## 2 Materials and Methods  
### Device Geometry  
We begin with a brief description of the geometry of the functional microfluidic device for causing active microscale immunoassay driven by electrothermal convection. One straight microfluidic channel, 30 \(\upmu\)m in height and 390 \(\upmu\)m in length, is arranged along the horizontal direction. Twelve identical metal strips are deposited on the channel bottom surface, which serves as a three-period discrete electrode array of four phase-shifted electrode strips in every repeating cycle. In the simulation model, for the convenience of result exhibition, it is assumed that the bottom discrete electrode array is coincidentally laid in the central portion of the device channel. Each conducting metal strip in the electrode array has a span of 10 \(\upmu\)m, and the interelectrode gap size is fixed at 10 \(\upmu\)m.  
A composite sinusoidal voltage signal, which is composed of either a standing wave (SW) or a traveling wave (TW), or their combination (SW+TW), is externally imposed on the discrete electrode array by a multi-channel AC function generator. The SW voltage has a voltage amplitude of A\({}_{\text{SW}}\) and frequency f\({}_{\text{SW}}\), and the voltage signal is sequentially phase-shifted by 180\({}^{\circ}\) along the consecutively distributed metal strips. On the other hand, the TW voltage has a voltage amplitude of A\({}_{\text{TW}}\) and frequency of f\({}_{\text{TW}}\), and it propagates in the direction of the decreasing voltage phase towards downstream, namely, the adjacent electrodes are successively reduced by 90\({}^{\circ}\) in the voltage phase along the positive x axis. It is supposed herein that only the sixth strip within the electrode array serves as the functional electrode, whose surface in direct contact with the buffer medium is coated with antibody probes. When all the electrodes are not activated by the AC power supply, there is no electrokinetic fluid motion; the antigen samples enter the channel inlet merely by pure thermal diffusion, as shown schematically in Figure 1A. In this situation, the diffusion motion of incoming analytes is extremely slow, so they cannot effectively reach the functionalized surface of the sixth electrode strip, resulting in a negligible immune reaction in the fluidic channel. Switching on the hybrid AC voltage input to the electrode sequence, the dual-component Joule heating source causes an inhomogeneous temperature field, leading to anisotropic conductivity and dielectric constant of the bulk fluid phase. Under the action of multi-frequency alternating electric fields, the fluid medium undergoes Maxwell-Wagner structural polarization. The interaction between its heterogeneous electrical properties and the applied field induces space charge clouds within the bulk liquid. These charges experience Coulomb forces and dielectric forces imparted by the electric field, ultimately exciting multi-frequency electrothermal convection, as illustrated in Figure 1B. In this regime, incoming antigen molecules are simultaneously subjected to horizontal pumping and transverse stirring through the combined effects of electrothermal convection and molecular diffusion. Upon reaching the region above the sixth electrode strip, specific antigen-antibody binding reactions occur at the functionalized surface, forming a localized depletion diffusion boundary layer. The mechanism of MET convection significantly en  
Figure 1: A schematic diagram of enhanced binding kinetics between free antigen and fixed antibody probe in microfluidic immunoassay by the phenomenon of multiple-frequency electrothermal flow (MET), which are driven by hybrid SW and TW voltage signals of distinct field frequencies and phase transition features imposed along a discrete metal strip array deposited on the bottom surface of a straight microchannel. (**A**) The slow diffusion motion of incoming antigen leads to almost no binding reaction on the functionalized surfaces of the sixth electrode strip.