Access the full text.
Sign up today, get DeepDyve free for 14 days.
N. Harris, M. Hill, R. Torah, R. Townsend, S. Beeby, N. White, J. Ding (2006)
A multilayer thick-film PZT actuator for MEMs applicationsSensors and Actuators A-physical, 132
R. Haldkar, Abhay Khalatkar, V. Gupta, T. Sheorey (2020)
New piezoelectric actuator design for enhance the micropump flowMaterials Today: Proceedings
Jiantao Wang, Y. Liu, Yanhu Shen, Song Chen, Zhigang Yang (2016)
A Resonant Piezoelectric Diaphragm Pump Transferring Gas with Compact StructureMicromachines, 7
H. Ma, R. Chen, N. Yu, Y. Hsu (2016)
A miniature circular pump with a piezoelectric bimorph and a disposable chamber for biomedical applicationsSensors and Actuators A-physical, 251
Samira Kaviani, M. Bahrami, A. Esfahani, B. Parsi (2014)
A modeling and vibration analysis of a piezoelectric micro-pump diaphragmComptes Rendus Mecanique, 342
A. Amnache, G. Laguna, É. Léveillé, R. Pandiyan, L. Collin, Montse Villarrubi, S. Hamel, J. Barrau, L. Fréchette (2020)
Fabrication and Demonstration of a Self-Adaptive Microvalve Array for Distributed Liquid Cooling in Microelectronic InterposersJournal of Microelectromechanical Systems, 29
Yuanlin Hu, Xin Liang, W. Wang (2017)
A theoretical solution of resonant circular diaphragm-type piezoactuators with added mass loadsSensors and Actuators A-physical, 258
S. Mi, Pu Haitao, Xia Shengyue, Wei Sun (2020)
A Minimized Valveless Electromagnetic Micropump for Microfluidic Actuation on Organ ChipsSensors and Actuators A-physical, 301
O. Jeong, S. Konishi (2007)
Fabrication and drive test of pneumatic PDMS micro pumpSensors and Actuators A-physical, 135
Lihong Zhang, U. Kleine (2002)
A genetic approach to analog module placement with simulated annealing2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 1
C. Mo, Rika Wright, W. Slaughter, W. Clark (2006)
Behaviour of a unimorph circular piezoelectric actuatorSmart Materials and Structures, 15
P.-H. Cazorla, O. Fuchs, M. Cochet, S. Maubert, G. Rhun, Y. Fouillet, E. Defay (2016)
A low voltage silicon micro-pump based on piezoelectric thin filmsSensors and Actuators A-physical, 250
A. Esfahani, M. Bahrami (2016)
Vibration analysis of a circular thin polymeric piezoelectric diaphragm with fluid interactionInternational Journal of Mechanics and Materials in Design, 12
Jingshi Dong, Ruidong Liu, Wei Liu, Quanqu Chen, Yang Yang, Wu Yue, Zhigang Yang, B. Lin (2017)
Design of a piezoelectric pump with dual vibratorsSensors and Actuators A-physical, 257
Y. Liu, Z. Hao, J. Yu, X. Zhou, Pooi Lee, Y. Sun, Z. Mu, F. Zeng (2019)
A high-performance soft actuator based on a poly(vinylidene fluoride) piezoelectric bimorphSmart Materials and Structures, 28
A. Gunda, G. Özkayar, M. Tichem, And Ghatkesar (2020)
Proportional Microvalve Using a Unimorph Piezoelectric MicroactuatorMicromachines, 11
Shawn Le, H. Hegab (2017)
Investigation of a multistage micro gas compressor cascaded in series for increase pressure riseSensors and Actuators A-physical, 256
Jiahao Gong, Qifu Wang, Bingxin Liu, Huimin Zhang, L. Gui (2021)
A Novel On-Chip Liquid-Metal-Enabled MicrovalveMicromachines, 12
Chiang-Ho Cheng, A. Yang, Chih-Jer Lin, Wei-Jui Huang (2017)
Characteristic studies of a novel piezoelectric impedance micropumpMicrosystem Technologies, 23
R. Haldkar, V. Gupta, T. Sheorey, I. Parinov (2021)
Design, Modeling, and Analysis of Piezoelectric-Actuated Device for Blood SamplingApplied Sciences
J. Cunneen, Yu-Cheng Lin, S. Caraffini, J. Boyd, P. Hesketh, S. Lunte, G. Wilson (1998)
A positive displacement micropump for microdialysisMechatronics, 8
Zilin Chen, Ping Wang, Hsueh-Chia Chang (2005)
An electro-osmotic micro-pump based on monolithic silica for micro-flow analyses and electro-spraysAnalytical and Bioanalytical Chemistry, 382
K. Sravani, Desala Ramakrishna, P. Chandh, Kuncham Sathvik, K. Rao (2022)
Design of Micropump with two stacked ring type piezoelectric actuators for drug deliveryJournal of Micro-Bio Robotics
Andreas Loth, R. Forster (2016)
Disposable high pressure peristaltic micro pump for standalone and on-chip applications2016 IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems (NEMS)
Kotaro Nishikata, Masataka Nakamura, Yuto Arai, N. Futai (2022)
An Integrated Pulsation-Free, Backflow-Free Micropump Using the Analog Waveform-Driven Braille ActuatorMicromachines, 13
Y. Alvarez-Braña, J. Etxebarria-Elezgarai, L. Larrinaga-Vicente, F. Benito‐Lopez, L. Basabe‐Desmonts (2021)
