Tuning AC Electrokinetic Flow to Enhance Nanoparticle Accumulation in Low‐Conductivity Solutions

This study presents a novel AC electrokinetics‐based microfluidic approach for nanoparticle trapping and accumulation in low‐conductive aqueous solutions. The concentration performance is systematically investigated by tuning the applied voltage and frequency, showing that AC electrothermal flow (ACET)‐induced vortex trapping provides a field strength‐dependent concentration enhancement and a high concentration factor. The findings reveal a substantial enhancement in the concentration of polystyrene nanoparticles with sizes of 100 nm. Specifically, a 16‐fold enrichment in the concentration is achieved compared with the initial concentration of the sample. In addition, the effectiveness of a high‐frequency AC voltage (50–150 kHz) versus a low‐frequency accumulation (1–20 kHz) for nanoparticle accumulation is compared and it is determined that at high frequencies, the trapped nanoparticles accumulate at a single area at the electrode gap, which differs from the low‐frequency accumulation observed in previous studies. The complex behavior of nanoparticle accumulation is analyzed, including the differences in the hydrodynamic flow patterns between AC electroosmosis and ACET flow. The proposed technique provides a powerful tool for the efficient and controllable manipulation of nanoparticles and contributes to a highly sensitive characterization of nanomaterials in low‐conductivity liquid samples in microfluidic systems through efficient particle trapping.


Introduction
Microfluidic-based analytical techniques in biological and engineering applications have recently attracted considerable DOI: 10.1002/admi.202300478[3] However, with microfluidics, analysis is frequently performed on a small proportion of the available samples, [4][5][6] which may restrict the overall detection sensitivity, particularly for the detection of low-concentration species in a sample.Analyzing only a small proportion of the available sample increases the probability of missing rare or low-concentration species that may exist in other regions of the sample.For example, when a small volume of a biological sample is analyzed, the detection of low-abundance biomolecules or cells present in other parts of the sample may not be possible, resulting in a lack of sensitivity in the analysis. [4,5]Moreover, controlling the behavior and movement of the nanoscale target is challenging due to their small size and Brownian motion, [7] which can cause nanoscale target to diffuse and disperse in solution.To address these issues, researchers have developed various techniques to improve the detection sensitivity in microfluidic analyses.These include methods for sample preconcentration, such as microfluidic trapping or filtration, [6,[8][9][10][11] and signal amplification, such as surface-enhanced Raman spectroscopy or fluorescence amplification. [12,13]By improving the sensitivity of microfluidic analyses, these techniques can enable the detection of low-concentration species and increase the overall diagnostic and analytical value of microfluidic platforms.
Various particle trapping approaches have been investigated in microfluidics using passive and active mechanisms. [14,15]Passive approaches rely on inertial flow or sophisticated channel construction, whereas active approaches have a low dependence on channel construction and employ an additional external force to move the particles.Furthermore, their performance may be flexibly altered by adjusting the control signal.[21][22][23] In particular, electrokinetic forces are used in these techniques to concentrate particles because they are ideally suited for microfluidic applications and can easily create a high field strength with a minimal voltage across a wide frequency range. [7]In addition, their handling is easier compared with other techniques.
Electrokinetics is a well-known phenomenon for transporting particles in solution in microfluidic devices.The electrokinetic concentrators have electrodes embedded in a microchannel to generate fluid motion when a voltage is applied.The electrical properties of the fluid, including its conductivity and permittivity, as well as its voltage characteristics, have a significant impact on the fluid motion and strength of the induced flow. [24]A DC or AC field can be used to create electrokinetic effects.The AC method offers various advantages over the DC method, including a lower temperature rise due to Joule heating and less electrolysis of the solution. [7]C electrokinetics is an efficient approach for particle manipulation, [25] concentration [26] and focusing, [27][28][29] demonstrating its potential for use in various applications.In AC electrokinetic techniques, particles are driven through a microfluidic device, and forces, such as dielectrophoretic (DEP), AC electroosmosis (ACEO), or AC electrothermal flow (ACET), are applied to the particles or solution to manipulate the particles. [30]For example, DEP is used to trap and manipulate nanoparticles in microchannels and uses the electric field gradients generated by patterned electrodes to generate forces that act on the particles. [31,32]EP is especially effective near the edge of the electrode and decays rapidly away from the electrode due to its dependence on the gradient of the square of the electric field.Elaborately, DEP arises when the local electric field interacts with the induced charge on the particle's surface, which includes both free and bound charges.This phenomenon occurs because of Maxwell-Wagner interfacial polarization, often associated with the effect of induced double-layer polarization on polarizable colloids or the non-uniform surface electrokinetic transport of counterions within the native double layer on insulating charged particles. [33]n addition, it is influenced by the particle size and its electrical characteristics.Furthermore, for small particles with diameters of approximately 100 nm, the Brownian motion will likely become comparable to or dominate trapping DEP forces.][36] In addition, as the size of the particles becomes smaller, the particle motion induced by the fluid flow will remain constant and could even dominate over the other forces.Thus, utilizing ACEO and ACET has the potential to improve the particle accumulation, especially for submicron and nanoparticles.
The ACEO phenomenon can effectively be used to manipulate particles in low-conductivity solutions with electric conductivities less than 1 × 10 −2 S m −1 [37] or 1 × 10 −1 S m −1 . [38]In highconductivity solutions, such as saline or buffer solutions, which are intensively used in biological research, ACEO cannot be used because of the compression of the electrical double layer at high ionic concentrations in a biofluid. [38]Our previous studies have reported the successful accumulation of microscale particles in a low-conductivity solution with an electric conductivity of 44 × 10 −4 S m −1 using ACEO in a microfluidic channel, resulting in an overall concentration rate of nearly 98%. [28]For nanoscale particles, an additional electrode geometry was required to control the accumulation position and improve the accumulation perfor-mance due to the intrinsic diffusive motion of the particles. [29]On the other hand, ACET occurs when a fluid experiences temperature gradients induced by an external electric field.These temperature variations within the fluid lead to changes in its electrical properties like conductivity, permittivity, viscosity, and density.As a result, the interplay of these gradients with the electric field gives rise to fluid motion and bulk fluid forces.Several models have been developed to explain ACET, considering scenarios with small temperature gradients, [30] assuming a uniform salt concentration distribution throughout the microfluidic device, [39] and even considering a microscopic model where the salt concentration distribution is unknown beforehand. [40]ACET flow is effective for a range of conductivities of 1 S m −1 because it needs Joule heating to generate the driving body force on the fluid. [38]evertheless, it has limitation of the applied voltage, which can lead to overheating and affect the stability and accuracy of the flow.Furthermore, if the fluid conductivity is too high, the generated electric field may cause undesirable effects, such as bubble formation or particle aggregation. [41]While ACET can typically only be used in a limited capacity for high-conductivity solutions, it remains applicable for low-conductivity solutions.In addition, utilizing ACET in low-conductivity solutions presents an opportunity to avoid the limitations that arise in high-conductivity solutions, thereby enhancing the potential for concentration improvement.
In this study, highly efficient nanoparticle accumulation is studied using the ACET.Specifically, the concentration behavior of 100-nm-polystyrene nanoparticles (PsNPs) dispersed in a low-conductivity solution is investigated with an electric conductivity of 1 × 10 −4 S m −1 within a microfluidic device comprising symmetric coplanar electrodes attached to a microchannel.The concentration performance is systematically analyzed under various voltage characteristics and suggest the optimal frequency and amplitude settings to achieve the highest concentration factor (CF) within the device.These findings demonstrate the potential of this approach for enhancing the concentration and accumulation of nanoparticles in a precise and controlled manner.The technique has potential applications in various fields to enhance the detection sensitivity.

