Energy-Efficient AC Electrothermal Microfluidic Pumping via Localized External Heating

Abstract

In this study, we present a comprehensive numerical investigation of alternating-current electrothermal (ACET) pumping strategies tailored for energy-efficient microfluidic applications. Using coupled electrokinetic and thermal multiphysics simulations in narrow microchannels, we systematically explore the effects of channel geometry, electrode asymmetry and external heating on flow performance and thermal management. A rigorous mesh convergence study confirms velocity deviations below ±0.006 µm/s across the entire operating envelope, ensuring reliable prediction of ACET-driven flows. We demonstrate that increasing channel height from 100 µm to 500 µm reduces peak temperatures by up to 79 K at a constant 2 W heat input, highlighting the critical role of channel dimensions in convective heat dissipation. Introducing a localized external heat source beneath asymmetric electrode pairs enhances convective circulations, while doubling the fluid’s electrical conductivity yields a ~29% increase in net flow rate. From these results, we derive practical design guidelines—combining asymmetric electrode layouts, tailored channel heights, and external heat bias—to realize self-regulating, low-power microfluidic pumps. Such devices hold significant promises for on-chip semiconductor cooling, lab-on-a-chip assays and real-time thermal control in high-performance microelectronic and analytical systems.

1. Introduction

AC Electroosmotic (ACEO) flow is a microfluidic technique that utilizes a time-varying electric field between electrodes to induce fluid movement [1,2,3,4,5]. By applying an alternating-current (AC) field between two electrodes, ACEO generates both normal and tangential forces within the channel. ACEO forms an electrical double layer (EDL) along the electrodes, where alternating polarization creates ionic movement and fluid flow. A benefit of this process is that lower voltages than direct-current (DC) electroosmosis are required, offering a more efficient means to manipulate fluid dynamics by adjusting the waveform, voltage, and frequency of the applied electric field [1,6]. As a result, ACEO has proven effective in various microfluidic applications such as particle manipulation, cell sorting, and fluid mixing and has played a critical role in developing advanced lab-on-a-chip devices [1,2,3,4,5,6,7,8,9,10,11,12,13]. ACEO can significantly enhance thermal management in semiconductor applications by regulating cooling fluid flow across densely packed chips. What may follow implementation for high-power devices such as GPUs and CPUs is more efficient heat dissipation from critical areas, preventing both overheating and the cessation of valuable work due to such [14,15,16]. ACEO’s low voltage and precise control make it an ideal solution for integrating compact, efficient thermal management systems into modern semiconductor packaging.

AC Electrothermal Flow (ACET) can further extend the capabilities of microfluidic devices by introducing temperature gradients created through Joule heating, which interact with the electric field to drive fluid flow [17,18,19,20,21,22,23,24,25,26,27,28]. These gradients cause fluid properties such as conductivity and permittivity variations, resulting in fluid motion even in electrically diverse environments. ACET offers significant value for microfluidic tasks such as mixing, pumping, and concentrating chemical samples especially in lab-on-a-chip systems where mechanical pumps are impractical. Unlike ACEO, ACET has been shown to be effective in a wide range of frequencies, whereas ACEO is more common at low frequencies and relatively low salt concentrations [22,29]. The precision of ACET in manipulating fluids at the micro-scale makes it indispensable for various biomedical and industrial applications. Ren et al. showed the ACET phenomenon works well for pumping non-Newtonian fluid, like blood, in ring electrode-equipped 3D microfluidic devices [30]. Their devices pump non-Newtonian fluid more efficiently than Newtonian fluid. Kunti et al. used microfluidics devices for mixing non-Newtonian fluid using ACET phenomenon [31], demonstrating that the shear-dependent viscosity of the non-Newtonian fluid influences both mixing and flow rate.

ACET research has importance for improving fluid dynamics and thermal management system design within chip design, processes, and applications. Examples of processes that can be positively illuminated are in performance optimization, particularly in semiconductor cooling, by modeling the interactions between electric fields, temperature gradients, and fluid properties [1,6,17,19,23]. Computational tools also help researchers explore scaling effects and predict the challenges of integrating ACET into new applications. Through the ability to enable improved versatility in fluid control, ACET offers significant potential for enhancing microfluidic systems in the semiconductor industry, which is crucial for managing heat dissipation in densely packed chips and ensuring the consistent performance of MEMS [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,32,33,34,35,36]. The core implications are that valid findings from these simulations are more energy-efficient heat management in microfluidic devices and semiconductor applications and, quite possibly, by extension, a contribution to the development of sustainable thermal management technologies.