Modular Micropumps Fabricated by 3D Printed Technologies for Polymeric Microfluidic Device ApplicationsSensors and Actuators B-chemical, 342
M. Arik, S. Zurn, A. Bar-Cohen, D. Polla (2005)
Design, fabrication, and characterization of thin film PZT membranes for high flux electronics cooling applicationsSmart Materials and Structures, 14
P. Gravesen, J. Branebjerg, O. Jensen (1993)
Microfluidics-a reviewJournal of Micromechanics and Microengineering, 3
N. Lobontiu (2020)
Compliant Mechanisms
B. Parsi, Lihong Zhang, V. Mašek (2019)
Disposable Off-Chip Micro-Dispenser for Accurate Droplet TransportationIEEE Sensors Journal, 19
A. Bamido, A. Thyagarajan, N. Shettigar, D. Banerjee (2020)
A Thermally Actuated Microvalve for Irrigation in Precision Agriculture ApplicationsASME 2020 Heat Transfer Summer Conference
Yujun Song, D. Cheng, Liang Zhao (2018)
Microfluidics: Fundamental, Devices and Applications: Fundamentals and Applications
Chao Qi, T. Shinshi (2021)
A Disposable Bidirectional Micropump With Three Diaphragms Driven by a Rotating Multi-pole Magnet2021 IEEE 30th International Symposium on Industrial Electronics (ISIE)
In this paper, we propose a new method to use cost-effective multi-sheet off-the-shelf piezoelectric material (e.g. PZT) as an actuator for micropumps. Instead of one customized single PZT sheet that is typically expensive, multiple commer- cially available PZT sheets are utilized to decrease the cost of fabrication. For this purpose, we have derived analytic equations for expressing the natural frequency and mode shape of the actuator. The FEM simulations are utilized to ver- ify the analytic equations. Thanks to their high accuracy, we can utilize the derived analytic equations as fitness functions of genetic algorithm (GA) for the optimization purpose of PZT physical aspects. Our experimental measurement results show that the GA is capable of optimizing multiple physical parameters of the piezoelectric actuator. Moreover, one-way compliant microflaps are presented for the first time to act as one-way valves for a PZT micropump aided by our pro- posed multi-sheet PZT actuator. The flow rate of this configuration is compared with a single-sheet PZT actuator in order to demonstrate the effect of the optimized PZT actuators in the practical applications of micropumps. Keywords Mechanical micropumps, compliant mechanism, microflap, piezoelectric material, genetic algorithm, FEM simulations, and micropumps Date received: 5 August 2022; accepted: 2 February 2023 Handling Editor: Chenhui Liang Micropumps have been serving as a device of inter- Introduction est for many applications such as lab-on-a-chip or The concept of microfluidics was introduced over 8 organ chips. In 2019, Mi et al.’s team developed a val- 1 2 50 years ago by IBM. Later Gravesen et al. published veless electromagnetic microfluidic pump using varied a review paper about micropumping technologies and internal pressures, which were actuated by vibrating a different actuating principles. Afterward many new PDMS membrane. While successful, they admitted that fabrication technologies and in turn new micropump more work would be needed to stabilize their energy techniques have been developed, such as the positive displacement micropump by Cunneen et al., the electro-osmotic micropump by Chen et al., the pneu- Department of Electrical and Computer Engineering, Faculty of matic polydimethylsiloxane (PDMS) micropump by Engineering and Applied Science, Memorial University of Newfoundland, Jeong and Konishi, the piezoelectric micropump by St. John’s, NL, Canada Kaviani et al., and the high-pressure peristaltic micro- 7 Corresponding author: pump by Loth and Fo¨ rster. These are just some exam- Aylar Abouzarkhanifard, Department of Electrical and Computer ples of the new fabrication methods in the microfluidics Engineering, Faculty of Engineering and Applied Science, Memorial area, where the micropump design is highly dependent University of Newfoundland, St. John’s, NL A1B3X5, Canada. on specific applications. Email: aabouzarkhan@mun.ca Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 2 Advances in Mechanical Engineering supply for better control. Their device was able to In the past few years, there have been many different reach a flow rate of 4.5 microL/min. A couple of years trials involving microvalves within various projects. In 9 17 