A valveless piezoelectric pump with novel flow path design of function of rectification to improve energy efficiency

Abstract

Existing valveless piezoelectric pumps are mostly based on the flow resistance mechanism to generate unidirectional fluid pumping, resulting in inefficient energy conversion because the majority of mechanical energy is consumed in terms of parasitic loss. In this paper, a novel tube structure composed of a Y-shaped tube and a ȹ-shaped tube was proposed considering theory of jet inertia and vortex dissipation for the first time to improve energy efficiency. After verifying its feasibility through the flow field simulation, the proposed tubes were integrated into a piezo-driven chamber, and a novel valveless piezoelectric pump with the function of rectification (NVPPFR) was reported. Unlike previous pumps, the reported pump directed the reflux fluid to another flow channel different from the pumping fluid, thus improving pumping efficiency. Then, mathematical modeling was established, including the kinetic analysis of vibrator, flow loss analysis of fluid, and pumping efficiency. Eventually, experiments were designed, and results showed that NVPPFR had the function of rectification and net pumping effect. The maximum flow rate reached 6.89 mL/min, and the pumping efficiency was up to 27%. The development of NVPPFR compensated for the inefficiency of traditional valveless piezoelectric pumps, broadening the application prospect in biomedicine and biology fields.

Key words： composite tube; valveless piezoelectric pump; rectification; energy efficiency

Appendix

Figure A1 is the simplified hydrodynamic model of fluid flow in the composite tube. In Fig. A1(a), the average velocity u_{13} of the fluid at cross-section 3‒3 was regarded as equally distributed velocity when the fluid flowed in direction 1. At Section A, the fluid was considered jet flow, the diffusion angle of jet flow was \beta, and the thickness of the jet diffused in a linear manner. Thus, the velocity u_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }} of the fluid on the cross-section {\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime } was approximately in the form of Gaussian normal distribution. Therefore, the velocity equation on the cross-section {\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime } could be expressed as

Fig.A1 Model of fluid dynamics in composite tube: fluid dynamics at (a) Section A and (b) Section B.

\begin{array}{}\text{(A1)}& u_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}=u_{\text{1m}}\exp \left(-\frac{y_1^2}{b_{\text{half-1}}^2}\right),\end{array}

where u_{1\text{m}} is the maximum velocity of the fluid flowing in direction 1 at cross-section {\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }, and b_{\text{half-1}} is the half characteristic thickness of the jet in direction 1, which is equal to the distance from the place with velocity u_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}=u_{1\text{m}}/\phantom{u_{1\text{m}}\text{e}}\text{e} to axis x_{\text{1}}. When jet thickness diffusion coefficient in direction 1 is {\epsilon }_{\text{coef-1}} and jet thickness in direction 1 is b_{\text{thi-1}}, half-characteristic thickness b_{\text{half-1}} is given by b_{\text{half-1}}={\epsilon }_{\text{coef-1}}{b}_{\text{thi-1}}.

According to the conservation of momentum flux of the jet between sections mn and {\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }, the following relationship could be obtained:

\begin{array}{}\text{(A2)}& \rho u_{13}^{2}d={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\rho u_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}^2\mathrm{d}{y}_1.\end{array}

Substituting Eq. (A1) into Eq. (A2), the maximum velocity u_{\text{1m}} could be written as

\begin{array}{}\text{(A3)}& u_{\text{1m}}={\left(\frac{2d^2}{\text{π}{b}_{\text{half-1}}^2}\right)}^{\frac{1}{2}}{u}_{13}.\end{array}

Therefore, on the x₁‒y₁ plane, the flow rates Q_{\text{S15}} and Q_{\text{S17}} for the flow of the fluid from Section 3‒3 to Sections 5‒5 and 7‒7 are expressed as a matrix for

\begin{array}{}\text{(A4)}& \left[\begin{array}{c}{Q}_{\text{S15}}\\ Q_{\text{S17}}\end{array}\right]=\left[\begin{array}{c}{\int }_{d/2}^{\mathrm{\infty }}{u}_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}\mathrm{d}{y}_1\\ {\int }_{-\mathrm{\infty }}^{d/2}{u}_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}\mathrm{d}{y}_1\end{array}\right].\end{array}