2. Materials and Methods

2.1. Mathematical Methods

AC Electrothermal Flows are caused by the interaction of an electric field with permittivity by temperature-driven conductivity. Fluid motion is governed by the incompressible Navier–Stokes equations and continuity equations.

$${\rho }_f\left({\displaystyle \frac{\partial \mathit{u}}{\partial t}}+\left(\mathit{u}·▽\right)\mathit{u}\right)=-\nabla p+\mu {▽}^2\mathit{u}+{\mathit{F}}_{\mathit{e}}+{\mathit{F}}_{\mathit{b}\mathit{u}\mathit{o}\mathit{y}\mathit{a}\mathit{n}\mathit{c}\mathit{y}}$$

(1)

$$\nabla ·\mathit{u}=0$$

(2)

In Equation (1), ${\rho }_f$ is the fluid density, μ represents the dynamic viscosity of the fluid, u is the fluid velocity, p is fluid pressure$,$ ${\mathit{F}}_{\mathit{B}\mathit{u}\mathit{o}\mathit{y}\mathit{a}\mathit{n}\mathit{c}\mathit{y}}$ is the buoyancy force due to temperature-dependent density, and ${\mathit{F}}_{\mathit{e}}$ is the electrothermal force acting on the fluid due to inhomogeneous electric properties (conductivity and permittivity) of fluid. The buoyancy force can be expressed by

$${\mathit{F}}_{\mathit{b}\mathit{u}\mathit{o}\mathit{y}\mathit{a}\mathit{n}\mathit{c}\mathit{y}}=\left(\rho -{\rho }_r\right)\mathit{g}$$

(3)

where ${\rho }_r$ is the density of fluid at $T_0=273.15 \mathrm{K}$, $\rho$ is the temperature-dependent fluid density, and $\mathit{g}$ is gravitational acceleration.

The electrothermal force acting on the incompressible fluid is given by the Equation (4) [23] as

$${\mathbf{F}}_{\mathit{e}}={\mathsf{\rho }}_{\mathrm{q}}\mathbf{E}-{\displaystyle \frac{1}{2}}{\left|\mathbf{E}\right|}^2▽\mathsf{\epsilon }$$

(4)

On the right-hand side, the first term is Coulomb force, and the second term is dielectric force. ${\mathsf{\rho }}_{\mathrm{q}}$ is the charge density, $\mathbf{E}$ is the electric field and $\mathsf{\epsilon }$ is the permissivity.

We are studying the behavior of a fluid under AC conditions so we must consider the electrothermal force as a time-averaged force per unit volume, which can be written as [23]:

$${\mathit{F}}_{\mathit{e}}={\displaystyle \frac{1}{2}}·{\displaystyle \frac{\epsilon \left(\alpha -\beta \right)}{1+{\left(\raisebox{1ex}{$\omega \epsilon $}\!\left/ \!\raisebox{-1ex}{$\sigma $}\right.\right)}^2}}\left(▽T·\mathit{E}\right)\mathit{E}-{\displaystyle \frac{1}{4}}\epsilon \alpha {\left|E\right|}^2$$

(5)

Joule heating is produced in the solution when the electric field is applied. To calculate the temperature distribution inside the simulation region, heat transfer Equation (6) is used and $\mathsf{\sigma }$ is electrical conductivity, T is the temperature, k is the thermal conductivity, c is the specific heat and ${\mathsf{\rho }}_m$ is the medium density.

$${\mathsf{\rho }}_m\mathrm{c}\left({\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{t}}}+\mathbf{u}·▽\mathrm{T}\right)=\mathrm{k}{▽}^2\mathrm{T}+\mathsf{\sigma }{\mathrm{E}}^2$$

(6)

Electric potential $\mathbf{\varnothing }$ is governed by the following equations.

$${▽}^2\mathbf{\varnothing }=0$$

(7)

$$\mathbf{E}=-▽\mathrm{\varnothing }$$

(8)

2.2. AC Electrothermal Schematic

Figure 1 shows a simplified schematic representative of the channels used in this study. Here, Inlet has been labeled on the left and Outlet on the right of the schematic in Figure 1 for demonstration purposes, meant to indicate the direction of flow. Two pairs of anodes and cathodes formed the two electrodes arranged in line on the bottom of the channel in what is referred to as an asymmetrical arrangement. We use the term asymmetrical to describe the size, or length, of the electrode components in the channel and that in this case, the anode and cathode are different lengths. In our research, the length of anode was greater than the cathode while the gap between each remained a consistent distance. The 80 μm anode and 20 μm cathode are separated by a 20 μm gap between them. Labeled hot spot on the schematic, a heating element is centered between the two electrodes. This hot spot slightly increased the local temperature by a few degrees Kelvin. On the schematic this interaction is illustrated by the positive and negative charges illustrated in light blue circles. Here, we show how a negative charge is created in the fluid at the site of the anode, or positive side of the electrode, and a positive charge created in the fluid at the cathode, where a negative charge is active. Fluid on the opposite side of the channel maintains a positive charge while the bulk fluid on either end of the electrode array contains both anions and cations. Our research is particularly interested in the application of the small amounts of heat for controlling the flow of fluids through microchannels, known as ACET. In all trials, a heat flux of 2 W is added at the hot spot designated in Figure 1. Channel height is intentionally varied as a variable parameter in some cases, but all channel heights are otherwise H = 100 μm. Channel lengths were all fixed at L = 2090 μm. As illustrated in Figure 1, each negatively charged anode is 20 μm in length with a gap of 20 μm separating it from the positively charged 80 μm cathode. Together these make up one electrode. These are arranged on either side of the 50 μm hot spot separated by a 20 μm gap.

