A simulation and experimental study of a valveless piezoelectric micropump based on the synthetic jet principle

Over the past few years, piezoelectric (PE) micropump technology has developed rapidly in fields including biomedicine and microfluidic control. Research on valved and valveless PE pumps has also become a hot topic.^1,2 Traditional valved-based PE pumps use valves to control the flow direction of a fluid, which can prevent backflow during operation.^3,4 However, the valve structure makes it difficult to further increase the output flow rate. In addition, valves are prone to wear and clogging during use, affecting the pump stability and reliability.^5,6 Valved-based PE pumps also require larger sizes to contain their valves, which limits their applicability in miniaturized and portable devices.

Valveless PE pumps have been widely utilized because of their small sizes, low power consumption, and ease of miniaturization. Currently, most valveless PE pumps utilize differently shaped inlet and outlet ports to achieve unidirectional flow.^7,8 This design principle helps to create a directional flow of the fluid, which is essential for the effective operation of the pump. However, one significant challenge faced by these pumps is the inherent issue of backflow.^9,10 Backflow results in a decrease in the conversion efficiency of the pump and hinders its overall performance. In addition to the traditional valveless PE pump, there is also a bionic valveless PE pump inspired by the structure and movement principles of biological organisms.^11,12 The specific structure and movement principles required to mimic biological systems often result in complex and delicate designs. This complexity can make the pumps more challenging to manufacture and integrate into various systems, thus greatly limiting their use scenarios.

Glezer first discovered and studied the synthetic jet phenomenon and proposed the principle of the synthetic jet, opening up a new direction for research on valveless PE micropumps.¹³ Since then, further research has shown that the output flow rate of PE micropumps designed using the synthetic jet principle is greater than the change in the internal volume of the cavity.^14,15 When the micropump is in the suction stage, it has no impact on the discharged fluid flow rate, which greatly improves the efficiency of the pump. Valveless PE pumps based on the synthetic jet principle utilize vortices formed by jet orifices to achieve unidirectional flow. Clever designs of the structure and channel shape of micropumps can improve their efficiency and performance while also achieving miniaturization and a high output flow rate. The synthetic jet pump is also widely used in heat dissipation.^16–18 High-flowrate, miniaturized synthetic jet pumps are very suitable for embedding in electronic devices to provide heat dissipation for microdevices. Liu and Zhu developed two models of synthetic jet direct-injection piezoelectric pumps, called the single-chamber and dual-chamber models.¹⁹ Under the excitation of a sinusoidal voltage signal of 150 V_pp and 2.85 kHz, the output flow rates of the single-chamber and dual-chamber pumps reached 2.1 L/min and 2.43 L/min, respectively, providing a new foundation for the development of synthetic jet piezoelectric pumps in the electronic cooling field. However, noise generated in the low-frequency resonant state has also become an urgent problem. Ghaffari et al. proposed an investigation into the flow and heat transfer of an ultrasonic micro-blower device for electronics cooling applications.²⁰ Their study found that ultrasonic frequencies above 20 kHz can be used as the first-order resonant frequencies of synthetic jet actuators to solve the problem of excessive noise when the device works at the resonant point. However, this does result in a certain performance loss. Table I summarizes the critical contributions of some researchers in the field of synthetic jet micropumps, but there have been few studies on the output of significant flow rates at ultrasonic frequencies.

This work proposes a PE micropump design based on the synthetic jet principle, with a size of 22 × 22 × 5 mm³. The designed structure is numerically simulated using COMSOL Multiphysics simulation software to improve the output performance, and a prototype is made for experimental research using a laser cutting method. First, the vibration mode and impedance curve of the PE micropump are simulated using the two-dimensional axisymmetric model, and the process of synthetic jet formation within a cycle is simulated. Second, the influence of structural parameters such as the jet hole, outlet diameter, inlet, and jet cavity height of the synthetic jet PE micropump on the performance of the PE micropump are simulated and analyzed. Finally, a PE micropump is fabricated based on the simulation structure for experimental analysis. The experimental results show that under the excitation of 42 V_pp and 22.5 kHz sinusoidal wave signals, the central displacement of the PE actuator and the maximum output flow rate of the PE pump can reach 12.3 um and 618 mL/min, and the power dissipation does not exceed 600 mW. It is ultimately determined that a PE micropump based on the synthetic jet principle proposed in this paper can operate in the ultrasonic frequency band above 20 kHz with a high flow rate and low power dissipation, providing a feasible solution for the application of PE micropumps in chip heat dissipation and gas transportation.

The working principle of the PE pump is shown in Fig. 1(a). Under the excitation of an alternating signal, the PE actuator vibrates vertically and periodically. When the PE actuator moves downward, the volume in the jet chamber becomes larger, and as the gas pressure decreases, the gas is sucked into the chamber through the air inlets on both sides. In the next stage, when the PE actuator moves upward, gas flows out through the jet orifice.