When flowing in direction 1, dimensionless parameter {\lambda }_1 can be used to express the velocity ratios of fluid in Channels 1 and 2. Thus, the velocity ratios was approximated as

\begin{array}{}\text{(A5)}& {\lambda }_{\text{1}}=\frac{Q_{\text{S15}}}{Q_{\text{S17}}}=\frac{{\int }_{d/2}^{\mathrm{\infty }}{u}_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}\mathrm{d}{y}_1}{{\int }_{-\mathrm{\infty }}^{d/2}{u}_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}\mathrm{d}{y}_1}.\end{array}

Given that kinetic energy is a quadratic function of velocity, the relationship of the kinetic energy of fluid in Channels 1 and 2 was expressed as

\begin{array}{}\text{(A6)}& \frac{E_{r11}}{E_{r12}}={\lambda }_1^2,\end{array}

where E_{r11} is the kinetic energy of fluid in Channel 1 when fluid flows in direction 1, and E_{r12} is the kinetic energy of fluid in Channel 2 when fluid flows in direction 1.

The fluid dynamics at Section B was also analyzed based on the flow characteristics of the jet. In Fig. A1(b), when the fluid flowed from direction 2, the velocity equation on Section {\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime } was expressed as

\begin{array}{}\text{(A7)}& u_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}=u_{\text{2m}}\exp \left(-\frac{y_2^2}{b_{\text{half-}2}^2}\right),\end{array}

where u_{\text{2m}} is the maximum velocity of the fluid flowing in direction 2 at cross-section {\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }, and b_{\text{half-2}} is the half-characteristic thickness of jet, which is equal to the distance from the place with velocity u_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}=u_{\text{2m}}/\phantom{u_{\text{2m}}\text{e}}\text{e} to axis x_{\text{2}}. When thickness diffusion coefficient of the jet is {\epsilon }_{\text{coef-}2} and jet thickness is b_{\text{thi-2}}, half-characteristic thickness b_{\text{half-2}} is given by b_{\text{half-2}}={\epsilon }_{\text{coef-}2}{b}_{\text{thi-2}}.

Therefore, on thex₂‒y₂ plane, flow rates Q_{\text{S26}}, Q_{\text{S27}}, and Q_{\text{S28}} for the flow of the fluid from Section 9‒9 to Sections 6‒6, 7‒7, and 8‒8 were expressed as a matrix for

\begin{array}{}\text{(A8)}& \left[\begin{array}{c}{Q}_{\text{S26}}\\ Q_{\text{S27}}\\ Q_{\text{S28}}\end{array}\right]=\left[\begin{array}{c}{\int }_{d/2}^{\mathrm{\infty }}{u}_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}\mathrm{d}{y}_2\\ {\int }_{-\mathrm{\infty }}^{d/2}{u}_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}\mathrm{d}{y}_2\\ 2{\int }_0^{d/2}{u}_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}\mathrm{d}{y}_2\end{array}\right].\end{array}

When the fluid flowed in direction 2, dimensionless parameter {\lambda }_2 can be used to express the velocity ratios of fluid in Channels 1 and 2. Thus, {\lambda }_2 can be written as

\begin{array}{}\text{(A9)}& {\lambda }_2\text{=}\frac{Q_{\text{S28}}}{Q_{\text{S26}}+Q_{\text{S27}}}=\frac{{\int }_0^{d/2}{u}_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}\mathrm{d}{y}_2}{{\int }_{d/2}^{\mathrm{\infty }}{u}_{{\mathrm{g}}^{\prime }{\mathrm{h}}^{\prime }}\mathrm{d}{y}_2}.\end{array}

Therefore, the relationship of the kinetic energy of fluid in Channels 1 and 2 was expressed as

\begin{array}{}\text{(A10)}& \frac{E_{r22}}{E_{r21}}={\lambda }_2^2,\end{array}

where E_{r21} is the kinetic energy of fluid in Channel 1 when fluid flowed in direction 2, and E_{r22} is the kinetic energy of fluid in Channel 2 when fluid flowed in direction 2.