2.3. Boundary Conditions

In order to solve for the coupled governing equations of fluid, heat transfer, and electric field, the following boundary conditions are applied. The inertia term was neglected in Equation (1) for a low Reynolds number. Buoyancy force and electrothermal force are included in the Navier–Stokes equation.

At the inlet and outlet, pressure is set to zero, thermal insulation is used, i.e.,

$$\mathit{p}=0\mathrm{Pa}, \mathit{T}={\mathit{T}}_0, \mathit{n}·▽\mathbf{V}=0$$

(9)

Electric potential is applied at the anode and cathode:

$$\mathit{V}=5\mathbf{V} \left(\mathrm{Anode}\right), \mathit{V}=-5\mathbf{V} \left(\mathrm{Cathode}\right), \mathit{u}=0, -\mathit{k}{\displaystyle \frac{\partial \mathit{T}}{\partial \mathit{y}}}=\mathit{h}(\mathit{T}-{\mathit{T}}_0), \mathit{n}·▽\mathbf{V}=0$$

(10)

where $k$ is thermal conductivity, $h$ is the heat transfer coefficient and $T_0$ is the temperature of air at room temperature.

$$\mathrm{At} \mathrm{the} \mathrm{hot} \mathrm{spot}, \mathrm{heat} \mathrm{flux}, \dot{\mathit{q}}=2 \mathrm{W}, \mathit{u}=0, \mathit{n}·▽\mathbf{\varnothing }=0$$

(11)

$$\mathrm{On} \mathrm{other} \mathrm{walls}, -k{\displaystyle \frac{\partial T}{\partial y}}=h(T-T_0),\mathit{u}=0, \mathit{n}·▽\mathbf{\varnothing }=0,$$

(12)

COMSOL Multiphysics 5.3a. was used to solve Equations from (1) through (8) using the above boundary conditions.

2.4. Mesh

This study was performed in an entirely simulated environment using COMSOL software. Laminar flow module, transport of diluted species module, electric-current module, heat transfer module are used to solve for the governing Equations (1)–(8) and boundary conditions (9)–(12). The parameters used in the simulation are listed in

Table 1. Physical properties and parameters.

Parameter	Value	Description
Σ	0.1 [S/m]	Conductivity of the ionic solution
$\epsilon$	80.8 × 8.85 × 10−12 [F/m]	Relative permittivity
V0	5 [V]	Maximum value of the applied voltage
${\rho }_f$	1000 [kg/m3]	Water density
T0	293.15 [K]	Room temperature
L	2090 [µm]	Channel length
H	100 [µm]	Channel height
$g$	9.81 [m/s2]	Acceleration due to gravity
µ	0.001 [Pa·s]	Dynamic viscosity of the water
cc	4184 [J/kg °C]	Specific heat capacity of water
kk	0.6 [W/(m·K)]	Thermal conductivity of water

.

To assure the accuracy of our findings and accommodate reliability in computational performance, we conducted mesh-independence study. In order to use velocity as a parameter, we had to assign a mesh of measurable areas to the inside of the channel. Considering these necessities, we used a course-grained mesh provided by COMSOL with a range of 2 μm to 15 μm to record velocity variation in the channel, which still provided plenty of measurable points for our study. To ensure quality and consistency, we tested the variance in simulated average velocities across the mesh at 2 μm, 3 μm, 4 μm, 10 μm, 12 μm and 15 μm. The average velocity of 1.0491 μm/s at the 2 μm mesh size represents the theoretical average velocity at this mesh area. Successive readings for 3 μm, 4 μm, 10 μm, 12 μm and 15 μm were 1.0494 μm/s, 1.095 μm/s, 1.0471 μm/s, 1.0423 μm/s and 1.0326 μm/s, respectively.

When plotted with average velocity (μm/s) vs. grid size (μm), as seen in Figure 2, we can see a relationship between and increase in mesh area size and lower recorded average velocity values. We also note that smaller mesh areas correspond to higher recorded velocities. Percent error for these velocities was calculated by dividing the difference of the true value from the measured value over the true value, then multiplying by 100 as an absolute value. The percent error values of velocity for the 3 μm, 4 μm, 10 μm, 12 μm and 15 μm mesh sizes were found to be 0.029%, 0.038%, 0.191%, 0.648% and 1.573%, respectively. These percent error values are extremely small, demonstrating the dependability of the simulations and results found in this report. With maximum mesh size changing from 2 to 15 µm, we calculated the percentage change in the velocity, and it showed that, when the maximum mesh size is reduced to 0.029%, the calculated velocity will not change. Thus, in the remaining calculations, a maximum mesh size of 2 µm is used.

