#### 2.1. Basic Design of the Circulating Electrode Structure

Complicated multilayer fabrication procedure has to be implemented for manufacturing a metal-strip TW electrode array [

46]. To evade complex interconnections, we make use of a coplanar polynomial-shaped electrode design to produce a traveling potential wave circulating above the channel bottom surface (

Figure 1). By applying 90°-phase-shifted sinusoidal voltage signals to the typical four-electrode configuration with increasing phase in the clockwise direction, a TW electric field is produced above the gaps and propagates anticlockwise in the direction of decreasing field phase. The transient potential imposed on the sequential electrodes is

V_{1} =

$A\mathrm{cos}\left(\omega t\right)$,

V_{2} =

$A\mathrm{cos}\left(\omega t+90\xb0\right)$,

V_{3} =

$A\mathrm{cos}\left(\omega t+180\xb0\right)$, and

V_{4} =

$A\mathrm{cos}\left(\omega t+270\xb0\right)$, respectively. Here,

A is the voltage amplitude,

ω is the angular field frequency of the applied voltage wave (

Table 1). On this basis, electric field vector at the center of circulating electrode array is approximately of the following form:

Such an electric field of constant magnitude ${E}_{0}$ ≈ 2A/d revolves with a circular trajectory in the direction of the signal-phase propagation, and is referred to as a “rotating electric field”. Here, d = 50 μm denotes the nearest distance between opposing electrodes of 180° difference in voltage phase.

#### 2.3. Sample Preparation and Experimental Setup

In the experiment, we employ KCl electrolyte solution as the working fluid, as made by adding KCl electrolyte into Deionized (DI) water medium. A conductivity meter is applied to monitor the solution ionic strength until the electric conductivity increases up to $\sigma $ = 0.05 S/m. The electrolyte bulk has a characteristic charge relaxation frequency ${f}_{c1}=\sigma /2\pi \epsilon $ = 11 MHz, beyond which displacement current begins to dominate over Ohmic conduction. 500 nm-diameter fluorescent latex spheres are suspended in the electrolyte solution at a moderate number concentration to keep track of the electrothermal fluid motion. A commercial multi-phase function generator (TGA12104, TTi, Buckinghamshire, UK) was employed to produce sinusoidal voltage waves in a broad frequency range from 1 MHz to 35 MHz. Four-phase AC voltage signals are applied to the four circulating electrodes so that there is a 90° phase shift between the AC signals imposed on every adjacent phase. Waveform of these phase-shifted voltages is monitored by a multi-channel digital oscilloscope (TDS2024, Tektronix, Beaverton, OR, USA).

After injecting the fluorescence bead suspension into the microchamber and switching on the anticlockwise rotating electric field, rotating motion of tracer particles is observed in real time by an optical microscope (BX53, Olympus, Tokyo, Japan). During the experimental observation, focuser knob of the optical microscope should be adjusted at first, to make the electrode array most clearly presented. At this time, it is assumed that the focus plane is right on the surface of coplanar electrode array. Since the flow rotation due to ROT-ETF occurs at a certain height away from the electrode plane, the focuser knob need another regulation to make the observation plane levitated a vertical distance of 70 μm (on the order of electrode separation) above the electrode array on the basis of previous adjustment.

We take consecutive snapshots with a high-speed charge-coupled device (CCD) camera (RETIGA2000R, Qimaging, Surrey, Canada) and then superimpose the image frames in a software called ImageJ. The experimental images with particle streamlines due to superimposition operation are shown in

Figure 1d and

Figure 2. Horizontal rotating speed of latex beads due to the action of out-of-phase TWET streaming is calculated manually by dividing the physical distance moved for a particle by the time elapsed under the assistance of ImageJ software, with the measurement results shown in Figure 6a,b. The standard deviation for each data point was obtained by five repeated measurements under the same experimental conditions.

#### 2.4. Flow Components of Electrothermal Streaming in Rotating Electric Fields

In a circularly-polarized rotating electric field, sufficiently large electrolyte conductivity can induce a vertical bulk temperature gradient through Joule medium heating. This results in inhomogeneous electric properties of liquid medium across the thin fluid layer. Such dielectric gradients interact with the applied rotating field, inducing a volumetric free charge distribution that lags behind the propagation of applied voltage wave. These charged ions experience a Coulomb force in the same electric field which forces them into electrophoretic motion, and drag the surrounding fluid along through viscous effect. The bulk polarization process described above effectively leads to electrothermal vortex flow on the phase-shifted polynomial microelectrode array. According to the basic theory of Maxwell-Wagner structural polarization, ROT-ETF includes two sets of EHD flow components [

41]:

(1) TWET component due to out-of-phase induced polarization

Out-of-phase component of the induced polarization generates one horizontal induction vortex rotating along the

z axis above the circulating electrode array. The TWET whirlpool is maximized if the period of AC voltage waves is commensurate with the characteristic relaxation time of the dielectric dispersion process [

47,

48,

49]. That is, the horizontal flow rotation induced by the vertical electrorotational torque is most evident at Debye frequency of the fluid medium

${f}_{c1}=\frac{\sigma}{2\pi \epsilon}$ for onset of bulk ionic screening.