Accumulation Mechanism
The primary objective of this study was to enhance the accumulation of nanoparticles dispersed in low-conductivity solutions.To achieve this, a microfluidic device was fabricated and used to observe the behavior of nanoparticles under the influence of an AC voltage.Conventional lithography techniques were used to pattern a pair of indium tin oxide (ITO) electrodes onto a glass substrate, which were then assembled into the microchannel.Figure 1a shows a schematic of the microfluidic device, which features a pair of symmetric coplanar electrodes in contact with an aqueous solution and was used to investigate the basic mechanisms of nanoparticle accumulation.By applying AC voltages with different amplitudes and frequencies across the electrodes, the resulting accumulation of nanoparticles was observed using fluorescence microscopy.The results demonstrate the versatility and dramatic capabilities of AC electrokinetics.By adjusting the frequency alone, different behaviors of particle motion and accumulation regimes could be observed.Figure 1b shows an example of the rotational fluid motion and accumulation positions of nanoparticles under an AC electric field in a cross-sectional view of the microfluidic device.Figure 1c indicates a special device design used specifically for lateral observation purposes.The lateral observation technique [29] is utilized to investigate the flow pattern under an AC field.In this design, the electrode gap becomes perpendicular to the main flow direction, and the inlet and outlet of the channel are shifted.The distance between the channel wall and device edge is decreased to facilitate observation.The unique device design in Figure 1c allows for a more precise and detailed investigation of nanoparticle accumulation and behavior under the applied AC electric field, providing valuable insights for particle movement in the entire cross-sectional area induced by AC electrokinetics.The transportation of particles is effective as long as the convective motion by the transporting flow overcomes the inherent diffusive motion of the particles.As a result, the particles are concentrated at the balance position of the advective force and diffusive behavior.
The Clausius-Mossotti (CM) factor is a mathematical function that depends on the complex permittivity of both the particle and surrounding medium, and its value ranges from 1 to -0.5.When a particle has a higher degree of polarizability than its surrounding medium, the CM factor is positive, and the particle exhibits a positive DEP, which causes it to move toward regions of higher electric fields.Conversely, if the particle is less polarizable than the medium, it exhibits a negative DEP and moves toward regions of lower electric fields. [42]At all experimental conditions in this study (1 -150 kHz), the real part of the CM factor, shown in Figure 2, is greater than zero, indicating that the particles experienced a positive DEP and were moving toward areas of higher electric fields.
In the case of low frequencies, the particles experienced strong ACEO and were entrained to the electrode surface far from the electrode edge. [24]Although a positive DEP was not dominant in these conditions, it still existed and assisted in attracting the particles toward the electrode edge.Eventually, the particles experienced a combination of DEP and ACEO forces, which caused them to accumulate along the electrode in two different area, which were far from the edge. [27]In contrast, at high frequencies, the advective forces pushed the particles toward the gap center, where they accumulated in a single area.This accumulation mode inside the electrode gap has not been reported previously.
Figure 3 shows the accumulation behaviors of 100-nm-PsNPs in the device before and after the application of an AC electric field.The pair of yellow dashed lines in Figure 3 represent the position of the electrode edges, and the area between them corresponds to the electrode gap. Figure 3a shows the initial case before the application of a voltage, where the intensity distribution of the PsNPs served as a reference to observe the change in intensity distribution after a voltage was applied.At low frequencies where the ACEO flow was dominant, the accumulation sites were only present along the electrode at approximately 100 μm from the centerline on both sides, as shown in Figure 3b.When the frequency was increased to the range where the ACEO effect was diminished, the nanoparticles accumulated along the electrode inside the gap, as indicated in Figure 3c.This suggested that the position of the nanoparticle accumulation could be changed and predetermined by controlling the AC frequency, which could be used to improve the efficiency of the nanoparticle concentration and accumulation.Therefore, tuning the AC electrokinetic conditions is a promising approach for enhancing the accumulation of nanoparticles in low-conductivity solutions.