2.5. Validation

Figure 3 shows the temperature rise vs. applied voltage graph in a microchannel, where the red line represents simulation results and the black line represents experimental results by Lu, Y. et al. [23]. There was a 273.15 K temperature rise when a voltage of 1 V was applied in the electrodes and a 293.31 K rise when applied a voltage of 8 V was applied. There was a temperature change of 20.16 K when voltages from 1 to 8 V were applied. Our simulation results are a very good match with experimental results by Lu, Y. et al. [23]. Our numerical work is validated through experimental work by Lu, Y. et al. [23], as they match on a quantitative level. Figure 3 from our own simulations is provided alongside one generated by Lu, Y. et al. [23] as a quantitative comparison meant to illustrate the viability of our results.

3. Simulations and Results

3.1. The Electrical Potential

ACET depends on electrodes operating under an alternating current to generate unique flow patterns through the fluid. Figure 4 shows a surface graph of the electrical potential inside the microchannel model used throughout this study. We enhance the effects of the alternating current by using the asymmetrical arrangement of electrodes with regular spacing between the anodes and cathodes as described in Section 1 in conjunction with the alternating current. Figure 4 shows a channel height and length representative of those used in our study. We can also see that the area contained within the electrode array is a dense region of a positive electrical potential which shapes the results of how fluids will flow and be visualized in this study. In our study, we systematically varied parameters to study the resultant flow patterns in this effected channel region.

3.2. Electrode Size

As a means to understand the role electrode size plays in these trials, we ran four simulations where electrode size was set to 20 μm, 40 μm, 60 μm and 80 μm for a channel height of 100 μm, 200 μm, 300 μm, 400 μm and 500 μm. All other parameters were left to default boundary conditions outlined in Section 2.3. Electrode size (μm) refers to the perpendicular length of the electrode across the channel. The size of the hot spot and 20 μm gap and 80 μm positive side of the electrode remain the same. Only the size of the negative electrode was altered. Referring to Figure 5, we see a graph of the relationship between velocity (μm/s) on the y-axis and channel height (μm) on the x-axis corresponding to each increase in electrode size as represented by the color-coded legend contained therein.

We note the identical parabolic shape to the relationship for each electrode size and velocity relative to channel height. This consistently scaled relationship between the two demonstrates not only that an increase in electrode size increases the maximum velocity in the cannel, but that this relationship scales uniformly. This uniform scaling indicates that electrode size should be considered a reliable constant variable in the simulations for this study.

3.3. Fluid Velocities

Seven inlet velocities were tested with a voltage of 5 V supplied to the electrode array. ACET produces modest fluid movement in the absence of any inlet flow by interaction of normal forces generated in the fluid. The resulting flow pattern depends on factors such as electrode dimensions and layout, as well as variables like voltage and frequency, among others, that we have used as variable parameters in this study. This resulting non-uniform electric field in the fluid is examined herein. This flow is visible in areas of higher velocity and a corresponding lower pressure consistent with the Navier–Stokes and continuity equations described above. Inlet velocities and flow rate are given in μm/s and μm₃/s alone and our channel height remains constant at 100 μm. To properly understand Figure 6a we need to point out that these images show color-coded velocities in the microchannel using relative mapping and are more for quantitative purposes, meaning that we are interested in the velocity difference within the channel and not representing the actual measured velocities. The actual measured velocities are visible, however, in Figure 6b, where flow rate (μm³/s) is plotted against inlet velocity (μm/s). We would like to note that this pairing of qualitative surface graphics with quantitative graphs is used throughout this study for a more wholistic understanding of the results.

At an inlet velocity of 0 μm/s, shown in the uppermost graphic in Figure 6a, the asymmetrical electrode array produces distinct areas of higher velocity just above the array in two multi-lobed vortices on either side of the array. It can also be seen that of the lobed regions, the lower two have a greater velocity than all other regions in these 0 μm/s inlet velocity trials. The flow rate in the channel was recorded as 0 ${\mathsf{\mu }\mathrm{m}}^3$/s.

The lowest active inlet flow of 0.5 μm/s can be seen as the second from the top graphic in Figure 6a. Now we can see that the bulk fluid in the channel has a slight increase in velocity as indicated by the change in color from the 0 μm/s graphic above it, and the flow pattern created from the ACET begins to become distorted. Now we see velocity in the lower right lobe decrease while the upper right region expands, elongating slightly. Meanwhile, the lower lobe of the left vortices has a similar elongation with a distinctly higher velocity than anywhere else in the channel. Outside the electrode-affected region, the bulk fluid remains constant with the inlet velocity.

In the 0.5 μm/s trial, we that the distortion in the ACET flow pattern beginning to occur in the previous trial is exaggerate further. Here, the upper left and lower right lobes have diminished significantly as their measured velocities near that of the bulk fluid flow initiated by the inlet velocity where a flow rate of 49.83 ${\mathsf{\mu }\mathrm{m}}^3$/s was recorded.