According to jet inertia, the larger the flow velocity u of the fluid is, the smaller the diffusion angle of the jet. Thus, the value of dimensionless parameter {\lambda }_i satisfies the following relationship:

\begin{array}{}\text{(A11)}& \underset{u\to \mathrm{\infty }}{lim}{\lambda }_i=\mathrm{\infty }.\end{array}

Nomenclature

b_{\text{half-}i}	Half characteristic thickness of jet in direction i
b_{\text{thi-}i}	Jet thickness in direction i
C_{\text{ε}}	Damping of the vibrator
C_{\text{H}}	Attachment damping causing by fluid coupling
d	Diameter of cross-section of tube
D	Diameter of pump chamber
D0	Diameter of piezoelectric vibrator
E	Mechanical energy generated by the deformation of entire surface of piezoelectric vibrator
E0	Initial kinetic energy of fluid
\mathrm{\Delta }E	Kinetic energy loss of fluid
{\mathit{E}}_{ir}	Kinetic energy of the fluid
\mathrm{\Delta }{\mathit{E}}_i	Total energy loss of fluid flowing
\mathrm{\Delta }{\mathit{E}}_{i\text{e}}	Extra kinetic energy loss of fluid
\mathrm{\Delta }{\mathit{E}}_{ir}	Kinetic energy loss of fluid
E\left(r,\theta \right)	Kinetic energy at the point above the piezoelectric vibrator
f	Working frequency of the piezoelectric vibrator
f_{max}	Function that takes the maximum value
f_{min}	Function that takes the minimum value
f_n	Resonance frequency
F	Vector sum of the exciting force
h	Chamber height
H	Distance between composite tubes and pump chamber
K	Stiffness of the elastic system
K_{\mathrm{H}}	Attachment stiffness causing by fluid coupling
K_{\text{ε}}	Stiffness of the vibrator
L_1	Length of the confluence tube
L_2	Length of the straight tube
l_{ir}	Prandtl mixing length
m	Mass of the piezoelectric vibrator
M	Mass of elastic system
M_{\mathrm{H}}	Attachment mass causing by fluid coupling
M_{\text{ε}}	Mass of the vibrator
P_{\text{f}}, P_{\text{r}}	Forward and reverse pressures, respectively
q, \dot{q}, \ddot{q}	Displacement, velocity, and acceleration of the piezoelectric vibrator, respectively
Q	Flow rate of pump
R_0	Radius of bend tube
R1, R2	Radii of the semi-arc tube
s	Distance between chamber outlets
S	Sectional area of the composite tube
t	Time
u	Sum of velocity vectors of fluid at the outer joint
u_0	Fluid velocity of the chamber outlet
u_{1\text{m}}	Maximum velocity of the fluid flowing in direction 1 at cross-section {\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }
u_{{\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }}	Velocity of the fluid on the cross-section {\mathrm{m}}^{\prime }{\mathrm{n}}^{\prime }
\mathrm{\Delta }V	Volume variation of pump chamber in a half period
\left(r,\theta \right)	Polar point
\alpha	Bifurcation angle of tubes
\beta	Diffusion angle of jet flow
{\epsilon }_{\text{coef-}i}	Thickness diffusion coefficient in direction i
\rho	Density of the fluid
\eta	Pumping efficiency in the outer joint
{\eta }_r	Pumping efficiency in Channel r
{\mathit{\zeta }}_{ir}	Energy loss coefficient in the direction i inside flow channel r
{\mathit{\zeta }}_{i\text{e}}	Extra energy loss coefficient when fluid flowed in the direction i
{\tau }_{ir1}	Shear stress in the direction i
{\tau }_{ir2}	Turbulent shear stress in the direction i
{\lambda }_i	Velocity ratios of fluid between Channels 1 and 2
{\mu }_{ir}	Dynamic coefficient of viscosity
{\displaystyle \frac{\mathrm{d}{\mu }_{ir}}{\mathrm{d}{y}_{ir}}}	Velocity gradient of fluid
Subscript
i (i = 1,2)	Flow direction i
r (r = 1,2)	Flow channel r

Credit author statement

Jianhui Zhang: methodology, formal analysis, project administration, resources, and funding acquisition. Xiaosheng Chen: formal analysis, validation, investigation, and writing (original draft, review and editing). Zhenlin Chen: software and formal analysis. Jietao Dai: software and visualization. Fan Zhang: writing (review and editing). Mingdong Ma: data curation. Yuxuan Huo: data curation. Zhenzhen Gui: conceptualization, formal analysis, project administration, resources, supervision, and funding acquisition.

Acknowledgements

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. This work was financially supported by Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2019B1515120017), Regional Joint Youth Fund Project of Guangdong Basic and Applied Basic Research, China (Grant No. 2020A1515110619), and Guangzhou Science and Technology Plan Project, China (Grant No. 202002030356).