Accumulation Position
AC electrokinetics can be used to control the accumulation position of suspended particles along an electrode surface. [43]The position of particle accumulation is dependent on the applied AC frequency.To investigate this effect, an experiment was conducted to accumulate 100-nm-PsNPs at a fixed voltage of 10 V pp under different frequency conditions.The distance between the electrodes (w) was 16 μm, and the characteristic electric field strength (E) was calculated to be 0.6 × 10 6 V m −1 .This calculation is based on the simple assumption that the E in volts per meter (V m −1 ) can be expressed as V pp /w, where V pp is the peak-to-peak voltage in volts (V) and w is the distance between the electrodes.The electrical conductivity () of the solution was set to 10 −4 S m −1 .Figure 4 shows the accumulation positions of PsNPs at frequencies in the range of 0.7-70 kHz.The yellow parts in Figure 4 represent the surface of the electrode, and the area between them corresponds to the electrode gap.At lower frequencies, typically between 0.7 and 20 kHz, all accumulation positions were located on the surface of the electrode at an almost equal distance from the center of the electrode gap (60 μm for 0.7 kHz and 20 μm for 20 kHz).As the frequency increased, the peak positions moved inward and closer to the electrode gap.In a transient frequency range of 25-45 kHz, the accumulation positions appeared inside the electrode gap.Two accumulation areas were located approximately 5 μm from the gap center at frequencies of 25 and 30 kHz.As the frequency increased further, the areas moved closer to the center line, eventually overlapping to form a single peak that was nearly in the center of the gap at 70 kHz.These results demonstrate the potential of tuning the AC electrokinetic flow to accu- mulate particles in a single or two predetermined areas using a single pair of electrodes.