later, the research group under Alvarez-Bran˜ a et al. 2020, Gunda et al. developed a low power, propor- worked on micropumps through 3D printing technol- tionally controlled piezoelectric microvalve. They were ogy. They found that the material and design used to able to achieve a device that could work with as high as print were related to the power output of the pump. 1 bar driving pressure with very little leakage (0.8% of The designs they used had a maximum flow rate of the open flow). Around the same time, Bamido et al. 4.1 microL/min. Within the same year of 2021, Qi and were working on thermally actuated microvalves which Shinshi focused on a bidirectional micropump, which were meant to aid in optimizing water usage in agricul- was driven by cylindrical magnets. These magnets ture. With their apparatus formed through soft- exerted a force on three diaphragms, which could drive lithography techniques, they achieved 60% less flow the fluid at a flow rate of 8.5 microL/min forward and rate. Near the end of 2020, another team led by a flow rate of 9 microL/min backwards. Amnache et al. worked on a novel idea of self- In 2022, at least two more research teams have con- adaptive microvalves that were sensitive to environ- tributed to this area. Under the leadership of Sravani mental conditions to help minimize pumping power. et al., a design was developed focusing on the use of a While the process was proven effective, the team admit- stacked style of single layer piezoelectric actuators ted integration of such a device onto microchips is still within the micropump in order to maximize flow rate a challenge to overcome. Furthermore, Gong et al.’s while minimizing power input. Their device worked at a research group worked on a new on-chip liquid-metal- driving frequency of 100 Hz to achieve an 800 microL/ enabled mechanism. Through their research, they min flow rate. But no piezoelectric actuator modeling achieved a highly flexible, low leak rate device, which or its performance analysis was reported from this can be controlled to form a deformable valve boss to work. Nishikata et al. and his group went to another block the flow path. direction, looking at a new waveform-driven braille Above we introduce the recent advancement mainly actuator for smoother flow. While achieving a in the single-sheet PZT actuators (unimorph actuator). 7.4 microL/min flow rate, they also reduced pulsating Harris et al. presented a multilayer PZT actuator and flow by 79% and backflow in the pump by 63%. introduced a technique for replacing the conventional In general, being applied a voltage, a piezoelectric bonded bulk PZT transducer. Following them, Haldkar 13 22 (e.g. PZT) single layer bends inwards as a micropump. et al.’s team conducted their work on multilayer strip This action can push fluid out of the chamber through piezoelectric bimorphs joined with silicone diaphragm, the outlet valve. In the suction mode, when the voltage which improved performance compared to the circular is removed, the PZT layer would back up to allow the PZT actuator. They claimed the new actuator could fluid to enter the chamber. This reciprocating process increase the flow rate by 12 times, with a lower applied would eventually cause the pumping action. A recent voltage. Another work was done by Liu et al. to inves- attempt of improving PZT micropump was done by Hu tigate a bimorph PZT actuator. They conducted both et al., who added a new passive layer to the previous experiment and FEM simulations and observed an single layer design to decrease the resonant frequency enhancement in the deformation. However, they did as an advantage. The authors verified the finite element not offer a systematic design and optimization metho- method (FEM) model with their experimental setup. dology, which would allow rapid estimation of critical Moreover, an analytic modeling for a single layer design parameters (e.g. layer thickness) in order to circular piezoelectric actuator was developed by Mo enable faster development of such systems for higher et al. They investigated the effect of the thickness performance without a need of invoking computation- ratio and the radius of the piezoelectric layer, which is ally expensive FEM simulations. bonded to a metallic layer with the maximum deflec- Despite the recent advances (e.g. the strip piezo tion by using their proposed analytic model. In addi- bimorph