References

1 CastillaR, Gamez-MonteroP J, ErtürkN, VernetA, CoussiratM, CodinaE. Numerical simulation of turbulent flow in the suction chamber of a gearpump using deforming mesh and mesh replacement. International Journal of Mechanical Sciences, 2010, 52( 10): 1334– 1342

2 Arun ShankarV K, SubramaniamU, ParamasivamS, HanigovszkiN. A comprehensive review on energy efficiency enhancement initiatives in centrifugal pumping system. Applied Energy, 2016, 181 : 495– 513

3 WangT, WangC, KongF Y, GouQ Q, YangS S. Theoretical, experimental, and numerical study of special impeller used in turbine mode of centrifugal pump as turbine. Energy, 2017, 130 : 473– 485

4 WangZ Y, QianZ D, LuJ, WuP F. Effects of flow rate and rotational speed on pressure fluctuations in a double-suction centrifugal pump. Energy, 2019, 170 : 212– 227

5 LiuH, ZhaoB Y, ZhangZ P, LiH B, HuB, WangR Z. Experimental validation of an advanced heat pump system with high-efficiency centrifugal compressor. Energy, 2020, 213 : 118968

6 NguyenN T, HuangX Y, ChuanT K. MEMS-micropumps: a review. Journal of Fluids Engineering, 2002, 124( 2): 384– 392

7 NguyenN T, TruongT Q. A fully polymeric micropump with piezoelectric actuator. Sensors and Actuators B: Chemical, 2004, 97( 1): 137– 143

8 ChoiS B, YooJ K, ChoM S, LeeY S. Position control of a cylinder system using a piezoactuator-driven pump. Mechatronics, 2005, 15( 2): 239– 249

9 Yakut AliM, KuangC F, KhanJ, WangG R. A dynamic piezoelectric micropumping phenomenon. Microfluidics and Nanofluidics, 2010, 9( 2–3): 385– 396

10 ZhangR H, YouF, LvZ H, HeZ C, WangH W, HuangL. Development and characterization a single-active-chamber piezoelectric membrane pump with multiple passive check valves. Sensors, 2016, 16( 12): 2108

11 ZhangJ H, WangY, HuangJ. Advances in valveless piezoelectric pump with cone-shaped tubes. Chinese Journal of Mechanical Engineering, 2017, 30( 4): 766– 781

12 YeY, ChenJ, RenY J, FengZ H. Valve improvement for high flow rate piezoelectric pump with PDMS film valves. Sensors and Actuators A: Physical, 2018, 283 : 245– 253

13 BaoQ B, ZhangJ H, TangM, HuangZ, LaiL Y, HuangJ, WuC Y. A novel PZT pump with built-in compliant structures. Sensors, 2019, 19( 6): 1301

14 PengT J, GuoQ Q, YangJ, XiaoJ F, WangH, LouY, LiangX. A high-flow, self-filling piezoelectric pump driven by hybrid connected multiple chambers with umbrella-shaped valves. Sensors and Actuators B: Chemical, 2019, 301 : 126961

15 WooJ, SohnD K, KoH S. Performance and flow analysis of small piezo pump. Sensors and Actuators A: Physical, 2020, 301 : 111766

16 LiH Y, LiuJ K, LiK, LiuY X. A review of recent studies on piezoelectric pumps and their applications. Mechanical Systems and Signal Processing, 2021, 151 : 107393

17 ValdovinosJ, WilliamsR J, LeviD S, CarmanG P. Evaluating piezoelectric hydraulic pumps as drivers for pulsatile pediatric ventricular assist devices. Journal of Intelligent Material Systems and Structures, 2014, 25( 10): 1276– 1285

18 MaH K, ChenR H, YuN S, HsuY H. A miniature circular pump with a piezoelectric bimorph and a disposable chamber for biomedical applications. Sensors and Actuators A: Physical, 2016, 251 : 108– 118

19 OpekarF, NesměrákK, TůmaP. Electrokinetic injection of samples into a short electrophoretic capillary controlled by piezoelectric micropumps. Electrophoresis, 2016, 37( 4): 595– 600

20 HaberJ M, GascoyneP R C, SokolovK. Rapid real-time recirculating PCR using localized surface plasmon resonance (LSPR) and piezo-electric pumping. Lab on a Chip, 2017, 17( 16): 2821– 2830