Particles Movement Analysis
The behavior of particles under non-uniform AC electric fields can be attributed to three predominant AC electrokinetic phenomena, namely DEP, ACEO, and ACET.DEP occurs when particles are subjected to a non-uniform electric field.Particles experience a net force toward either the region of higher or lower E (positive and negative DEP, respectively).A positive DEP causes particles to accumulate at the electrode edge, while a negative DEP causes particles to be repelled from this region and accumulate at areas with lower E values, such as the center of the electrode surface or above/between the electrodes. [42]n contrast to DEP, both ACEO and ACET are hydrodynamic phenomena that cause fluid motion, which in turn affects the movement of suspended particles.ACEO is the motion of fluid induced by the interaction between an electric field and the induced-charge layer formed at the electrode surface. [42]ACEO generates a set of continuous counter-rotating vortices that cause particles to orbit out of the plane near the electrode or collect on the electrode surface.Similarly, the ACET could have a rotational pattern and is caused by temperature gradients induced by Joule heating.These gradients create a variation in the electrical conductivity and permittivity of the fluid, which induce fluid motion through their interaction with the electric field. [30]he experimental results presented in Figure 5 depict the cross-sectional view of the movement of 100-nm-PsNPs under an AC electric field applied at several frequencies.The E and solution electrical conductivity were 0.6 × 10 6 V m −1 and 10 −4 S m −1 , respectively.The pair of yellow rectangles represent the ITO electrode positions, with the area between them corresponding to the gap.A clear vortex-like rotational flow pattern is observed in the low-frequency range where the ACEO is dominant.The direction of the particle movement is indicated by the red arrows in Figure 5.At a frequency of 1 kHz, the vortices entrain the particles from the bulk approximately 135 μm above the electrode surface.The tangential component of the electric field interacting with the electric double layers (EDL) causes particles to travel along the electrode surface and accumulate at two positions far from the electrode edge.Here, the fluorescent particles accumulated on the electrode surface approximately 140 μm from the centerline between the electrodes.As the frequency increased, the ACEO forces decayed, the rotational flow decreased, and the vortex size became smaller.Specifically, the vortex height decreased from 130 μm at 1 kHz to 40 μm at 50 kHz before disappearing at a higher frequency.This represents a decrease in the area of the bulk that can be manipulated.
The vortex height typically decreased as the frequency of the applied voltage increased due to the reduced ACEO effect.This is because at higher frequencies, the AC electric field did not penetrate as deeply into the solution, [44] and not enough induced net electrical charge was accumulated, [45] leading to a shallower depth of the induced charges and a weaker electrohydrodynamic force.As a result, the fluid motion near the electrode surface was less intense and the vortex height was reduced.At extremely high frequencies, the fluid motion became negligible, and the system behaved more like a purely capacitive system.At a frequency of 70 kHz, an accumulation area appeared between the electrodes.As mentioned earlier, the frequency range employed in our experiments corresponds to a region where positive DEP exist, rather than negative DEP.The negative DEP frequency range, as indicated by the C-M factor curve, shown in Figure 2, is higher than the range investigated in this study.Although the experiment conditions were in the positive DEP region, particle attraction to the high electric field region was not observed.Considering this information, we attribute the observed shift in particle accumu-lation to the formation of counter vortexes created by the ACET phenomenon rather than the influence of DEP.These counter vortexes play a significant role in directing particle accumulation towards the center of the gap.Here, the accumulation between the electrode at 70 kHz was attributed to the ACET.
In the absence of any applied voltage to the electrodes, the ions in an aqueous solution are uniformly dispersed and no forces are exerted on them.However, with the application of an AC electric field, the ions in the solution respond to the charge on the electrodes during each half-cycle.When the voltage is initially turned on, current flows through the electrolyte, causing the ions in the solution to migrate toward the electrodes along the electric field lines.This leads to the formation of an EDL over the electrodes, with the strongest electric field being present at the edges of the electrodes.The EDL at this location charges quickly and is significantly screened at a characteristic charging time.As the EDL continues to charge, the electric field lines in the fluid bulk are deflected around the screened electrode edges, producing a tangential component of the electric field.
In this case, the ions present in both the EDL and aqueous solution affect fluid motion.The sensitivity of the EDL to the frequency of the AC electric field is significant.At low frequencies, where the frequency is less than the relaxation frequency of the system, the slow oscillation of the electrode charge gives ions sufficient time to respond.Consequently, the electrode is fully charged, and the complete formation of an EDL occurs.After the EDL is fully charged, no electric force is exerted on the ions present in the aqueous solution, and the force produced by ions in the EDL dominates, causing the ACEO flow.
Conversely, at high frequencies, where the frequency is larger than the relaxation frequency of the system, there is insufficient time to form the EDL, and the effect of ions present in the EDL weakens.As the frequency increases further above the transient level, the force produced by ions in the EDL becomes so weak that the forces produced by ions in the bulk solution become dominant.
An ACET is generated by the interaction between a nonuniform electric field and a temperature gradient induced by Joule heating in a conductive fluid.At high frequencies, the electric field changes rapidly, and the temperature gradient is unable to equilibrate with the fluid before the next cycle begins.As a result, the temperature gradient lags behind the electric field, and the resulting ACET is dominated by the electric field rather than thermal convection.In addition, at high frequencies, the ACEO effect becomes weaker, allowing the dominant effect of the ACET to emerge.This allows for a highly controllable and efficient means of fluid manipulation, including particle transportation and concentration, in microfluidic devices.