disk technique), there is still a need for a reli- tion, an analytic modeling method based on the thin able low-cost micropump. On the top of the various plate theory and Kelvin–Voigt laws for a single-layer modeling methods achieved in the existing works above, piezoelectric actuator was proposed by Monemian a dedicated optimization process can even boost the per- Esfahani and Bahrami. The authors also studied the formance of actuators and in turn micropumps. Toward vibration of an edge clamp for a rectangular PZT this objective, in this paper we are motivated to analyti- actuator in a fluidic environment. Although effective, cally model and optimize a multilayer PZT actuator with the derived analytic modeling in those two works above genetic algorithm (GA) for the fluid pumping purpose. was not used in any follow-up optimization flow and The optimized multilayer PZT actuator can be used in there was no report from them on the performance micropumps to control the flow rate. Moreover, the comparison between single layer and multilayer piezo- micropump valves can be better designed by using the electric actuators. proposed pseudo rigid-body model technique. Parsi et al. 3 w are the displacement of the piezoelectric layer and diaphragm layer respectively, k is the stiffness coeffi- cient of the epoxy layer, m and m are the mass per 1 2 unit area of the piezoelectric layer and diaphragm layer, respectively. The piezoelectric layer, which may physically include multiple PZT sheets, is clamped along the edge such that there is no displacement. As a Figure 1. Schematic view of a typical piezoelectric actuator. result, the boundary condition equations can be written as follows: This paper is organized as follows. In Section II, the wðÞ r , t = 0, w (0, t) 6¼ ‘ðÞ i = 1or2 : ð2Þ i o i governing analytic equations of the optimized PZT layer with a bonding layer will be presented with their Moreover, the PZT layer has no initial velocity: natural frequency and mode shape derived. In Section III our GA-based optimization flow will be discussed, ∂w wðÞ r, 0 = w , ðÞ r, 0 = 0: ð3Þ i 0 while the actuator design along with FEM simulation ∂t and measurement setup will be presented in Section IV. By applying the separation variation method, w and In Section V, we discuss the design of a typical micro- w can be rewritten as follows: pump with either a single-PZT-sheet actuator or a dou- ble-PZT-sheet actuator. Then the experimental results wðÞ r, t = R ðÞ r ZtðÞ, ð4 1Þ 1 1 will be presented in Section VI. Finally, a conclusion is drawn in Section VII. wðÞ r, t = R ðÞ r ZtðÞ, ð4 2Þ 2 2 2 2 ∂ R ðÞ r 1 ∂R ðÞ r ∂ ZtðÞ 1 1 ZtðÞ T + = m R ðÞ r 1 1 1 Analytic modeling 2 2 ∂r r ∂r ∂t The primary purpose of an optimized piezoelectric + k ðÞ R ðÞ r ZtðÞ R ðÞ r ZtðÞ , 1 2 actuator is to provide sufficient bending displacement ð5 1Þ in the transverse direction. As illustrated in Figure 1, a 2 2 piezoelectric (e.g. PZT) layer, which might be physically ∂ R ðÞ r 1 ∂R ðÞ r ∂ ZtðÞ 2 2 ZtðÞ T + = m R ðÞ r 2 2 2 2 2 implemented by multiple PZT sheets, is glued with the ∂r r ∂r ∂t diaphragm layer. These two layers are assumed to con- k ðÞ R ðÞ r ZtðÞ R ðÞ r ZtðÞ : 1 2 nect each other by a massless and linear epoxy bonding ð5 2Þ layer. The radius of the PZT layer and bonding layer is r , while their thicknesses are t and t , respectively. In O p b ivt Let’s assume ZtðÞ = Z e , then: this model, since the thickness of the electrodes is less than 0.5mm, their effect on the deflection of the PZT 2 ∂ R ðÞ r 1 ∂R ðÞ r 1 1 ivt Z e T + layer will be ignored. 0 1 ∂r r ∂r To derive the analytic expression of the natural fre- ivt 2 = m R ðÞ r Z e v 1 1 0 quency and mode shape, the dynamic behavior of the ivt ivt actuator has to be studied. By utilizing the Lagrangian + k R ðÞ r Z e R ðÞ r Z e , 1 0 2 0 method, we can derive the axisymmetric governing ð6 1Þ equations as follows : ∂ R ðÞ r 1 ∂R ðÞ r 2 2 ivt 2 2 Z e T + 0 2 ∂ wðÞ r, t 1 ∂wðÞ r, t ∂ w (r, t) 2 1 1 1 ∂r r ∂r T + = m 1 1 2 2 ∂r r ∂r ∂t ivt 2 = m R ðÞ r Z e v 2 2 0 + k ðÞ wðÞ r, t wðÞ r, t , 1 2 ivt ivt k R ðÞ r Z e R ðÞ r Z e : 1 0 2 0 ð1 1Þ ð6 2Þ 2 2 ∂ wðÞ r, t 1 ∂wðÞ r, t ∂ wðÞ r, t 2 2 2 T + = m These equations can be rewritten as: 2 2 2 2 ∂r r ∂r ∂t k ðÞ wðÞ r, t wðÞ r, t , 1 2 ∂ R ðÞ r 1 ∂R ðÞ r 1 1 ivt Z e T + 0 1 ∂r r ∂r ð1 2Þ ð7 1Þ ivt 2 = m R ðÞ r Z e v 1 1 0 where T and T are the applied tension on the piezo- 1 2 ivt + k Z e ðÞ R ðÞ r R ðÞ r , electric layer and diaphragm layer respectively, w and 0 1 2 1 4 Advances in Mechanical Engineering ∂ R ðÞ r 1 ∂R ðÞ r quickly for different dimensions without any computa- 2 2 ivt Z e T + 0 2 tionally expensive FEM simulations. To calculate the ∂r r ∂r ð7 2Þ ivt 2 mode shape function, (12) has to be solved. The general = m R ðÞ r Z e v 2 2 0 solution can be achieved as follows: ivt k Z e ðÞ R ðÞ r R ðÞ r : 0 1 2 With simplification: R = (a JðÞ C r + b YðÞ C r ), ð14Þ 1 i 0 i i 0 i i = 1 ∂ R ðÞ r 1 ∂R ðÞ r 1 1 T + = m v R ðÞ r X 1 1 1 ∂r r ∂r R = d (a JðÞ C r + b YðÞ C r ), ð15Þ 2 i i 0 i i 0 i i = 1 + k ðÞ R ðÞ r R ðÞ r , 1 2 ð8 1Þ where d is: ∂ R ðÞ r 1 ∂R ðÞ r 2 2 2 2 T + = m v R ðÞ r 2 2 2 d = m v + T C + k : ð16Þ i 1 1 2 i ∂r r ∂r k ðÞ R ðÞ r R ðÞ r : 1 2 By applying the first boundary condition, because of R (0) 6¼ ‘, b should be equal to zero. In addition, by ð8 2Þ 1i i applying the second boundary condition R ðÞ r , t = 0, 1i o ∂ R (r) 1 ∂R (r) i i we can get the following equations: Let’s define rR = + . By putting ∂r r ∂r rR into the equations, the following equations will be a JðÞ C r + a JðÞ C r = 0 1 0 1 0 2 0 2 0 , ð17Þ obtained: d a JðÞ C r + d a JðÞ C r = 0 1 1 0 1 0 2 2 0 2 0 or in the matrix form: T rR + m v k R ðÞ r + k R ðÞ r = 0 , 1 1 1 1 2 ð9 1Þ JðÞ C r JðÞ C r a 0 0 1 0 0 2 0 1 = : ð18Þ d JðÞ C r d JðÞ C r a 0 T rR + m v k R ðÞ r + k R ðÞ r = 0: 1 0 1 0 2 0 2 0 2 2 2 2 2 1 ð9 2Þ In order to have a non-zero solution in (18), the follow- ing condition must be satisfied: By eliminating R from these equations, the following equation can be obtained: ðÞ d d JðÞ C r JðÞ C r = 0: ð19Þ 1 2 0 1 0 0 2 0 2 2 r + C r + C R = 0, ð10Þ 1 In the end, the characteristic equation will be obtained 1 2 as: where C and C are equal to: 1 2 JðÞ C r = 0 or J ðÞ d = 0, ð20Þ o n o o n 2 2 C = ðÞ m T +m Tv ðÞ T +Tk 2 1 1 2 1 2 1,2 T T where d is the root of the Bessel function, and n 1 2 n 2 2 2 4 2 2 4 2 2 2 2 denotes the n-the root of the Bessel function. Now by 6 2T T k +T m v +T m v +T k +T k 1 2 2 1 1 2 2 1 solving this simple algebraic equation, natural fre- 2 2 2 2 4 2m v T k+2m T v k2m m T T v 2 1 2 1 1 2 1 2 quency v of the system can be calculated. In addition, 2 2 +2m T T kv ) the mode shapes of the piezoelectric layer and dia- 1 1 2 phragm layer can be expressed respectively as follows: ð11Þ R ðÞ r = a JðÞ C r , ð21 1Þ The solution of this equation can be represented as 1 1n o n the sum of the roots from the Bessel function as R ðÞ r = d a JðÞ C r , ð21 2Þ 2 i 1n o n follows: where a is equal to: 1n R = a JðÞ C r + b Y (C r), ð12Þ 1i i o i i o i JðÞ C r = 0 or J ðÞ d = 0, ð13Þ a = : ð21 3Þ o i o o 1n 2 p r r JðÞ C r n o o 1 where d is the root of the Bessel function. Now by sol- ving this simple algebraic equation, natural frequency v Optimization algorithm of the system can be derived. We can see that this analy- tic model is very valuable, since the designers can use it The genetic algorithm (GA) is an evolutionary compu- to estimate the natural frequency of a new PZT layer tation algorithm for optimizing sophisticated problems Parsi et al. 5 Table 1. The optimization and input parameters of the system. Optimized Optimized Radius diaphragm piezoelectric layer thickness layer thickness Value 117 mm 92.95 mm 7.5 mm aspects of the piezoelectric layer to increase the displa- cement of the diaphragm. The coverage of the electro- des is defined to be identical to the size of the piezoelectric film. In the following section, the capabil- ity of the GA-based optimization methodology will be further studied. Actuator design Since the analytic equations, which show the relation- ship among the thickness of the piezoelectric layer, the thickness of the diaphragm layer, the radius of the Figure 2. Working mechanism flowchart of the GA layers, and the maximum deflection of the layers as dis- optimization algorithm. cussed in Section II, are able to accurately estimate the thicknesses of the piezoelectric and diaphragm layers in by mimicking biological evolution. As depicted in addition to the radius, we have deployed them (mainly Figure 2, the GA optimization starts with the initializa- (21-2)) as a fitness function of our GA optimization tion block, where the variables are coded in the form of algorithm. We may include multiple physical variables fixed length binary strings. Each variable can be ran- as optimizable parameters such as the