## 4 Conclusions  
In summary, we provided new physical perspectives through both a scaling analysis and a numerical investigation to introduce the novel concept of AC field-effect control of ICEO streaming next to metal-dielectric Janus micropillars, namely, the unique configuration of the AC flow-field-effect transistor using Janus cylinders (Janus AC-FFET). This new operational tool for stratified sample streams in microfluidics arises from the time-averaged Coulomb force exerted by external AC-driven electric fields on the gate-voltage-induced diffuse screening cloud on the unevenly polarizable surface of a Janus post, the metal phase of which is subjected to an arbitrary gate-voltage supply. Our mathematical analysis clarifies for the first time that AC field-effect-mediated ICEO can produce horizontal pump \(\mathrm{u_{x}}\) and transversal mixing-flow components \(\mathrm{u_{y}}\) that are orthogonal to each other simultaneously in microfluidic channels. This kind of field-effect-reconfigurable AC electroconvection driven by nonlinear electro-osmosis is conceivably related to several challenging on-chip applications requiring liquid-phase actuation in multiple directions, such as the concurrent active pumping and mixing of sample analytes, the 3D-profile scanning and dielectric characterization of biological cells, and localized particle stacking in microfabricated fluid networks. The axial propelling component \(\mathrm{u_{x}}\), due to the left-right ICEO flow symmetry breaking from the inhomogeneous polarizability of the Janus pillar, and the transversal rotating component \(\mathrm{u_{y}}\), due to the up-down symmetry breaking in the electrokinetic vortex flow pattern from the biased AC powering scheme, are responsible for the pumping and mixing of the microflows, respectively. When applying an adjustable gate-voltage offset to the metal phase of the Janus entity, AC field-effect flow control tends to selectively control the mechanical behavior of \(\mathrm{u_{y}}\) rather than \(\mathrm{u_{x}}\), and the magnitude of \(\mathrm{u_{y}}\) can be separately controlled by varying the gate bias while not exerting an evident influence on \(\mathrm{u_{x}}\). Moreover, automatic conversion in the rotating direction of \(\mathrm{u_{y}}\) is conveniently realizable by simply reversing the gate voltage polarity. Inspired by this, we further proposed an advanced microfluidic pump and mixer driven by the bipolar Janus AC-FFET, in which each pair of neighboring pillars is sequentially subjected to two oppositely polarized gate voltages along an array of discrete Janus micropillars integrated into the middle of the device channel. When inducing active zigzag streamlines, these asymmetric ICEO whirlpools with constantly changing swirling directions between adjacent array elements greatly facilitate on-demand sample mixing via the improved Janus AC-FFET using bipolar gate terminals. Unlike all the other geometric and voltage parameters, which always require an elaborate trade-off kin the device's dual functionality, AC field-effect flow control allows the simultaneous enhancement of the pump ability and mixing efficiency of the integrated device's design, which is therefore defined as the core physical content of AC field-effect-mediated ICEO fluid motion using metal-dielectric Janus micropillars. Many more investigations still need to be conducted in the future. For instance, although the present physical model can describe the phenomenon of ICEO streaming around solid objects with arbitrary electrical polarizability, it is only valid under the Debye-Huckel limit, and reasonable extensions--which include a theoretical study on large double-layer voltage-drop effects--are necessary. Under these conditions, the linear asymptotic analysis for sinusoidal AC actuation used herein may malfunction, and newly developed physical descriptions must consider the various nonlinear dynamics in electrochemical transport systems when the Dukhin number is not negligibly small.