Enhancing the Accumulation Ability
The CF is a commonly used metric to evaluate the efficiency of particle accumulation. [23,46]In fluorescence microscopy, the CF can be defined as the ratio of the fluorescence intensity of particles after applying a voltage (I after ) to that before applying voltage (I before ), i.e., CF ≡ I after /I before .The CF provides a quantitative measure of the degree of particle accumulation achieved through AC electrokinetics and can be used to compare the performance of different devices and experimental conditions.
Various approaches have been employed to improve particle accumulation by AC electrokinetics.One approach is to optimize the design of the electrode arrays used in AC electrokinetic devices.The geometry, size, and spacing of the electrodes can significantly affect the magnitude and distribution of the electric field, which in turn affects the particle accumulation.For example, the use of a chevron electrode upstream of the accumulation zone to align the particles around the high electric field region led to a CF of 3.4 being achieved for 50-nm-latex particles, [29] or the use of inclined zig-zag electrodes to increase the applied forces to concentrate sub-100-nm-particles led to a CF of 11 being achieved, [26] which improved the efficiency of the particle trapping and accu- mulation.In addition, reducing the space between electrodes to nanometer sizes improved the E and led to the accumulation of species with nanometer sizes. [47,48]Another approach is to tune the frequency and amplitude of the AC electric field.By selecting the appropriate frequency and amplitude, the electric field can be tailored to specific characteristics to enhance particle accumulation.Generally, higher voltages increase the magnitude of the AC electrokinetic phenomena.However, for high-conductivity solutions, an increased voltage may cause unwanted phenomena to occur. [41]In this study, for low-conductivity solutions, the aim was to increase the E by increasing the applied voltage to improve particle accumulation.
To enhance the accumulation ability, an investigation of the voltage dependency was conducted by using the prepared device.Based on the preliminary investigation of the behavior of the particles under different frequencies, a frequency that attains the accumulation inside the gap between electrodes and the application of a wide range of amplitudes without causing damage to the electrode was selected, namely 50 kHz, and was used for the voltagedependency experiment.Figure 6 depicts the CF distribution of 100-nm-PsNPs in the device at different E values oscillating at 50 kHz.The CF value shown in Figure 6 is averaged along the streamwise direction in the channel.In AC electrokinetics, the CF is influenced by various parameters, including the frequency and strength of the applied electric field.For high frequencies, such as 50 kHz, increasing the E by increasing the applied voltage led to an improved CF.Specifically, the CF increased from 1.47 to 16.3 as the E was increased from 1 × 10 6 to 3.5 × 10 6 V m −1 .For all the E values in this experiment, the accumulation peak was observed to be inside the gap between the electrodes.Note that the typical field strength applied to the high-conductivity solutions used in ACET applications is less than 1 × 10 6 V m −1 due to the limitation of the excess heating. [42,49]Throughout our experimental observations, we would like to clarify that we did not observe any negative impact, such as bubble generation or electrode corrosion, even when using a high electric field strength.This favorable outcome can be attributed to the relatively low electric conductivity of the solution used in our experiments and the high electric field frequency.Therefore, it is concluded that increasing the voltage will lead to an increased CF.
To determine the appropriate frequency that should be used for particle accumulation, an additional experiment was conducted to explore the performance of the AC electrokinetic device at higher frequencies, and the results are illustrated in Figure 7.
The plot shows a comparison of the CF values at different E values, with the frequencies oscillating between 50 and 150 kHz.The data points in the plot reveal an overall increasing trend in the CF values at all frequencies as the E is increased, indicating an improvement in the particle accumulation performance.This is due to the ACET effect, where under the influence of an electric field, the Joule heating effect causes a temperature gradient across the microfluidic channel, leading to the migration of particles toward regions of higher temperature.The increase in E results in a higher temperature gradient, which enhances the migration of particles toward the desired location and thus, increases the accumulation efficiency.
Notably, the maximum CF was achieved at 50 kHz.The slight change in the CF at a higher frequency is attributed to the change in the ACET velocity, which is expected to be independent of the frequency for a given solution at a fixed voltage amplitude, except for a range of cross-frequencies. [30]Around the cross-frequency, 50 kHz is proven to be the optimal frequency.These findings emphasize the importance of carefully considering the frequency conditions for particle accumulation applications using ACET.

Accumulation Under High Electric Field Strengths
In this section, the accumulation behavior of particles with high frequencies are explored under a high E. Figure 8 shows a sequence of raw images that provide insight into the accumulation behavior of particles at several time points (from 0 to 40 s) in the presence of an applied voltage with a high frequency.The E was 2.7 × 10 6 V m −1 , and the frequency was 150 kHz.The intensity indicates the presence of particles.Two yellow rectangles are added to each image to highlight the position of the electrode and the gap between them.The color bar features a logarithmic scale that indicates the intensity values.At time t = 0 s, the intensity distribution is nearly homogeneous, indicating no particle accumulation in the absence of the applied field.At time t = 0.2 s, a high-intensity spot appears in the middle of the gap, with two dark regions near the electrode edge.This suggests that the nonuniform electric field generates an ACET that causes particle accumulation.At time t = 1 s, a vortex-like shape is observed around each electrode edge, which is indicative of the developing process of the ACET.The rotational vortices initiated by the ACET effect begin to transport particles toward the gap, resulting in an increased concentration of particles inside the gap.The vortex size increases over time, leading to an increase in the accumulation of particles inside the gap.In addition, the distance from which particles are transported toward the gap also increases as the vortex width expands on each side from approximately 50 μm at t = 1 s to approximately 200 μm at t = 40 s.The vortex height also increases from a few microns to over 150 μm during the same period.These observations suggest that the ACET effect plays a significant role in the particle accumulation at high voltages and frequency regimes since it drives the flow of particles toward the electrode gap and enhances their accumulation.
The spatial analysis of particle accumulation under the ACET is essential for a better understanding of the accumulation phenomena.The accumulation behavior can be studied by analyzing the intensity values of particles over time.A comparison of the time evolution in the intensity values at different regions inside the electrode gap is presented in Figure 9, which provides valuable insights into the particle accumulation behavior.The saturation level of the intensity is rapidly reached within a few seconds at all regions, indicating that particle accumulation is a rapid process.However, the saturation value is reached at different times for different regions.Region A reaches saturation at t = 4 s, while regions B and C reach saturation at approximately 11 s.This difference in saturation times suggests that the particle movement occurs successively, with particles initially moving toward the center of the gap and subsequently expanding to fill the entire gap.These findings indicate that the particle accumulation behavior in the gap is highly dynamic.In addition, it indicates the absence of a positive DEP in this regime, as the particles were not attracted to the electrode edge as a high field strength area.