With an inlet velocity of 1 μm/s there is considerable movement in the bulk fluid throughout the channel, indicated by the lighter region in the surface graphic in Figure 6a, and the ACET flow pattern is entirely altered from its original symmetrical 5-lobed pattern. Here, with a recorded flow rate of 99.65 ${\mathsf{\mu }\mathrm{m}}^3$/s, we notice that the lower left region remains an area of highest velocity, but the down-current lower lobe is effectively gone. We can see that at 1 μm/s inlet velocity the ACET phenomenon just moderately manipulates the flow of the bulk fluid through the channel.

At a 2.5 μm/s inlet velocity, this area of flow distortion is even less pronounced as the bulk fluid velocity is more consistently distributed in the channel from left to right where a flow rate of 249.14 ${\mathsf{\mu }\mathrm{m}}^3$/s was recorded. We still observe areas of higher velocity at the same lower left and upper right regions near the electrode arrays, but the difference between these areas and the bulk fluid velocity are now very small as the pattern is mostly reduced to a disturbance in the flow.

At a 5 μm/s inlet velocity, a flow rate of 498.28 ${\mathsf{\mu }\mathrm{m}}^3$/s was recorded. We note that the distortion created by the electrodes is now even more minimized, represented only by a disturbance in the flow pattern with regions of high velocity remaining at the upstream and downstream locations seen in previous trials. The areas of low velocity which previously helped define the flow distortion at the array are gone and the flow is more consistent across the channel. This can be explained when considering the relationship depends on pressure-driven flow alone in correlation with the Navier–Stokes and continuity equations. At 10 μm/s and 15 μm/s inlet velocity, the flow rate of 996.57 ${\mathsf{\mu }\mathrm{m}}^3$/s and 1494.8 ${\mathsf{\mu }\mathrm{m}}^3$/s were recorded, respectively. Pressure-driven flow dominated fluid movement when inlet velocity was 15 μm/s and ACET was less effective at high inlet velocity.

3.4. Channel Dimensions

Channel heights were tests in 100 μm increments from 100 μm to 500 μm. Observing Figure 7, we see that flow patterns at the electrode array change with a corresponding increase in channel height. As expected, by increasing the channel height a corresponding decrease in pressures between the upper and lower wall occurs, resulting in an increase in velocity. At a channel height of 100 μm, the flow rate was measured at 0.0073 ${\mathsf{\mu }\mathrm{m}}^3$/s. Here, lobed vortices are located on either side of the electrode array with the highest velocities in the lower lobes and lower velocities in the less pronounced inner regions. With an increase in channel height to 200 μm these two separate lobed vortices lose the inner regions of movement entirely but remain separate. Here, flow rate of 0.175 ${\mathsf{\mu }\mathrm{m}}^3$/s was recorded in the channel. The simulation at 400 μm continues the upward trend in velocity with increase in channel height. Here, the flow rate was recorded to be 2.9324 ${\mathsf{\mu }\mathrm{m}}^3$/s, and we note that the lighter region of lower velocity that joined the two vortices observed in the 200 μm simulation is now distinctly joined, and the vortices appear in a single configuration with four distinct lobes of higher velocity, the highest of which are located on the bottom two lobes. At a 500 μm channel height, the lobed pattern is yet more pronounced with a region of high velocity in the ventral connecting region. A flow rate of 6.41 ${\mathsf{\mu }\mathrm{m}}^3$/s was recorded at this height.

3.5. Pressure Gradients

In accordance with Navier–Stokes and continuity equations, static pressure and velocity are inversely proportional. Areas of higher velocity experience lower pressure and lower velocity, higher pressure. Figure 8a,b shows the clear correlation between an increased channel width and greater pressure capacities, with color-coded gradient lines measured in Pa for each different channel of the four heights studied here. In Figure 8a, a channel height of 100 $\mathsf{\mu }$m results in tight pressure contours in the channel with lower pressures on the bottom of the channel interior at the site of the electrodes. The lowest pressure recorded here was −0.185 Pa, while maximum pressure was measured at 0.184 Pa. This higher pressure is located on the upper portion of the channel as indicated by the red contours presented in the qualitative visualization provided in Figure 8a. In this figure, we observe that the tightness of the line’s changes pressure readings, indicating the steepness of the pressure gradient observed in the 100 μm simulation. With an increase in channel height to 200 μm, low pressure lines in the surface graphic remain tight around the electrode array but notably spread out as pressure increases on the opposite side of the channel, indicating a potential decrease in the pressure gradient as pressures increase across the channel vertically. In the 200 μm simulation, a low pressure of −0.22 Pa was recorded at the site of the array, while a high pressure of 0.21 Pa was recorded on the upper side of the channel, as indicated by the red contours. Low pressures for these trials were −0.237 and −0.230 Pa, respectively, and high pressures were recorded to be 0.20 Pa and 0.18 Pa, for channel height 400 µm and 500 µm, respectively. This relationship between an increase in channel height and lower pressures created at the electrode array is displayed quantitively in Figure 8b, where pressure (Pa) is plotted on the y-axis and channel height (μm) is plotted on the x-axis. Here, the relationship between pressure and channel height is indicated by the black line while the drop in pressure is represented by the red line.