piezoelectric domly selected with equal probability. Usually, the first thickness (h ) and diaphragm layer thickness (h ). p d operator that performs on a population is the repro- We have implemented the GA-based optimization duction, which strives to find appropriate individuals method in MATLAB by using its genetic algorithm tool in a population and interpolate them into a mating box (Version 2017) in order to enhance the vertical dis- pool. A number of methods for individual selection placement amplitude of the layers. The applied fitness function and constraints of the optimization are defined have been proposed in the literature, although the main by (22): idea of this operation is to choose, duplicate, and insert certain preferable individuals from the current popula- Maximize : fR g, tion into the pool. The next operator within GA is the 2 crossover, where typically two individuals are selected Subjectto : design rules of the optimizable parameters: from the mating pool and a certain quota of these indi- ð22Þ viduals are exchanged in between. In other words, the recombination between these pairs produces new indi- For the optimizable physical parameters (e.g. h or h ), p d viduals, called offspring. Finally, the mutation operator the upper and lower bounds can be defined as per their is performed to change 1 b from 1 to 0 or vice versa. design rule constraints (e.g. [1m, 1000 m]). According to This process is also random with a very low probability the listed resultant data in Table 1, the optimized thick- (called mutation rate) on the entire population. ness for the piezoelectric layer is 92.95 mm. In other All the three genetic operators above are performed word, based on the other factors and parameters, such on the entire population in one GA generation. Thus, a thickness of the piezoelectric layer can offer the maxi- the search and optimization aspect of GA is mainly mum displacement performance. Instead of using any provided by the crossover and mutation operators. The expensive customized one-layer piezoelectric material, multi-dimensional search capability offered by GA can this required thickness can be achieved by bonding mul- effectively prevent it from being entrapped by local tiple cost-effective commercially available off-the-shelf optima. Therefore, a significant feature of GA in com- piezoelectric sheets. For our case study, we have chosen parison with the conventional optimization approaches to use standard commercial piezoelectric sheets (i.e. is its advantageous access to the global optimum. In PZT7BB) with constant radius (i.e. 7.5 mm). By using this study, our proposed GA-based optimization the closest integer with reference to the optimized piezo- method is performed to identify the best physical electric layer thickness of 92.95 mm (unimorph actuator) 6 Advances in Mechanical Engineering Table 2. Material properties within the system. Mechanical Diaphragm layer Bonding layer PZT (lead property (silicon nitride) (epoxy resin) zirconate titanate) 3 3 3 Mass density 3290 (Kg/m ) 2000 (Kg/m ) 7500 (Kg/m ) Elastic modulus 310 (GPa) 5.17 (GPa) 9.5 (GPa) Poisson’s ratio 0.27 0.31 0.30 Figure 4. The natural frequencies of the multiple PZT sheets along with the epoxy bonding layer (Group-2) in COMSOL Multiphysics: (a) the first mode shape, (b) the second mode shape, and (c) the third mode shape. frequency v of the system can be also derived. To vali- date our methodology, we have run two groups of FEM simulations. In Group-1, one piezoelectric layer (unimorph actuator) with the optimized thickness was simulated in COMSOL Multiphysics (Version 5.3). Figure 3 shows the natural frequencies and mode shapes of these simulations. In the simulations for Figure 3. The natural frequencies of the optimized PZT layer Group-2, the equivalent thickness was managed by (Group-1) in COMSOL Multiphysics: (a) the first mode shape, (b) the second mode shape, and (c) the third mode shape. attaching multiple piezoelectric sheets together (bimorph actuator) along with the epoxy bonding layer. The results of the simulations are shown in as shown in Table 1, we have deployed two PZT sheets Figure 4. To better compare the performance, all the (bimorph actuator) with the same radius and thickness conditions (i.e. radius, initial conditions, and boundary (i.e. 42 mm). The material properties within the system conditions) are the same in both groups of