Mapping Local Concentration Factor
To further investigate the particle accumulation performance in the microchannel, a mapping of the local CF was performed at two different frequency regimes.Figure 10 shows the color maps of the accumulation performance at low and high frequencies, namely 0.8 and 150 kHz, respectively, where each map corresponds to a specific region in the YZ plane of the device.The color bar indicates the intensity of the CF, with blue representing high CF values and red representing low CF values.
In the low-frequency regime, two high CF areas located at approximately 100 μm on each side of the electrode surface were observed far from the gap region.The low CF region above the surface of the electrode was at a height of approximately 70 μm.The accumulation of particles in these high CF spots is caused by the ACEO flow, which entrains particles from the bulk toward the electrode surface. [27]The CF values in these regions reached up to five times the initial concentration.The intensity distribution after applying voltage was normalized by using the image obtained without voltage.
In contrast, at high-frequency operations, a single high CF area inside the gap between the electrodes was observed.The CF value in this region reached up to 30 times the initial concentration.The low CF region, where particles move away from this region, expanded to approximately 200 μm on each side of the electrode surface, as well as in the bulk with a height of approximately 150 μm.The formation of ACET vortices was observed in this regime, which transported particles toward the gap region and lead to the accumulation of particles in the center of the gap.
These results suggest that the particle accumulation behavior in the microfluidic device is highly dependent on the frequency regime of the applied voltage.The presence of an ACEO flow at a low-frequency operation results in the accumulation of particles at two areas on the electrode surface, whereas the formation of ACET vortices at a high-frequency operation leads to the accumulation of particles in the center of the gap.

Discussion
The accumulation of nanoparticles using ACET has proven to be a powerful technique in microfluidics, allowing the efficient trapping and manipulation of particles in solution.One interesting feature of this phenomenon is the trapping of particles at the stagnation point between counter vortices, which highlights the complexity of the underlying physics governing the accumulation behavior of particles.
[52][53][54][55] The results obtained from these studies have demonstrated the potential of using vortex trapping as a useful tool.In addition to the ACET, other studies have utilized vortex trapping with different driving forces to achieve particle trapping and enrichment.For example, induced-charge electrokinetic (ICEK) phenomena have been used to continuously trap and enrich micro-and nanoparticles by employing a combination of ICEK vortical flow, electroosmosis, electrophoresis, and dielectrophoresis.The critical factors for successful particle trapping and enrichment in this method were identified as the ICEK vortical flow and dielectrophoresis over the edge of the conducting strip. [53]Noninvasive hydrodynamic methods have also been used to confine and release bioparticles using micro-vortices generated by the in-plane resonating motion of a microplate. [54]n this study, the effectiveness of vortex trapping by manipulating the ACET in a low-conductivity sample is demonstrated through numerical simulations to compare the temperature and velocity fields of the ACET in high-and low-conductivity solutions of 1 and 10 −4 S m −1 , respectively.For a comprehensive presentation of the simulation model, including its components and interactions (Figure S1), as well as the governing equations and boundary conditions (Figure S2 and Table S1), please refer to the supporting information file.
Figure 11a-1 shows the temperature distribution for a highconductivity solution inside the microchannel after applying 10 V pp oscillating at 50 kHz for 7 s.The temperature gradient is observed around the gap area, with a maximum temperature value of approximately 100°C (phase change is neglected in this simulation).This temperature increase can cause bubble formation, which could affect the accumulation performance of the system.In contrast, Figure 11b-1 shows the temperature distribution for a low-conductivity solution under an applied voltage of 100 V pp at 50 kHz.Although the applied voltage in this case is 10 times higher than that used for the high-conductivity solution, the maximum temperature reached was only 23.8°C.These results suggest the potential for improving the accumulation performance in low-conductivity solutions by increasing the applied voltage.
In addition to the temperature field, the velocity field was also simulated to compare the accumulation behavior of particles in high-and low-conductivity solutions shown in Figure 11a-2 and 11b-2, respectively.It can be observed that the maximum velocity in the high-conductivity solution was 6.31 × 10 2 μm s −1 , while that in the low-conductivity solution was 1.54 × 10 3 μm s −1 .The difference in velocity can be attributed to the difference in conductivity and applied voltage amplitude between the two solutions.In the ACET, the induced flow velocity is expected to be independent of the frequency for a given solution at a fixed voltage amplitude, except for a range of cross-frequencies. [30]However, the simulation results showed a slight frequency dependence in the low-conductivity solution at a constant voltage amplitude.For example, at 100 V pp , the maximum velocity decreased from 6.76 × 10 3 to 5.1 × 10 3 μm s −1 when the frequency was increased from 50 to 150 kHz.This observation may explain the difference in the CF values depicted in Figure 7. Hence, it is essential to consider the frequency dependence of the ACET when designing microfluidic devices that utilize this phenomenon for particle manipulation.
Interestingly, despite the difference in velocities, flow patterns and the location of the stagnation point, where particles are accumulated, in the high-and low-conductivity solutions were nearly identical.The stagnation point appeared at approximately x = 0, which is the center of the gap between the electrodes.This fact suggests that the ACET can potentially be used to trap and accumulate nanoparticles in low-conductivity solutions.The accumulation of particles at the stagnation point between the counter vortices is a unique feature of the ACET phenomenon.The vortex trapping mechanism plays a crucial role in the accumulation behavior of particles in solution.The induced vortical flow generated by the oscillating electric field causes the particles to be collected at the stagnation point, where the counter vortices meet.The results of this study highlight the potential of the ACET for particle manipulation and accumulation in microfluidic systems.The unique vortex trapping mechanism of the ACET, which results in the accumulation of particles at the stagnation point, can be exploited to develop novel microfluidic devices with enhanced capabilities.The observed flow patterns and stagnation point in both high-and low-conductivity solutions indicate the potential of the ACET for broader applications beyond high-conductivity solutions.For example, particle and droplet manipulation, [22] trapping particles and cells in low-conductivity solutions, [55] fluid mixing, and micro-reactions. [56]The findings of this study provide insights that can guide the development of more efficient and versatile microfluidic devices for various applications.

