3.1. Microfluidic Device

A schematic of the microfluidic device used in this study is shown in Fig. 2(a). The device consists of a polydimethylsiloxane (PDMS) microchannel bonded to a glass substrate with patterned coplanar electrodes. The PDMS microchannel has a straight rectangular cross-section with a width and height of 100 and 50 μm, respectively.

For the optical observation of fluorescent particles through the sidewall of the channel, the wall must be sufficiently thin and optically flat. The sidewall thickness is set to 117 μm, which is optimized to obtain clear particle images without leakage. The outer surface of the sidewall is fabricated to be as flat as a coverslip because it is commonly used as the bottom substrate in micro-PIV measurements. During the molding process in softlithography, a flat glass plate was used as part of the mold to achieve the required surface flatness. In addition, an objective lens with a correction collar is used to reduce spherical aberration caused by differences in the optical path length between the sample and objective lens. The \(xy\)- and \(xz\)-plane observations through the glass substrate and PDMS sidewall exhibit different optical paths; therefore, the correction collar is adjusted for each observation direction to improve the particle-image quality. This adjustment is important for reducing view-dependent optical aberrations in the sidewall observation.

The electrodes were fabricated from indium tin oxide (ITO) by sputtering and patterned using a wet-etching process. The ITO film is highly transparent in the visible wavelength range; therefore, optical measurements can be performed through a glass substrate with ITO pattern beneath the microfluidic device. Two types of electrode patterns were used, as shown in Fig. 2(b). One pattern has an electrode gap oriented perpendicular to the direction of the main flow, while the other has an inclined gap with an angle of 60° relative to the main flow direction.

Ultrapure Milli-Q water and an aqueous KCl solution were used as the working fluids to measure pressure-driven laminar and electrokinetic flows, respectively. The pressure drop in the microchannel was generated by the difference in liquid levels between the inlet and outlet reservoirs. The electrical conductivity of the KCl solution (Wako) was adjusted to 1.5 S/m. Fluorescent polystyrene particles with a diameter of 0.5 μm (Fluoro-Max G500, ThermoFisher) were added as tracer particles. The excitation and emission wavelengths of the fluorescent particles were 505 and 515 nm, respectively.

3.2. Measurement System and Procedure

Figure 3 illustrates the schematic of the experimental setup. The measurement system was based on an inverted microscope equipped with common components for fluorescence imaging, including an objective lens, a filter set, an illumination source, a camera, and a motorized stage.

The objective lens (Nikon, CFI Plan Fluor 40\(\times\)) had a magnification of 40\(\times\) and a numerical aperture of 0.6. A continuous mercury lamp (Nikon, C-HGFL) was used as an illumination source. Fluorescence emitted from tracer particles was recorded using a scientific complementary metal-oxide-semiconductor camera (Hamamatsu, ORCA-Flash2.8) with a pixel size of 3.63 μm, an image resolution of \(1920 \times 1440\) pixels, and a 16-bit dynamic range. The target stage was controlled to scan the focal plane with a positioning accuracy of 0.1 μm. Electrodes on the bottom wall of the microfluidic device were connected to a function generator (Tektronix, AFG3102) to apply an AC voltage with controlled amplitude and frequency (5–10 V\(_\textrm{p-p}\) at 1 MHz).

In the correlation-based micro-PIV analysis, the calculated particle displacement represents the spatially averaged displacement of tracer particles within an interrogation window. The measurement plane in micro-PIV has a finite depth determined by the optical characteristics of the imaging system. Therefore, the interrogation region can be considered a measurement volume. In the present experiments, the measurement depth ²⁰ was 7 μm based on the optical parameters of the objective lens and fluorescence wavelength. The remaining analysis parameters were set similar to those used in conventional micro-PIV. The horizontal spatial resolution defined by the interrogation window size used in the correlation analysis was set to \(7.08 \times 7.08\) μm\(^2\), which is comparable to the measurement depth. Therefore, the spatial resolution of the reconstructed 3D–3C velocity field can be considered nearly isotropic.

Fluorescent images were acquired under low-particle-concentration conditions to improve the signal-to-noise ratio of recorded images. Before the correlation analysis, background noise reduction and image superposition were performed to enhance particle visibility. Finally, 100 instantaneous velocity fields were averaged to reduce uncertainty caused by the inherent Brownian motion of tracer particles in the fluid.

4.1. Verification of 3D Velocity Reconstruction

In this study, the validity of the developed orthogonal-plane micro-PIV technique was verified prior to the measurement of electrokinetic flow under an AC electric field in the microfluidic device. As a preliminary experiment, a tilted rectangular microchannel was employed as a reference flow. In this configuration, the microfluidic device was tilted with respect to the \(z\)-axis, as illustrated in Fig. 4. Subsequently, the focal plane of the objective lens was scanned along the depth direction to obtain the volumetric velocity field.

The analytical solution of the streamwise velocity \(u_{0}(y,z)\) for fully developed laminar flow in a rectangular straight channel without tilt is given as ²¹

In a simple pressure-driven flow in a horizontally aligned microchannel, only the streamwise velocity component is nonzero. However, a \({z}\)-component of velocity \({w}\) appears and increases with increasing tilt angle when the channel is tilted by an angle \(\gamma\) with respect to the \({z}\) direction. Therefore, velocity components in the tilted channel (\(u_{\gamma}\), \(w_{\gamma}\)) can be expressed as

Figure 5 shows the velocity distribution measured in the center plane of the microchannel. The circles represent the experimentally measured velocities, while the solid line represents the analytical laminar velocity profile calculated using Eqs. (7) and (8), respectively. In this experiment, the pressure gradient \({dp}/{dx}\) was not directly measured; however, fitting the analytical velocity distribution to the measured velocity profile using \({dp}/{dx}\) as a fitting parameter is sufficient to evaluate measurement accuracy ²¹.