simulations. are shown in Table 2. It is worth mentioning that here we focus on the In order to calculate the natural frequency by using amounts of the natural frequencies instead of the dis- the analytic method, equation (20) must be solved. By placement amplitudes that are limited by the utilized solving this simple algebraic Bessel function, natural modal analysis method. Parsi et al. 7 Table 3. Comparison of the first, second, and third natural frequencies and mode shapes from the FEM simulations. Natural Group-1 FEM Group-1 FEM Group-2 FEM Group-2 FEM Absolute frequency optimized optimized model multi-sheet multi-sheet model percentage model (Hz) displacement (mm) model (Hz) displacement (mm) error (APD) st 1 2400.2 401.5 2528.3 35.9 5.07 nd 2 4994.7 187 5261.2 18.4 5.33 rd 3 8189.5 100.9 8630.4 10.7 5.32 Table 4. Comparison of the first, second, and third natural frequencies between the analytic computation and FEM simulations for the optimized unimorph piezoelectric actuator. Natural Analytically FEM Absolute frequency computed simulation percentage model (Hz) (Hz) error (APD) st 1 2430 2400.2 1.26 nd 2 5620 4994.7 11.1 rd 3 8890 8189.5 7.87 Figure 5. Tresca stress at the boundary and displacement Table 3 shows the comparison between the multi- profile. sheet model and the optimized model. The absolute per- centage error (APD) is calculated by using the following the maximum deflection will be measured and com- equation: pared between the FEM simulation and experimental v v setup. F opt E = 100% , ð23Þ To verify the accuracy of the proposed model, we have built up an experimental measurement setup. A where v is the natural frequency output from the high voltage signal (i.e. 200sin(v t)) with the same fre- F i Group-2 FEM simulation, and v is the natural fre- quency v was applied to the system, while the maxi- opt quency of Group-1 also calculated by the FEM mum deflection was reported from both the FEM simulations. simulation and the experimental measurement setup. As listed in Table 4, the natural frequency compari- The absolute values of the system response are shown son between the analytically computed model and the in Figure 5. The maximum stress, which occurs at the FEM simulation for the optimized unimorph piezoelec- edge, is shown as a function of time in this figure. tric actuator above shows the acceptable accuracy of Figure 5 also reveals that the maximum deflection of our proposed analytic model. We can see that this ana- the system with respect to that excitation signal is equal lytic model is very valuable, since the designers can use to 121 mm as indicated by the reference scale located it to estimate the natural frequencies of a new system on the right. configuration with different geometric dimensions very The experimental measurement setup, as shown in efficiently and then realize it with the cost-effective off- Figure 6, includes a fixture, a high-precision laser mea- the-shelf commercial PZT sheets without any computa- surement sensor (LK-H022, resolution of 0.02 mm), a tionally expensive FEM simulations. Moreover, the signal generator, a high-precision high-voltage power transverse vibration of the optimized PZT layer can be amplifier (TEGAM-2350), and a data acquisition sys- turned into a time-dependent vibration when the input tem. In order to verify the FEM simulation with refer- voltage signal changes as a function of time. Thus, the ence to the experimental measurement results, an designers may opt to determine the best input signal, excitation signal was applied to the system. Figure 7 which can maximize the efficiency of the system. In shows the center deflection of the double PZT sheets. order to reach this goal, after calculating the natural As can be seen from this figure, the maximum value of frequencies, the first natural frequency will be chosen the deflection is equal to 117 mm, which is very close to to apply to the system. A high voltage signal with the the FEM result of 121mm with the error of 3.3% (i.e. will be applied to the system and same frequency v (1212 117)/121 = 3.3%). 