\), **(C)**\(\alpha=180^{\circ}\), and **(D)**\(\alpha=270^{\circ}\). **(E)** Position-dependent tangential ICEO slipping u\({}_{\rm{B}}\) on the dielectric surface of Janus post as a function of the polar angle for \(\alpha=0^{\circ}\). **(F)** A quantitative comparison of position-dependent tangential ICEO slipping u\({}_{\rm{B}}\) on the polarizable surface of Janus post as a function of the polar angle under \(\alpha=90^{\circ}\), \(180^{\circ}\), \(270^{\circ}\), and \(360^{\circ}\). **(G)** A vivid comparison of the net axial pump velocity u\({}_{\rm{x}}\) and transversal mixing velocity u\({}_{\rm{y}}\) as a function of the metal-phase angle. It is noteworthy that the metal-phase angle \(\alpha\) can be equivalently represented by the volumetric fraction of the metal phase V\({}_{\rm{fm}}\) in the inhomogeneous Janus pillar. Most importantly, the peak pump performance occurred when using a symmetric Janus post with equal dielectric and metal phases, as commonly seen in real experiments. Figure 4: Simulation results of the influence of the electric-field frequency on forward pumping of electrolyte via horizontal symmetry breaking in ICEO flow behavior for different radii of the Janus post under a given driving voltage \(\rm V_{D}=2~{}V\) (when the metal phase of the Janus pillar is free from external wiring).