21 SakumaS, KasaiY, HayakawaT, AraiF. On-chip cell sorting by high-speed local-flow control using dual membrane pumps. Lab on a Chip, 2017, 17( 16): 2760– 2767

22 WangY N, FuL M. Micropumps and biomedical applications—a review. Microelectronic Engineering, 2018, 195 : 121– 138

23 ChenS, LiuH D, JiJ J, KanJ W, JiangY H, ZhangZ H. An indirect drug delivery device driven by piezoelectric pump. Smart Materials and Structures, 2020, 29( 7): 075030

24 SinghalV, GarimellaS V, RamanA. Microscale pumping technologies for microchannel cooling systems. Applied Mechanics Reviews, 2004, 57( 3): 191– 221

25 TangY, JiaM Z, DingX R, LiZ T, WanZ P, LinQ H, FuT. Experimental investigation on thermal management performance of an integrated heat sink with a piezoelectric micropump. Applied Thermal Engineering, 2019, 161 : 114053

26 KaynakM, OzcelikA, NamaN, NourhaniA, LammertP E, CrespiV H, HuangT J. Acoustofluidic actuation of in situ fabricated microrotors. Lab on a Chip, 2016, 16( 18): 3532– 3537

27 WangX R, JiangH W, ChenY C, QiaoX, DongL. Microblower-based microfluidic pump. Sensors and Actuators A: Physical, 2017, 253 : 27– 34

28 ZhaoB, CuiX Y, RenW, XuF, LiuM, YeZ G. A controllable and integrated pump-enabled microfluidic chip and its application in droplets generating. Scientific Reports, 2017, 7( 1): 11319

29 ZhangT, WangQ M. Valveless piezoelectric micropump for fuel delivery in direct methanol fuel cell (DMFC) devices. Journal of Power Sources, 2005, 140( 1): 72– 80

30 MaH K, HuangS H, KuoY Z. A novel ribbed cathode polar plate design in piezoelectric proton exchange membrane fuel cells. Journal of Power Sources, 2008, 185( 2): 1154– 1161

31 DauV T, DinhT X, KatsuhikoT, SusumuS. A cross-junction channel valveless-micropump with PZT actuation. Microsystem Technologies, 2009, 15( 7): 1039– 1044

32 XiaQ X, ZhangJ H, LeiH, ChengW. Analysis on flow field of the valveless piezoelectric pump with two inlets and one outlet and a rotating unsymmetrical slopes element. Chinese Journal of Mechanical Engineering, 2012, 25( 3): 474– 483

33 TsengL Y, YangA S, LeeC Y, ChengC H. Investigation of a piezoelectric valveless micropump with an integrated stainless-steel diffuser/nozzle bulge-piece design. Smart Materials and Structures, 2013, 22( 8): 085023

34 HuangJ, ZhangJ H, XunX C, WangS Y. Theory and experimental verification on valveless piezoelectric pump with multistage Y-shape treelike bifurcate tubes. Chinese Journal of Mechanical Engineering, 2013, 26( 3): 462– 468

35 LengX F, ZhangJ H, JiangY, ZhangJ Y, SunX C, LinX G. Theory and experimental verification of spiral flow tube-type valveless piezoelectric pump with gyroscopic effect. Sensors and Actuators A: Physical, 2013, 195 : 1– 6

36 KimC N. Internal pressure characteristics and performance features of the piezoelectric micropumps with the diffuser/nozzle and electromagnetic resistance. Computers & Fluids, 2014, 104 : 30– 39

37 WeiY, TorahR, YangK, BeebyS, TudorJ. A novel fabrication process to realize a valveless micropump on a flexible substrate. Smart Materials and Structures, 2014, 23( 2): 025034

38 HuangJ, ZhangJ H, ShiW D, WangY. 3D FEM analyses on flow field characteristics of the valveless piezoelectric pump. Chinese Journal of Mechanical Engineering, 2016, 29( 4): 825– 831

39 HeX H, ZhuJ W, ZhangX T, XuL, YangS. The analysis of internal transient flow and the performance of valveless piezoelectric micropumps with planar diffuser/nozzles elements. Microsystem Technologies, 2017, 23( 1): 23– 37

40 ZhangJ H, WangY, HuangJ. Equivalent circuit modeling for a valveless piezoelectric pump. Sensors, 2018, 18( 9): 2881

41 JiJ J, ChenS, XieX Y, WangX M, KanJ W, ZhangZ H, LiJ P. Design and experimental verification on characteristics of valve-less piezoelectric pump effected by valve hole spacing. IEEE Access: Practical Innovations, Open Solutions, 2019, 7 : 36259– 36265