(2) SWET component due to in-phase induced polarization

Since electrodes with 180° phase difference are placed opposite to one another in the four-phase polynomial electrode configuration, potent SWET flow component behaving as multiple vortex pairs in perpendicular orientation to the electrode plane can be produced by the in-phase component of applied voltage wave. The vertical SWET streaming possesses a low-frequency conductivity plateau where motion of free charge dominates, as well as a high-frequency permittivity plateau where dielectric polarization plays an important role. Since the Coulomb force and dielectric force counterbalance one other, SWET vortex pairs across the thickness of fluid layer vanish at a characteristic crossover frequency

${f}_{c2}=\frac{\sigma}{2\pi \epsilon}\sqrt{\frac{-\beta}{\alpha}}=\frac{\sqrt{5}\sigma}{2\pi \epsilon}$ [

41]. Because flow field of SWET in DC limit is much stronger than that at high field frequencies, the horizontal TWET rotating whirlpool appears to dominate over the vertical SWET vortex pairs at

f >

f_{c2} =

$\frac{\sqrt{5}\sigma}{2\pi \epsilon}$. In addition, within low-frequency ranges

f <

f_{c1}, fluid motion of TWET whirlpool diminishes, while that of vertical SWET streaming enhances, which would exert a negative impact on the rotating flow pattern of out-of-phase induction vortex. Specifically, the horizontal TWET whirlpool shrinks in size, and exhibits more helical flow streamlines cascading downward at lower field frequencies.

#### 2.5. Computational Model

Two different heat transfer models are developed herein to reconstruct the heat transfer process across the gold microelectrode arrays for dealing with distinct experimental conditions:

(1) None-cooling condition

Since thickness of the electrode layer is extremely thin (~100 nm) compared to other geometric dimensions in the experimental chip, the electrodes are treated as transparent media for heat transfer. That is, both temperature and normal heat flux are continuous across the electrolyte/substrate interface, as if the circulating electrode array does not exist at all.

(2) Cooling condition

The electrodes are made of gold material in our device, which is of thermal conductivity k

_{Au} = 340 W·m

^{−1}·k

^{−1}, considerably higher than that of water solution k

_{water} = 0.6 W·m

^{−1}·k

^{−1} and glass substrate k

_{glass} = 1 W·m

^{−1}·k

^{−1}, so that the electrode structures can be treated as ideal thermal conductors which are effectively isothermal bodies. Then, for inputting voltage signals from function generator to the microelectrode arrays, external wire connection has to be achieved by fabricating large-scale electrode pads of millimeter dimension, as shown in

Figure 1a,b. In similar device configurations, heat exchange between metal electrode bars and ambient environment has a propensity to occur due to external natural convection. Since gold electrodes are good thermal conductors, they can transfer cooling energy from ambient environment to the device internal, which would make the electrode bars not only an isothermal body but also fixed at the referential temperature T

_{0} = 293.15 K of atmospheric condition for a sufficiently large heat transfer coefficient. That is, because gold microelectrodes of excellent heat dissipation capability are connected to external wires by large-scale metal pads, electrode cooling due to external natural convection ought to be taken into consideration and modeled by setting the electrode surface at the ambient temperature T

_{electrode} = T

_{0} = 293.15 K in the simulation analysis.

A commercial FEM software, Comsol Multiphysics 5.2 (COMSOL, Stockholm, Sweden), is used to solve the mathematical boundary-value problem for theoretically obtaining the electrothermal flow field, and detailed governing equations and boundary conditions have been presented in our previous work [

34]. For the circulating electrode array, shape of the polynomial electrode edge is represented by the following hyperbolic equation:

Rotating the hyperbolic curve by 45° around the

z axis, we obtain the electrode pattern in the first quadrant. Subsequently, by conducting several steps of mirror imaging operations, the electrode pattern within the entire

x-

y plane is digitally established, as shown in

Figure 3b. The non-isothermal harmonic electric field, heat transfer and electrothermal flow field are solved in a fully-coupled manner using the enhanced ACET model derived in [

34,

50]. In the numerical simulation, we only need to calculate the electric field and fluid motion in the electrolyte solution, while the energy balance equation for temperature field has to be solved within the entire fluidic device, including the fluid bulk, glass substrate and patterned gold electrodes (

Figure 3a):

(a) Glass substrate of 500 μm in thickness

This domain has a thermal conductivity k_{glass} = 1 [W·m^{−1}·k^{−1}], with the bottom surface of the fluidic device set at ambient temperature due to strong natural convection at the microscope platform.

(b) 500 μm-thick liquid layer

The electrolyte solution has an electric conductivity 0.05 [S/m], dielectric permittivity

$\epsilon $ = 7.08 × 10

^{−10} [F/m] and thermal conductivity k

_{water} = 0.6 [W·m

^{−1}·k

^{−1}], where several large-voltage effects including nonlinear Joule heating source, temperature-dependent dynamic viscosity and improved electrothermal body force are taken into account [

34,

50].

(c) Four-quadrant polynomial electrodes

The electrode array is applied with 90°-phase-shifted TW voltage signals in sequence, resulting in a counterclockwise-propagating rotating electric field. Accordingly, the complex amplitude of AC voltages imposed on the four electrodes corresponds to A, jA, -A, -jA, respectively, with j denoting the imaginary unit.