During the alternating inhalation and exhalation processes, the gas near the jet orifice is prone to intense shear forces, resulting in the formation of counter-rotating vortices. With proper structural design, these vortices carry the jet flow toward the outlet, thereby generating synthetic jets. Before the next inhalation process begins, the vortices move away from the jet orifice and are not drawn back into the jet chamber. Thus, the PE pump achieves unidirectional flow.

An expanded view of the PE pump is shown in Fig. 1(b). It consists primarily of three parts: the PE actuator, the jet chamber, and the shell. These components are assembled in a stacked manner to reduce assembly complexity. The PE actuator is composed of a basal plate and lead zirconate titanate (PZT) and is bonded to the lower surface of the jet chamber with epoxy resin glue. The jet chamber is formed by stacking three layers, with the outlet and inlet placed in the center and around the upper shell layers, respectively. These two shell layers enclose the entire pump body. Gas is drawn in through the inlet on both sides, flows through the jet chamber, where synthetic jets are formed near the jet orifices, and is finally expelled through the outlet on the upper shell.

To ensure the PE micropump works at an ultrasonic frequency and generates a synthetic jet phenomenon to increase the output flow rate, the sizes of the different components of the PE micropump are critical. In this paper, the diameter of the PE actuator is selected as 11 mm, and the diameter of the jet chamber is 14 mm. A finite element method (FEM) from COMSOL Multiphysics (COMSOL 6.0) was used to perform modal and fluid-structure interaction simulations. The jet orifice diameter, outlet diameter, inlet height, and jet chamber height of the PE micropump were simulated and optimized. The simulation model and boundary conditions are shown in Fig. 2(a). The key parameters in the simulation model are listed in Table II.

As the core component driving the PE micropump, the vibration mode of the PE actuator has a great influence on the output flow rate and pressure. An FEM simulation of the PE actuator was conducted, and its impedance curve was obtained in the range of 10–35 kHz. It was observed that the frequency value at the lowest impedance point was 22.5 kHz, which is the characteristic frequency point in the first-order mode of the PE actuator. The impedance curve and the central vibration displacement of the PE actuator as a function of frequency are shown in Fig. 2(b).

It is important for the PE pump to generate spray-type synthetic jets near the jet orifices during its operation. For the structure considered here, the diameter of the jet chamber is 14 mm, and the diameter of the jet orifice is 0.6 mm. According to Eq. (1), C is 4.7, which is much larger than the value required to form a synthetic jet. The simulated flow velocity results are shown in Fig. 3. Within a vibration cycle, the formation process of the synthetic jet can be easily observed. In the first half of the cycle, the pump is in the suction stage, and gas flows into the jet chamber from the inlet. In the second half of the cycle, the pump is in the exhaust stage, and the gas is discharged from the pump body through the outlet. The formation of a synthetic jet can be clearly seen near the jet orifice during the discharge stage. When the next cycle comes, the jet moves away from the jet orifice and is discharged through the outlet.

The effects of various structural parameters on the output flow rate of the PE micropump were examined. Using the control variable method, under the same voltage and frequency drive signal (42 V_pp, 22.5 kHz), simulations were conducted for different jet orifice diameters d₃ (0.4, 0.5, 0.6, 0.7, 0.8 mm), outlet diameters d₄ (0.6, 0.7, 0.8, 0.9, 1.0 mm), inlet heights h₁ (0.2, 0.3, 0.4, 0.5, 0.6 mm) and jet chamber heights h₂ (0.1, 0.12, 0.15, 0.18, 0.2 mm), and the output flow rates were obtained, as shown in Fig. 4.

As shown in Fig. 4(a), the output flow rate first increases and then decreases with an increase in the diameter d₃ of the jet orifice, and there is an optimal value of 0.6 mm. A substantial diameter can lead to a significant backflow of gas into the jet chamber, undermining the system's efficiency. Conversely, an overly small diameter increases resistance to gas discharge, thereby reducing the output flow rate. There is a critical value of 0.8 mm for the outlet diameter d₄, as shown in Fig. 4(b). This is because the diameter of the outlet is too small, which is not conducive to the smooth discharge of the vortex pair formed by the synthetic jet, and a larger outlet diameter means a greater backflow, resulting in a reduction in the output flow rate.

As shown in Fig. 4(c), the inlet height h₁ has a great influence on the output flow rate of the PE micropump. When the height of the inlet is too high, the distance between the jet orifice and the outlet is too large, and the output flow rate decreases. When the height is too small, the flow resistance increases, which also leads to a decrease in output gas. The optimal value is 0.4 mm. However, the jet chamber height h₂ has a limited effect on the output flow rate of the PE micropump, as shown in Fig. 4(d). Considering the thickness control of the overall device, a height of 0.15 mm was finally chosen.