3.6. Temperature

Four simulations were run testing the maximum measured temperature (K) in the microchannel relative increasing channel height. Here, the same heat flux (2 W) as mentioned in Section 2.3 was the only heat source in these trials. The first simulation run was with a channel height of 100 μm where the maximum recorded heat was 404.94 K. Referring to the surface graphic in Figure 9, we can see a qualitative representation of the distribution of temperature in the channel where reds indicate relatively lower temperatures and whiter, warmer. In this graphic, it is plain to see that regions of warmth are greatest at the site of the electrode pair on either side of the hot spot which itself. With an increase in channel height to 200 μm the two distinct regions of heating begin to merge over the hot spot and the warmest regions remain located over each electrode. The maximum temperature recorded in the channel for this trial was 362.51 K. At 400 μm, the depression is mostly gone with distinct areas of high temperature located over the electrodes where the maximum temperature was recorded as 333.11 K. At 500 μm, the region of warmer fluid is a perfect half-circle in shape while the warmer regions are still located over the electrodes. The maximum temperature recorded here was 325.86 K. It is clear to see by this graph how temperature decreases in these trials with an increase in channel height.

3.7. Fluid Conductivity

In our study, we are manipulating the fluid’s flow pattern with change in fluid conductivity. Our simulation measured two parameters affected by increasing fluid conductivity in our simulations. Figure 10a shows a graph of measured increases in flow rate (${\mathsf{\mu }\mathrm{m}}^3$/s) with incremental increases in conductivity (S/m). The flow rate recorded from simulations were 0.0008 ${\mathsf{\mu }\mathrm{m}}^3$/s, 0.003 ${\mathsf{\mu }\mathrm{m}}^3$/s, 0.005 ${\mathsf{\mu }\mathrm{m}}^3$/s, 0.007 ${\mathsf{\mu }\mathrm{m}}^3$/s, 0.009 ${\mathsf{\mu }\mathrm{m}}^3$/s and 0.013 ${\mathsf{\mu }\mathrm{m}}^3$/s for conductivities of 0.01 S/m, 0.05 S/m, 0.075 S/m, 0.1 S/m, 0.125 S/m and 0.15 S/m, respectively. In the second set of simulations for conductivity, maximum temperature (K) was recorded with increases in conductivity. The graph in Figure 10b displays the results of these simulations with maximum temperature (K) plotted on the y-axis and conductivity (S/m) on the x-axis indicating a slightly super-linear relationship between the two parameters. This simulation also used conductivities of 0.01 S/m, 0.05 S/m, 0.075 S/m, 0.1 S/m, 0.125 S/m and 0.15 S/m, where the values recorded were 320 K, 359 K, 382 K, 404 K, 427 K and 450 K, respectively. These results, graphed in Figure 10b, display the near-linear relationship between increases in conductivity and temperature in the microchannels in our study.

3.8. Voltage and Flow Rate

Figure 11 shows a graph of voltage (V) vs. flow rate (${\mathsf{\mu }\mathrm{m}}^3$/s). Each simulation was run with a channel height of 100 μm. At 1 V, we observe a vortices lobed patter similar to that seen in several other surface graphics from this study. This is located centrally over the electrode array, with the higher velocities located on the interior of these lobes, the highest velocities located in the lower two lobes. The flow rate recorded in this simulation was 0.0005 ${\mathsf{\mu }\mathrm{m}}^3$/s. The application of 2 V causes notable change in the movement pattern, as the single pattern in the previous simulation for 1 V seems to have spread horizontally along the channel, the high-velocity lobes separating from one another. A vortices shape mimicking that seen in the previous simulation seems to begin to emerge between these separated lobes, but at much lower speeds. The flow rate in this simulation was recorded to be 0.0001 ${\mathsf{\mu }\mathrm{m}}^3$/s. The flow rate recorded in the fluid from these simulations was 0.004 ${\mathsf{\mu }\mathrm{m}}^3$/s at 4 V. The flow rate was measured 0.011 µm³/s when applied voltage was 6 V. The graph in Figure 11 offers a quantitative visualization of how flow rate ${\mathsf{\mu }\mathrm{m}}^3$ (/s) increased with voltage (V) in our study. With flow rate (${\mathsf{\mu }\mathrm{m}}^3$/s) on the y-axis and voltage (V) on the x-axis, we observe higher voltage exhibits a super-linear relationship with velocity.

3.9. Power and Flow Rate

Figure 12 shows a power vs. flow rate graph. An external heat source was placed in the middle of the microchannel that can be seen in Figure 1. This study shows that the power of the heater increased as a result of the volumetric flow rate increase. Our devices achieved a flow rate of 0.0067 ${\mathsf{\mu }\mathrm{m}}^3$/s when 1 W power was applied to the external heater. We observed a linear relationship between power vs. flow rate up to 4 W. The maximum flow rate was recorded at 0.0091 ${\mathsf{\mu }\mathrm{m}}^3$/s when we applied 6 W power in the heater.