Experimental results agreed well with the analytical solutions, with deviations of 3.8% and 5.5% for the \({u}\) and \(w\) components, respectively. These deviations are smaller than the typical measurement uncertainty reported in the literature, which is \(\sim\)10% ¹³. Moreover, the tilt angle estimated from measured velocity components was in good agreement with the actual tilt angle of 2.64°. These results confirm the validity of the orthogonal-plane micro-PIV technique for 3D velocity measurements in microfluidic platforms.

4.2. Characterization of AC Electrothermal Flow

The ACET effect is a fluid motion induced by ACEK phenomena. Under an AC electric field, the fluid is locally heated by Joule dissipation, which produces spatial gradients in the electrical conductivity and permittivity of the fluid because of their intrinsic temperature dependence. In the presence of these property gradients and an applied electric field, an electrohydrodynamic body force acts on the fluid, resulting in ACET flow. According to theory ⁸, the ACET body force \(\mathbf{F}_{ET}\ \)can be expressed as

The volumetric heat generation in the fluid caused by Joule heating can be expressed as

Joule heating becomes more significant in conductive liquids; therefore, ACET flow is effectively generated in relatively high-conductivity solutions. The characteristic ACET velocity is proportional to the fourth power of the applied voltage \({V}\). Under the present experimental conditions, the temperature increase in the fluid is \(\sim\)1 K, indicating that the effects of heating on the electrolysis, evaporation, and chemical degradation are negligible.

Side-view measurements are performed using an orthogonal electrode device to observe the fundamental 2D structure of ACET flow. Fig. 6 shows the velocity field in the \({xz}\)-plane at the spanwise center of the channel under an applied voltage of 9 V\(_\textrm{p-p}\) at 1 MHz. A circular stirring flow was observed along the electrode gap, conveying fluid from the bulk region to the bottom surface of the microchannel. The flow field results from the superposition of the pressure-driven main and ACET flows. For the velocity field shown in Fig. 6, pressure-driven and ACET flows are considered to be of the same order of magnitude, resulting in the observed wavy flow pattern with rotational flow structures; this reflects a comparable contribution of ACET. The contribution of this vertical transport represented by the \({z}\)-component velocity is induced by the electric field; therefore, the average \(z\)-component velocity in the region \(-5 < x < 5\) μm and \(15 < z < 25\) μm was evaluated to quantify the voltage dependence of ACET flow. As shown in Fig. 7, the measured velocity followed a power-law dependence on the applied voltage with an exponent of 4.01, which is in excellent agreement with the theoretical \({V}^{4}\) scaling because Joule heating scales with \({V}^{2}\) and the electrohydrodynamic body force scales with \({E}^{2}\).

Furthermore, this result indicates that the observed flow was dominated by ACET rather than by other ACEK phenomena. For example, AC electroosmosis (ACEO) and dielectrophoresis (DEP) scale with the square of the applied voltage \({V}^{2}\). In addition, ACEO is prominent at considerably lower frequencies in the order of several kilohertz ²², whereas the experiments in this study were performed at 1 MHz. Under this condition, the DEP-induced motions of tracer particles were negligibly small. Therefore, the contribution of other ACEK mechanisms can reasonably be neglected.

A strong 3D ACET flow was generated in the channel when the inclined electrode geometry was employed. Fig. 8(a) shows the reconstructed 3D flow field in an inclined-electrode device at 10 V\(_\textrm{p-p}\) and 1 MHz; only half of the channel width is shown. A characteristic stirring motion was observed along the inclined electrode gap, and the inclination of the electrode introduced an additional spanwise component of fluid motion, as shown in Fig. 8(b). Consequently, the overall flow field was formed by the superposition of the pressure-driven laminar mainstream and inclined ACET-induced secondary flow.

In terms of mass transport, this 3D stirring motion enhanced the delivery of suspended analytes from the bulk fluid toward the reactive surface or adhered cell. The additional spanwise and wall-normal transport reduced local transport limitations near the bottom and increased the probability of interaction between suspended species and immobilized molecules on the surface. This mechanism explains the enhancement in the surface reaction efficiency induced by ACEK actuation.

Meanwhile, the present results suggest an additional implication for cell-based microfluidic systems. The ACET-induced flow introduces wall-normal recirculation and modifies the near-wall velocity gradient, and therefore, it locally alters the shear environment experienced by cells cultured on the substrate. Thus, the 3D flow structure that enhances surface transport can also provide localized mechanical stimulation to adherent cells through shear stress. The near-wall shear rate was estimated from the velocity distribution shown in Fig. 8. The inclined ACET flow increased the maximum near-wall velocity gradient by up to approximately twofold compared with the condition without voltage application. This is important in microphysiological systems and cell culture platforms, where cellular behavior is strongly affected not only by biochemical transport but also by hydrodynamic stimuli. A recent study ⁹ demonstrated that ACET flow modulation can enhance the osteogenic differentiation of human mesenchymal stem cells by generating pulsatile stimulation of adherent cells on a chip. However, the underlying 3D flow structure has not been characterized.

Consequently, the reconstructed 3D–3C velocity field is valuable for understanding reaction enhancement by ACEK flow and for quantitatively discussing how flow modulation by the ACEK effect contributes to localized shear stimulation near the culture surface.