Ultimately, the simulation results show that for the optimized PE pump under an excitation signal of 42 V_pp at 22.5 kHz, the central displacement of the PE actuator can reach 11.2 μm, and the output flow rate of the PE pump is around 597 mL/min.

In order to verify the accuracy of the simulation and the feasibility of the design, an experimental analysis of the displacement and flow rate of the PE pump was conducted. The pump chamber and basal plate of the jet pump were made by laser cutting stainless steel 304, while the upper and lower shells were made of 3D printed resin. The PE actuator and the jet chamber were bonded with epoxy resin glue, and the upper and lower shells were bonded with polyamide double-sided tape. The assembled synthetic jet pump is shown in Fig. 5(a), with an overall size of 22 × 22 × 5 mm³.

The flow rate, the displacement of the PE actuator, and the power dissipation of the synthetic jet pump prototype were tested. The test method was as follows: a sine wave signal was generated by a signal generator (RIGOL DG811), amplified by a power amplifier (Aigtek ATA-2022H), and connected to the two power supply terminals of the PE actuator. The flow rate was tested by a flowmeter (ASAIR 2106), the displacement of the PE actuator was tested by a laser scanning vibrometer (LV-RFS01), and the overall power dissipation of the synthetic jet pump was tested by a power meter (YOKOGAWA WT310).

Experiments for different structural parameters of the pump were conducted to evaluate the impact of each parameter on the output performance and the reliability of the simulation. The simulated optimal structural parameters were adopted as a control sample (Sample R). The key dimensions were a jet orifice diameter of 0.6 mm, an outlet diameter of 0.8 mm, an inlet height of 0.4 mm, and a jet chamber height of 0.15 mm. Samples were created to conduct comparative experiments by changing one parameter each time. The specific parameters of the samples are listed in Table III. Three different variables were selected for each parameter to determine the resulting trend. Using the same excitation signal, the output flow rate of each sample was determined, as shown in Fig. 5(b). The experimental results show that changes in the diameter of the jet orifice, the diameter of the outlet, and the height of the inlet have a significant impact on the flow rate, while the height of the jet chamber has little effect. This is consistent with the simulation results.

Further experimental analysis was performed on Sample 1. Driven by a sine wave signal with a peak-to-peak value of 42 V_pp, the output flow rate of the synthetic jet pump and the maximum central displacement of the PE actuator in the frequency range of 21.4–24.0 kHz were obtained, as shown in Fig. 6(a). The jet pump had a maximum output flow rate at a frequency between 21.6 and 22.5 kHz, and the flow rate was maintained at 618 mL/min. Additionally, the maximum central displacement of the PE actuator reached 12.3 μm, which is slightly smaller than the simulation result. The overall performance was consistent with the simulation results.

The output flow rate and the maximum central displacement of the PE actuator under the excitation of different amplitude voltage signals were also tested. It can be seen from Fig. 5(b) that the greater the sine wave driving voltage, the greater the output flow rate of the synthetic jet pump and the greater the maximum central displacement of the PE actuator.

The power dissipation of a synthetic jet pump also determines its application scenarios and efficiency. The power dissipation of the device under different voltages and frequencies was tested. As shown in Figs. 6(c) and 6(d), within the voltage range of 20–45 V_pp and the frequency range of 21.4–24.0 kHz, the power dissipation of the synthetic jet PE micropump did not exceed 600 mW.

This work has presented a valveless piezoelectric (PE) micropump driven by piezoelectric ceramics that applies the synthetic jet principle to achieve unidirectional gas flow and high output performance. The characteristics and performance of the pump were studied through simulation and experiments, and the effects of the key parameters of the pump on the flow rate performance were analyzed. Experimental results have shown that under sine wave excitation with an amplitude of 42 V_pp and a frequency of 22.5 kHz, the central displacement of the PE and the maximum output flow rate of the PE pump can reach 12.3 μm and 618 mL/min, respectively, consistent with finite element method (FEM) results. The PE micropump can achieve a higher output flow rate and a low power dissipation of no more than 600 mW at ultrasonic frequencies. The performance of the pump demonstrates the potential of this device in the fields of chip heat dissipation and gas transportation.

This work was funded by National Natural Science Foundation of China (No. U20A20172, U24A20222), Zhejiang Province Key R&D programs (No. 2023C01192). The work was supported by the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK239909299001).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Wencheng Lv was born in Zhejiang. He is currently pursuing an M.S. degree in integrated circuit engineering from Hangzhou Dianzi University. His research interest is the application of micro-nano devices in microfluidics.