4. Discussion

4.1. Results Discussion

The results above demonstrate the significant versatility of our platform, a diagram of which is shown in Figure 1. With this simulation configuration, we can effectively use heat and apply an alternating current to move solutions while modulating several parameters for the fluids within microchannels. A mesh study (Figure 2) confirms that our platform can maintain a stable volumetric flow rate throughout the tested range, a crucial factor for ensuring fluid integrity and transport. Surface velocities can be controlled by pressure-driven flow, as seen in (Figure 6a,b), but further simulations using COMSOL software in subsequent sections reveal novel innovations for moving fluids, managing heat and controlling pressure in microchannels.

Channel height created meaningful changes to the capacity of several parameters in microchannel simulations as heights of 100 μm, 200 μm, 400 μm and 500 μm returned meaningful changes in three sets of simulations (Figure 7, Figure 8 and Figure 9). As expected, changes to channel height elicited pressure gradients, which brought about increased flow rate and changing configurations of four-lobed pattern vortices at the site of the electrode array (Figure 7). This has been explained in prior work connecting papers [2,3,6]. Figure 8a,b shows that varying height can increase or decrease pressures across the architecture. Figure 8a,b demonstrate the potential for alteration of pressure (Pa) distribution across the channel, noting the qualitative change in pattern presented in Figure 8a. In the final height-based set of simulations, recorded temperatures decreased with channel height, as presented in Figure 9.

The remaining simulations were conducted with a consistent channel height of 100 μm. Increases in conductivity (S/m) increased flow rate as well as temperature in our simulations as seen from the graphs plotting the results in Figure 10a,b. We note that while the relationship appears slightly super-linear in the plot of conductivity vs. flow rate (${\mathsf{\mu }\mathrm{m}}^3$/s) in Figure 10a, it was very slightly sub-linear for the plot of conductivity vs. temperature (K) in Figure 10b. Another set of simulations were run gradually increasing the voltage (V) applied at the electrode array while monitoring flow rate (${\mathsf{\mu }\mathrm{m}}^3$/s) in the microchannel. We found that not only is the configuration of vortices in the channel affected, as can be seen in Figure 11, but a super-linear relationship became apparent for simulations of 1 V to 6 V.

Figure 6a shows fluid velocity increases when inlet velocity increases, this is due to the conservation of mass phenomena in the microchannel. A pressure difference is created inside the microchannel when the inlet velocity increases because fluid moves at higher velocity. The equation of continuity plays an important role for maximum velocity inside the channel and ACET are responsible for fluid flow. This study shows flow rate increases when channel height increases in Figure 7, this is due to higher channel height providing additional space for fluid flow. Fluid velocity is proportional to the height of the channel squared. At the same pressure gradient, fluid experiences less resistance, hence the microchannel observed higher fluid velocity with increasing channel height. This study shows that the flow rate increases when fluid conductivity increases, as shown in Figure 10a, due to electro thermal force. Higher-conductivity fluid interacts with electric fields, increasing the driving force and, consequently, the fluid velocity. The fluid flow rate increased when the electric field strength was increased, as shown in Figure 11, due to the AC Electrothermal Flow.

This work shows that the maximum temperature is decreased when channel height is increased in Figure 9. Here, the hot spot was placed in between the electrodes and applied power was 2 W in the hop spot. There was an approximately 79 K temperature rise when channel height changed from 100 µm to 500 µm. This temperature rise occurred due to convection heat transfer. A 500 µm channel height provides greater fluid flow and enhanced convective heat transfer. A taller channel height provides a greater heat transfer surface area; consequently, efficient heat transfer occurred between flowing fluid and channel wall. This study also shows a temperature rise with increasing applied voltages in Figure 3; this is due to the conservation of energy. Temperature and applied voltages are related to each other in Equation (6). Temperature increases with the increased strength of the electric field (5 V) in the electrodes, and we observed the same phenomenon in this project.

4.2. Potential Applications, Limitations, and Future Work Toward Validation

ACET-driven vortices can be intensified with thin-film heaters and further amplified by interdigitated electrodes that combine Joule heating and AC forcing. This body of work points toward a self-regulated, high-throughput circulation scheme capable, in principle, of removing heat from localized hotspots (e.g., GPU cores) and supports the broader vision of field-tunable, real-time thermal management beyond conventional semiconductor cooling [1,17,18,23,28,37].

By embedding ACET into microfluidic cooling layers, we introduce a testable hypothesis: that controlled, long-range vortices can meaningfully supplement today’s passive or pumped microchannel schemes for hotspot mitigation. When combined with centimeter-scale convection that sustains fluid motion over several millimeters, this concept could evolve into an energy-efficient, easily scaled add-on to existing heatsink designs. Past work and extrapolations [5] suggest ACET remains effective even with shear-thinning fluids, and recent modeling [35] outlines how a closed-loop controller might one day adjust the AC drive in response to on-chip temperature feedback.

