# Multiphase Actuation of AC Electrothermal Micropump

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. ACET Theory and Relevant Equations

^{−10}times smaller than joule heating. The convective heat term is also ignored since diffusion largely dominates heat transfer, and at sufficiently high frequencies used for electrothermal flow, the equation can be simplified to steady-state [24]. Occasionally, the left-hand term of Equation (1) is represented as 0.5$\sigma {\left|{E}_{peak}\right|}^{2}$ to account for the root-mean-square time-averaging of the electric field [17]. This temperature gradient causes gradients to form in the electrical properties of the fluid, including the permittivity and conductivity. This varying permittivity and conductivity create a charge density as follows [23]:

^{−1}and 2% K

^{−1}, respectively, for aqueous solutions at around 293 K [23]. The electrothermal force, ${F}_{et}$, is derived from the coulombic and dielectric forces acting on the charge density, which can be represented as [17,23]:

#### 2.2. COMSOL Simulation

## 3. Results

_{peak}as a benchmark, since above this fluid can begin to react with the electrodes and damage the device [26]. However, in Figure 2, flow rates are listed up to 10 V

_{peak}to provide an idea of flow rates that may be attainable in the future with ACET [31]. Figure 3a–d shows the real component of the voltage throughout the fluid for each phase, where the large electrodes are all set to ground and the small electrodes are set to 5 V

_{peak}. The complex voltage phasor is equivalent to $V\mathrm{cos}\theta +jV\mathrm{sin}\theta $, where $j=\sqrt{-1}$ and $\theta $ is the phase angle. The narrow electrode furthest to the left is set to 0°, while subsequent electrodes are set to 180° for 2-phase, 120° and 240° for 3-phase and 90°, 180° and 270° for 4-phase. In Figure 3d, the second and fourth narrow electrodes are shown as 0 V because at 90° and 270° the voltage is purely imaginary. Similarly, the electrodes at 0° and 180° have a 0 V imaginary component of the electric field, as shown in Figure 3e.

_{peak}is as follows: 294.56 K for 1-phase, 294.73 K for 2-phase, 294.70 K for 3-phase and 294.67 K. The temperature is shown to be lower overall for 1-phase as shown in Figure 4 compared to the multiphase cases. These temperatures are all within a safe range for biofluid and cellular transport (<311 K), allowing ACET micropumps to be safely used for medical devices without compromising on results [32]. Flow profiles are very similar in each case, so the flow profile is given for a two-phase micropump in Figure 5. Figure 2 shows the x-component of the velocity for each case vs. the peak voltage applied to the array. This shows that the 2-phase configuration results in the largest ACET velocity, however, 3- and 4-phase also result in an increased velocity as well compared to conventional singular phase ACET micropumps. A frequency sweep is also performed from 100 kHz to 10 GHz in Figure 6 to show the frequency dependence of ACET flow rates. As expected, flow rates tend to remain relatively constant but begin to fall at about 10 MHz as the coulombic force diminishes [16,17].

## 4. Discussion

_{peak}, compared to 1-phase. This is because the phase difference between electrode pairs results in a higher electric field strength between electrode pairs and therefore a greater ACET force. The average electric field strength between electrode pairs is 4680 V/m for 1-phase, 6890 V/m for 2-phase, 6790 V/m for 3-phase and 6610 V/m for 4-phase. Because the electric field strength directly impacts the temperature gradient and electrothermal force, the electrothermal force follows a similar pattern with the maximum force achieved using a 2-phase configuration and lower calculated forces for 3- and 4-phases. The 2-phase device results in the largest change in voltage over the geometry with an effective 180° phase difference between adjacent small electrodes, leading to the greatest electric field strength. In addition, the multiphase ACET device results in an immeasurably small change in maximum temperature and maintains a low voltage. This method therefore provides a safe way to improve flowrates without risking damage to biofluids due to overheating or undesirable electrochemical reactions.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**ACET micropump geometry used for COMSOL simulations. (

**a**) depicts the cross-sectional geometry of the channel, with the square dots representing the electrode locations at the bottom of the channel and (

**b**) shows a 3D model of the channel with electrode dimension definitions for gap 1 (G1), wide electrode (W), gap 2 (G2) and the narrow electrode (N). The x-y-z directions are added for reference in (

**a**,

**b**), where the z-direction points into the page in (

**a**).

**Figure 2.**Flow rates for 1-, 2-, 3- and 4-phase configurations at 100 kHz. The voltage given is the peak voltage used in simulations.

**Figure 3.**The real component of the voltage profiles is given for (

**a**) 1-phase, (

**b**) 2-phase (180° phase separation), (

**c**) 3-phase (120° phase separation) and (

**d**) 4-phase (90° phase separation) configurations at 5 V

_{peak}, where the far-left electrode is set to a phase angle of 0°. (

**e**) shows the imaginary component of the electric field corresponding to the 4-phase configuration in (

**d**). (

**f**) shows the legend for the voltage contours used in color plots a-e. These simulations are shown for the electrode geometry of 150/120/20/20 μm.

**Figure 4.**The temperature in an ACET channel, where black lines indicate the fluid-glass boundary, given for (

**a**) 1-phase, (

**b**) 2-phase (180° phase separation), (

**c**) 3-phase (120° phase separation) and (

**d**) 4-phase (90° phase separation) configurations at 5 V

_{peak}, where the far-left electrode is set to a phase angle of 0°. (

**e**) shows the color legend for the temperature profiles.

**Figure 6.**Frequency dependence of ACET flow rates at 5 V

_{peak}. The ACET flow rate remains relatively constant at lower frequencies but begins to drop off at around 10 MHz as the coulombic force quickly diminishes.

**Table 1.**This table provides all the fluid properties for PBS used in the simulations. The electrical conductivity is given for the measured conductivity of PBS during previous experimental ACET work [16].

Property | Symbol | Value |
---|---|---|

Relative permittivity | ${\epsilon}_{r}$ | 80.2 |

Electrical conductivity | $\sigma $ | 0.224 S/m |

Thermal conductivity | $k$ | 0.598 W/(m K) |

Density | $\rho $ | 999 kg/m^{3} |

Heat capacity at constant pressure | ${C}_{P}$ | 4181 J/(kg K) |

Ratio of specific heats | $\gamma $ | 1 |

Dynamic viscosity | $\mu $ | 1.05 × 10^{−3} (N s)/m^{2} |

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**MDPI and ACS Style**

Cenaiko, S.; Lijnse, T.; Dalton, C. Multiphase Actuation of AC Electrothermal Micropump. *Micromachines* **2023**, *14*, 758.
https://doi.org/10.3390/mi14040758

**AMA Style**

Cenaiko S, Lijnse T, Dalton C. Multiphase Actuation of AC Electrothermal Micropump. *Micromachines*. 2023; 14(4):758.
https://doi.org/10.3390/mi14040758

**Chicago/Turabian Style**

Cenaiko, Stirling, Thomas Lijnse, and Colin Dalton. 2023. "Multiphase Actuation of AC Electrothermal Micropump" *Micromachines* 14, no. 4: 758.
https://doi.org/10.3390/mi14040758