42 HuangJ, ZouL, TianP, ZhangQ, WangY, ZhangJ H. A valveless piezoelectric micropump based on projection micro litho stereo exposure technology. IEEE Access: Practical Innovations, Open Solutions, 2019, 7 : 77340– 77347

43 ParkJ H, YoshidaK, YokotaS. Resonantly driven piezoelectric micropump: fabrication of a micropump having high power density. Mechatronics, 1999, 9( 7): 687– 702

44 ParkJ H, YoshidaK, NakasuY, YokotaS, SetoT, TakagiK. A resonantly-driven piezoelectric micropump for microfactory. In: Proceedings of the 6th International Conference on Mechatronics Technology. Tokyo, 2002, 417– 422

45 ParkJ H, YoshidaK, YokotaS, SetoT, TakagiK. Development of micro machines using improved resonantly-driven piezoelectric micropumps. In: Proceedings of the 4th International Symposium on Fluid Power Transmission and Control (ISFP’2003). Wuhan, 2003, 536– 541

46 WangX Y, MaY T, YanG Y, FengZ H. A compact and high flow-rate piezoelectric micropump with a folded vibrator. Smart Materials and Structures, 2014, 23( 11): 115005

47 WangX Y, MaY T, YanG Y, HuangD, FengZ H. High flow-rate piezoelectric micropump with two fixed ends polydimethylsiloxane valves and compressible spaces. Sensors and Actuators A: Physical, 2014, 218 : 94– 104

48 MohithS, KaranthP N, KulkarniS M. Performance analysis of valveless micropump with disposable chamber actuated through amplified piezo actuator (APA) for biomedical application. Mechatronics, 2020, 67 : 102347

49 MohithS, MuralidharaR, KaranthP N, KulkarniS M, UpadhyaA R. Development and assessment of large stroke piezo-hydraulic actuator for micro positioning applications. Precision Engineering, 2021, 67 : 324– 338

50 MohithS, KaranthP N, KulkarniS M. Analysis of annularly excited bossed diaphragm for performance enhancement of mechanical micropump. Sensors and Actuators A: Physical, 2022, 335 : 113381

51 WuY, LiuY, LiuJ F, WangL, JiaoX Y, YangZ G. An improved resonantly driven piezoelectric gas pump. Journal of Mechanical Science and Technology, 2013, 27( 3): 793– 798

52 ChenJ, HuangD, FengZ H. A U-shaped piezoelectric resonator for a compact and high-performance pump system. Smart Materials and Structures, 2015, 24( 10): 105009

53 WangJ T, ZhaoX L, ChenX F, YangH R. A piezoelectric resonance pump based on a flexible support. Micromachines, 2019, 10( 3): 169

54 PanQ S, HeL G, HuangF S, WangX Y, FengZ H. Piezoelectric micropump using dual-frequency drive. Sensors and Actuators A: Physical, 2015, 229 : 86– 93

55 SayarE, FaroukB. Dynamic analysis of bulk acoustic wave piezoelectric micropumps: effects of inlet-outlet port angles and overall pump size. In: Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 10: Micro- and Nano-Systems Engineering and Packaging. San Diego: ASME, 2013, IMECE2013-66211, V010T11A027

56 MaH K, ChenR H, HsuY H. Development of a piezoelectric-driven miniature pump for biomedical applications. Sensors and Actuators A: Physical, 2015, 234 : 23– 33

57 ZhaoD, HeL P, LiW, HuangY, ChengG M. Experimental analysis of a valve-less piezoelectric micropump with crescent-shaped structure. Journal of Micromechanics and Microengineering, 2019, 29( 10): 105004

58 KaçarA, ÖzerM B, TaşcıoğluY. A novel artificial pancreas: energy efficient valveless piezoelectric actuated closed-loop insulin pump for T1DM. Applied Sciences, 2020, 10( 15): 5294

59 ZhangB C, HuangY, HeL P, XuQ W, ChengG M. Research on double-outlet valveless piezoelectric pump with fluid guiding body. Sensors and Actuators A: Physical, 2020, 302 : 111785

60 EggersJ, VillermauxE. Physics of liquid jets. Reports on Progress in Physics, 2008, 71( 3): 036601