## 3 Results and Discussion
### Numerical Characterization of Electrothermal Induced Convection
#### 3.1.3 Multiple-Frequency Electrothermal Induced Convection  
The flow behaviors of SWET and TWET have been analyzed sequentially, and their ideal working conditions were obtained. Since the characteristic operating frequencies of SWET and TWET convection are significantly different, the cross product of the induced space charge with the in situ electric field of another actuating frequency always averages to zero over time. In this way, SWET and TWET can be added together to the polarizable electrolyte solution at their respective ideal frequency to engender the phenomenon of MET convection, in which the SW and TW electric field is mutually coupled through the joint action of dual-component Joule heat to given rise to a new flow state, and the ideal synthetic fluid motion driven by hybrid voltage signals is obtainable through direct numerical simulation. Figure 5A-C shows the calculation results of the MET flow field at the ideal frequency combination of fsw = 100 khz and ftw = f MW, under varying SW voltages and a constant TW voltage Atw = 6 V. As shown in Figure 5A, for Asw = 2 V and Atw = 6 V, a brisk pump motion is induced by out-of-phase electrothermal effect in the working fluid, with only insignificant vortices at the inlet. Raising the SW voltage to Asw = 6 V with TW voltage kept unchanged, as shown in Figure 5B, chaotic vortices appear on electrode surfaces, the lateral stirring flow rate is greatly enhanced, and the horizontal flow rate is weakened. By further raising Asw to 12 V, as shown in Figure 5C, the pump effect almost disappears, and the resulting MET flow field is dominated by in-phase electrothermal micro-vortices. Figure 4: Quantitative characterization of TWET flow field as a function of the imposed TW field frequency. (**A**) fTW-dependent total flow velocity and its horizontal component; (**B**) fTW-dependent vorticity magnitude. The simulation results of parameterized scanning of SW voltage and TW voltage for given driving frequencies are exhibited in Figure 5D-I. Variation of the voltage amplitude ranging from 0 V to 12 V is defined in the numerical calculation, respectively, to explore the  
Figure 5: Simulation analysis of MET fluid motion driven by a hybrid SW/TW voltage signal at the ideal frequency combination in a straight microchannel. (**A–C**) A surface and streamline plot of the synthetic MET flow field under varying voltage amplitudes of SW and TW components, (**A**) at Asw = 2 V and Atw = 6 V, (**B**) at Asw = 6 V and Atw = 6 V, (**C**) at Asw = 12 V and Atw = 6 V. (**D**) Effect of Asw on maximum temperature elevation. (**E**) Effect of Atw on maximum temperature elevation. (**F**) Effect of Asw on electrothermal pump velocity. (**G**) Effect of Atw on electrothermal pump velocity. (**H**) Effect of Asw on electrothermal flow vorticity. (**I**) Effect of Atw on electrothermal flow vorticity. influence that SW voltage and TW voltage have on the temperature rise, pump capability, and rotating vorticity of the resulting MET fluid motion. In Figure 5D,E, the maximum temperature rise within the fluid increases with both SW and TW voltages, but under the same voltage magnitude of SW and TW signals, the temperature elevation is almost the same, so the two distinct electric field components have essentially similar contributions to the dual-component electric heat generation. Due to the small degree of temperature elevation of up to 6 K, the imposed multiple frequency AC signals will not affect the biological activity of target molecules such as antibodies. As shown in Figure 5F,G, the horizontal pump speed from MET rises from 125 \(\upmu\)m\(\cdot\)s\({}^{-1}\) to 520 \(\upmu\)m\(\cdot\)s\({}^{-1}\) when the amplitude of SW voltage is elevated from 0 to 12 V with a difference of 4.25 times, while the pump speed increases from 0 to 2100 \(\upmu\)m\(\cdot\)s\({}^{-1}\) when the TW voltage is enhanced from 0 to 12 V with a difference of infinity times.