Our own results confirm centimeter-scale ACET vortices and show how an external heater plus electrode geometry amplifies convective transport, but we have not yet validated this pump in a realistic heatsink assembly or linked its flow to a chip’s actual heat-flux profile. Nor have we measured end-to-end temperature drops in a plausible GPU-cooling stack. Filling those gaps for instance by integrating our ACET module into a full device-level thermal model or performing proof-of-principle experiments on a heated micro-die would directly connect our simulations to real-world cooling performance.

A logical next step would be to evaluate, in silico, how our ACET pump slots into a complete cooling chain and measurably lowers chip temperatures. To this end, one could begin by embedding the ACET module within a full device-level thermal simulation, incorporating a heated silicon die, thermal interface material (TIM), a microchannel plate, and a bulk heatsink, and then perform hot-spot removal transients under realistic power loads, comparing ΔT against a non-ACET baseline. Parallel to that, building a benchtop “mock GPU” test vehicle would allow direct experimental validation: the microfluidic pump would be integrated onto a microfabricated heater chip and instrumented with infrared thermography or micro-thermocouples to record temperature drops across a range of power densities. Finally, system-level gains should be quantified by correlating flow rate with ΔT and pumping power with cooling capacity, thereby assessing whether this ACET-enhanced approach can meet or exceed the performance of existing microchannel or heat-pipe cooling solutions. A future work that demonstrates each of these scenarios can elegantly link our ACET vortices in silico to tangible improvements in device-cooling performance.

4.3. On Overcoming Modeling Limitations

Many computer models used to study alternating-current electrothermal (ACET) systems are based on simplified assumptions. They often use flat, 2D designs, treat fluid and material properties as constant, and separate the interactions between heat, electricity, and fluid flow. These shortcuts can overlook essential effects, such as how heating alters the behavior of fluids and electric fields in small channels. Without more comprehensive comparisons to real experiments, these models can yield results that insufficiently match what happens in actual devices. To improve this, researchers need to develop more comprehensive models that account for the interaction between heat, fluid properties, and the simultaneous effects of electricity, heat, and flow. Using 3D designs and focusing on the most critical areas in the system can yield better results without requiring substantial amounts of computer power. Researchers should also evaluate their models physically, as resources allow, using tools such as high-speed cameras to track tiny flows or infrared sensors to measure heat so they can adjust and confirm that the models accurately match real-life behavior. By overcoming these modeling constraints, ACET research can move toward predictive, scalable design workflows that are better suited for application in biosensing, thermal regulation, and lab-on-chip platforms. Physically paired modeling will not only enable more profound insight into electrothermal flow physics but also accelerate the development of optimized, application-ready microfluidic devices through iterative simulation-experiment integration. A key challenge, among many, will be making physical model pairing less expensive through improved manufacturing capabilities; while this is beyond the scope of the paper, this does appear worth mentioning for thoughts on how to deepen the research.

5. Conclusions

In this study, we demonstrated the potential of AC Electrothermal Flow (ACET) to address the critical challenges of heat generation and thermal management in semiconductor systems. Our research has shown that these microfluidic techniques can regulate fluids, offering a versatile solution for thermal management and heat recycling. Specifically, our study revealed the significant impact of channel height variations on pressure gradients and fluid velocities. We observed that channel height modulations could increase fluid velocity, underscoring the importance of precise control over microfluidic geometries in optimizing ACET flow behavior. The fusion of ACET with AC Electroosmosis opens new possibilities for controlling fluid flows with high precision; by integrating these mechanisms, we achieved more granular fluid flow, highlighting their potential to improve cooling fluid management in semiconductor applications and provide a more energy-efficient approach to thermal regulation of chips in high-performance computing and sensitive bioassays. Our platform also demonstrated impressive stability, even in chaotic environments: under varying electrical conductivities and applied voltages, device stability and flow control remained versatile, ensuring consistent fluid velocity and temperature control. Furthermore, early modeling indicates that ACET remains robust even with complex, shear-dependent fluids. At the same time, adaptive closed-loop control can autonomously recalibrate the electrical drive to preserve optimal transport conditions without mechanical adjustment. This stability is crucial for applications where unpredictable or extreme conditions may arise. In addition to thermal management, our findings have significant implications for developing lab-on-a-chip devices and advanced computing elements. Furthermore, the increased fluid velocities and heat-transfer efficiencies we observed suggest routes toward enhanced chip designs that can cycle heat away from components prone to overheating, offering improved performance in critical areas of semiconductor design. While our study primarily focused on simulations, future work should explore alternative design configurations, including real-world testing and industrial scalability. By scaling up this platform, we could address the growing demand for robust, energy-efficient microfluidic systems in medical, computing, and other sectors. In summary, this research makes an essential contribution to incremental advancements in ACET technologies, and by continuing to refine these techniques, we can expect to see more efficient design paths that potentially transform thermal-management solutions for a wide range of industries.