Conclusion
This study demonstrated the effectiveness of AC electrokinetics in enhancing the accumulation of nanoparticles dispersed in a low-conductivity liquid in microfluidic devices.By adjusting the frequency of the applied electric field, distinct behaviors of particle motion and accumulation regimes were observed, with nanoparticles accumulating either along the electrode surface or within the gap between the electrodes.The results indicated that controlling the AC frequency could change the position of the nanoparticle accumulation through ACEO and ACET depending on the frequency, potentially improving the efficiency of the nanoparticle concentration and accumulation.Moreover, the cross-sectional visualizations in this study provided valuable insights into the behavior of the AC electrokinetic flow and the complex nature of particle accumulation.These experiments allowed for the differentiation between two hydrodynamic flow patterns observed under different AC electric field conditions, namely ACEO and ACET.The analysis of the accumulation behavior of particles at different points provided insights into the underlying mechanisms of particle trapping and accumulation.The observed formation of vortex patterns around the electrode edges suggested the presence of an AC electrokinetic flow, which transports particles from the bulk toward the gap and increases their concentration within it.These findings provide a deeper understanding of the fundamental principles underlying AC electrokinetic-based particle manipulation, which could aid in the design and optimization of microfluidic devices for various applications.In additional, this study explored the use of ACET trapping for particle manipulation and accumulation in microfluidic systems.The results demonstrated the effectiveness of vortex trapping by ACET in low-conductive samples, highlighting its potential as a powerful technique for efficient particle trapping and manipulation in solution.The vortex trapping mechanism of ACET played a crucial role in the accumulation behavior of particles in solution, resulting in their accumulation at the stagnation point between counter-rotating vortices.In addition, a high CF of up to 16.3 was achieved for 100-nm-PsNPs at an E of 3.5 × 10 6 V m −1 and frequency of 50 kHz.Furthermore, it was determined that the CF values increased with increasing E values, indicating the potential of AC electrokinetics for particle manipulation in low-conductive solutions.In summary, this study provides a comprehensive understanding of the performance of AC electrokinetic devices for particle manipulation and accumulation and offers insights into the design and optimization of such devices for specific applications.

Experimental Section
Device Geometry and Fabrication: The microfluidic platform for concentrating nanoparticles consisted of two parts, as shown in Figure 1a, namely a polydimethylsiloxane (PDMS) microchannel and a glass substrate with a coplanar symmetric electrode.The PDMS microchannel was fabricated by the standard soft lithography protocol.For the bottom-view observation (XY plane), the channel had a width, height, and streamwise length of 1 mm, 50 μm, and 30 mm, respectively.However, for the cross-sectional observation (YZ plane), the channel height was increased to 380 μm and the channel width was decreased to 50 μm, as shown in Figure 1c.Two cylindrical ports with diameters of 1 mm were created using a puncher in the PDMS part, where two perfluoroalkoxy tubes were connected as the inlet and outlet for the solution.The PDMS channel was bonded to a 0.7-mm-thick glass substrate coated with a transparent ITO film (Geomatic).The ITO film had a thickness of 150 nm.The use of ITO allowed the particle behavior over the electrode to be easily observed because of its optical transparency.The conventional wet etching process was employed for patterning the electrode shape.The electrode consisted of two parallel ITO strips with widths of 500 μm that were separated by a micro gap.Although all experiments in this study were conducted at a stationary flow with a bulk flow velocity of zero, the electrodes were set parallel to the main flow direction in the bottom-view observation experiments and inverted to perpendicular in the cross-sectional observation experiments for better observation results.
Samples and Experimental Setup: In the experiments, nanoparticles consisting of fluorescent polystyrene (Fluoro-Max Dyed, Thermo Fisher Scientific) with diameters of 100 nm were dispersed in ultrapure water (PURELAB flex, ELGA VEOLIA) and used as a working fluid.The fluorescent particles had excitation and emission wavelength of 468 and 508 nm, respectively.The electrical conductivity of the solution was tuned to 1 × 10 −4 S m −1 .The particle volume percentage in the aqueous solution was set to 0.02% to avoid particle-particle interactions.
The experimental setup is shown in Figure 12.PsNPs were visualized from the bottom side of the channel using an inverted microscope (TE-2000U, Nikon), as in Figure 12a.Figure 12b depicts the experimental setup utilized for the cross-sectional observation of the particle accumulation behavior in the YZ plane.To capture this behavior, a prism mirror was employed to reflect the particle image onto the camera, allowing the particle accumulation to be visualized and analyzed.This setup provided a valuable tool for investigating the deposition behavior of particles and further understanding the mechanisms driving particle accumulation.To capture the particle images, a 20× objective lens (NA 0.45, CFI S Plan Fluor ELWD 20x, Nikon) and a scientific CMOS (sCMOS) camera (2304 pixels × 2304 pixels, ORCA-Fusion, Hamamatsu Photonics) were used.The size of each pixel of the sensor on the sCMOS camera was 6.5 μm × 6.5 μm.Hence, the resultant spatial resolution of the image was 0.325 μm pixel −1 .The actual size of the imaging domain was 2304 pixels × 1500 pixels, which corresponded to 748.8 μm × 487.5 μm.In addition, the image acquisition frequency was 0.07 s.The evaluation method relied on volume illumination and the measurement of intensity variations induced by fluorescent particles.A continuous LED light (X-Cite 120LED, Lumen Dynamics) was used as the illumination source.The filter cube contained an exciter filter, emitter filter, and dichroic mirror that were tailored for effective particle excitation, and the collection of fluorescent light was included in the microscope.To optimize the AC voltage for transporting the nanoparticles, a function generator (AFG 3102, Tektronix) was used to produce the AC signal, which was then magnified to the target value by using a voltage amplifier (HSA4101, NF Corporation).