Jiafeng Ni was born in Zhejiang. He received an M.S. degree in electronic information engineering from Hangzhou Dianzi University. He is currently pursuing a Ph.D. degree in electronic science and technology at Zhejiang University, Hangzhou, China. His current research interests include microelectromechanical systems (MEMS) and microfluidics.

Weipeng Xuan received a Ph.D. degree in microelectronics and solid electronics from Zhejiang University, Hangzhou, China, in 2017. He is currently a professor at Hangzhou Dianzi University, Hangzhou, China. His current research interests include surface acoustic waves (SAW), bulk acoustic wave (BAW) devices, piezo-MEMS devices, energy harvesting devices, and their applications.

Yixing Li was born in Hunan. He is currently pursuing an M.S. degree in integrated circuit engineering from Hangzhou Dianzi University. His research interest is the application of micro-nano devices in microfluidics.

Xiwei Huang received a Ph.D. degree in circuits and systems from Nanyang Technological University, Singapore, in 2015. He is currently a Professor at Hangzhou Dianzi University, Hangzhou, China. His current research interests include biomedical circuits and systems, microfluidic sensor integrated microsystems, multimodal complementary metal-oxide semiconductor (CMOS) integrated sensors, biomedical artificial intelligence, and embedded medical detection systems.

Lingling Sun obtained a B.S. degree from Nanjing University of Posts and Telecommunications, Nanjing, China, in 1982 and an M.S. degree from the University of Electronic Science and Technology, Chengdu, China, in 1985. She is currently a professor of electronic engineering at Hangzhou Dianzi University, China, and the Chair of the IEEE EDS Hangzhou Branch. Her research interests include the design and computer-aided design (CAD) of radiofrequency (RF) / microwave integrated circuits (ICs) and systems for various applications and the development of intelligent systems and medical equipment. She is the director of the Key Laboratory of RF Circuits and Systems, Ministry of Education, China.

Shurong Dong graduated from the Department of Materials of Zhejiang University with a bachelor's degree and a master's degree, then graduated from the Department of Information Technology of Zhejiang University with a doctoral degree. He is the deputy director of the Institute of Micro-Electronics, the deputy director of the Zhejiang Micro Nano Intelligent System Application Laboratory, a professor, and a doctoral supervisor. He has published 120 papers in SCI journals such as ACS Nano and AM. He has also been interviewed twice on the home page of Electronic Express EL (about Film Bulk Acoustic Resonator and Electro-Static Discharge) and twice by Highlight, the highly-cited quarterly top 10 papers of the Royal Society of the United Kingdom, produced by Elsevier. From 2009 to 2010, he was a visiting professor at the University of Cambridge, and he was a visiting professor at the University of UCF from 2010 to 2011. His research interests include flexible electronics, sensors, and MEMS.

Hao Jin received his B.Sc. and Ph.D. degrees in electronic science and technology from Zhejiang University, P.R. China, in 2001 and 2006, respectively. After graduation, he worked as an RFIC engineer at Semiconductor Manufacturing International Corporation and Maxscend Technologies, P.R. China, to develop a highly accurate RF model of CMOS devices and to design RFIC circuits, respectively. In 2007, he went on to a post-doctoral fellowship and then worked as a faculty member in the Department of Information Science and Electronic Engineering at Zhejiang University, P.R. China. In 2011, he visited the University of Manchester, U.K., as an academic visitor supported by an EPSRC project, developing an FBAR model and investigating its application to biosensors. He became an associate professor of micro/nanodevices in 2012 and visited McMaster University, Canada, in 2017–2018, developing smart sensors and systems for water quality monitoring. His research interests include smart sensors and systems for healthcare and environment science, machine learning, RF/Microwave technology, and magnetron sputtering. His H-index is 22.

Jikui Luo received a Ph.D. degree from the University of Hokkaido, Japan, in 1989. He worked with Cardiff University, Cardiff, U.K., as a research fellow, then at Newport Wafer Fab Ltd., Duffryn, U.K., Philips Semiconductor Company, Manchester, U.K., and Cavendish Kinetics Ltd., Cambridge, U.K., as an engineer, a senior engineer, and a manager, respectively. In 2000, he worked as a senior researcher at Cambridge University, Cambridge, U.K. In January 2007, he became a professor of MEMS at the Institute for Material Research and Innovation (IMRI), University of Bolton, Bolton, U.K. In January 2020, he became a full professor at Zhejiang University, Hangzhou, China. He has published more than 300 peer-reviewed international articles and given more than 220 talks and presentations at international conferences, among which are over 40 plenary or keynote talks. His current research interests include nanomaterials and nanodevices, physical and biochemical sensors, microfluidics and laboratory-on-a-chip, flexible electronics, bioelectronics, energy harvesting technologies, and self-powered wireless microsystems.