Figure 1 .
Figure 1.Schematic of the microfluidic device.a) Top view of the device used for the bottom-view observation.b) Cross-sectional view showing the flow pattern (red arrows) and particle accumulation position at different frequencies.c) Top view of the device used for the cross-sectional observation.(Simplified schematic that is not drawn to scale).

Figure 3 .
Figure 3. Raw images of the accumulation behavior of nanoparticles under different frequency conditions.The pair of yellow dashed lines represent the position of the electrode edges, and the area between them corresponds to the electrode gap.a) Without applied voltage, the nanoparticles are homogeneously distributed.b) At a low frequency (0.7 kHz), the nanoparticles accumulated in two positions outside the gap.c) At a high frequency (70 kHz), the nanoparticles accumulated at a single position inside the gap.

Figure 4 .
Figure 4. PsNPs accumulation positions under a voltage of 10 V pp oscillating at different frequencies.The indium tin oxide (ITO) electrode positions are denoted by a pair of yellow rectangles, with the gap area between them being demarcated by dashed lines.In the frequency range below 20 kHz, particles accumulated at two positions, and the positions of the peaks are located outside the gap.At higher frequencies up to 35 kHz, particles accumulated at two positions, and the positions of the peaks are located inside the gap.The accumulation positions overlapped at a single position near the gap centerline at frequencies exceeding 40 kHz.

Figure 5 .
Figure 5. Raw images representing the cross-sectional view of moving 100-nm-PsNPs under an AC electric field applied with several frequencies.The electric field strength is 6.25 × 10 5 V m −1 .The pair of yellow rectangles represent the ITO electrode positions, with the black area between them corresponding to the gap.The vortex height is indicated as the z-position value in micrometers.The direction of the particle movement is indicated by the red arrows.The color bar displays a logarithmic scale.

Figure 6 .
Figure 6.Concentration factor (CF) distribution of 100-nm-PsNPs in the device at different electric field strengths (E) oscillating at 50 kHz.The CF value is averaged along the streamwise direction in each image.The particles are accumulated inside the gap and the CF is increased by increasing the E. The pair of yellow rectangles represent the ITO electrode positions, with the area between them corresponding to the gap.

Figure 7 .
Figure 7.The plot shows CF values at various electric field strengths, with the frequencies oscillating between 50 and 150 kHz.The data points in the plot reveal an overall increasing trend in the CF values as the E is increased.

Figure 8 .
Figure 8.A sequence of raw images that provide insight into the accumulation behavior of 100-nm-PsNPs at different time points (from 0 to 40 s) in the presence of an applied voltage.The E is 2.7 × 10 6 V m −1 .The pair of yellow rectangles represent the ITO electrode positions, with the area between them corresponding to the gap.The direction of the vortex movement is indicated by the red arrows.The color bar displays a logarithmic scale.

Figure 9 .
Figure 9. Intensity changes with time at three different positions inside the gap under an E of 2.7 × 10 6 V m −1 .Each analysis area is 1.6 μm × 3.2 μm.Position A is at the gap centerline, and Positions B and C are located near the electrode edge.

Figure 10 .
Figure 10.Color maps indicated the local CFs at low and high frequencies of 0.8 and 150 kHz, respectively.The color bar indicates the CF value, with blue and red representing high and low CF values, respectively.

Figure 11 .
Figure 11.Simulation results for temperature and velocity fields in a microchannel with AC electrothermal trapping.All results were measured after applying a voltage of 50 kHz for 7 s.a-1) Temperature distribution in a high-conductivity solution at 10 V pp .a-2) Velocity field simulation for a high-conductivity solution.b-1) Temperature distribution in a lowconductivity solution at 100 V pp .b-2) Velocity field simulation for a lowconductivity solution.

Figure 12 .
Figure 12.Schematic of the experiment setup for the fluorescence microscopy observation.Setup for the a) bottom-view and b) cross-sectionalview observations.