1 8 Advances in Mechanical Engineering Figure 8. Schematic view of micropump with one-way compliant microflaps. added in order to accurately predict the force-deflection relationship of the compliant microflap. The spring Figure 6. Experimental measurement setup: (1) Double PZT constant and deflection, and stress can be calculated as sheets, (2) Fixture, (3) Shaker, (4) High-precision laser follows: measurement sensor (LK-H022, resolution of 0.02mm), (5) Signal generator, (6) High-precision high-voltage power amplifier rk EI k = ð24Þ (TEGAM-2350), and (7) Data acquisition system. where k is spring constant, E is the Young’s module, I is the moment of inertia, and l is the length of micro- flap. r and k are the coefficients, which can be found from Howell. a = l(1 g + r cosY), ð25Þ b = lr sinY, ð26Þ PaðÞ + nb c nP s = 6 , ð27Þ max I A where s is maximum stress, a and b are the deflected max position of the beam end point as shown in Figure 9(b), c is the distance from the neutral axis to the outer sur- Figure 7. The center displacement response of the system face of the beam, Y is the pseudo rigid-body angle, n is under excitation signal of 200sin(v t). 1 25 a constant and can be found in Howell, nP is the verti- cal component of the force, and A is the beam cross sec- tion area. Micropump design The maximum pressure that can be produced by the In this section, the double-PZT-sheet actuator has been double-PZT-sheet actuator under excitation signal of modeled onto a micropump to explore the effect of this 200sin(v t) is equal to 0:00216sin(v t). By applying 1 1 optimized actuator on the flow rate of the micropump. this pressure to the microflap, the maximum stress will A typical configuration of the micropump with the be 1:01e pa while the FEM simulation, as shown in double-PZT-sheet actuator is modeled as shown in Figure 9(c), reveals 1.22e pa. As one major advantage, Figure 8. In order to design the microvalve, the pseudo- the pseudo rigid-body model makes it possible for the rigid-body model will be introduced. The purpose of designers to analyze the compliant valve and height of the pseudo-rigid-body model is to provide a simple channel without any computationally expensive FEM method for analyzing systems, which are under large simulations. nonlinear deflections. The pseudo rigid-body model For fabrication of microflaps and micropump, we concept is used to model the deflection of flexible seg- propose using PDMS, which is able to provide ments by using rigid-body segments, which have the unmatched advantages, including optical transparency, same force-deflection characteristics. bubble permeability, quick and low-cost processing. For each microflap, a pseudo rigid-body model can PDMS, which typically mold and reversibly bond with evaluate the deflection path of the flexible microflap. very good elasticity, can be used for leak-free valving. The motion will be modeled by rigid links attached at In contrast, silicon is opaque, bubble and gas imperme- pin joints. Figure 9(a) shows the original and deflected able, and known for its expensive fabrication process. position of microflap, while Figure 9(b) illustrates the Another reason why PDMS is chosen in this study is pseudo rigid-body model. In this model, the spring is its ability to form valves without leakage. Although the Parsi et al. 9 Figure 9. (a) Schematic view of microflap, (b) pseudo rigid-body model of microflap, and (c) the FEM modeling of microflap. silicon nitride or other inorganic materials have been Multiphysics as shown in Figure 11. The fully coupled used in the previous studies from the literature, they fluid-structure interaction (FSI) COMSOL Multiphy- actually cannot provide reliable seal due to surface sics module is utilized to combine the fluid flow, which roughness and particles. However, the PDMS valves is formulated by using an Eulerian description and a are able to provide more reliable sealing in presence of spatial frame, with the solid mechanics, which is formu- back pressure. lated by using a Lagrangian description and a material Figure 10 illustrates the fabrication process of frame. Figure 11(a) shows the micropump chamber in microfluid pump with one-way compliant microflaps. the suction mode, while Figure 11(b) exhibits the cham- Fabrication starts with the first wafer substrate (step ber of micropump in the pump mode. In those figures, 1), followed by the deposition of a photosensitive resist the first and second color bars on the right show the substrate (step 2). The photoresist is photolithographi- velocity and stress, respectively. cally patterned (step 3) and developed. The PDMS will In order to investigate the effect of the double-PZT- be first degassed and then is poured on top of the first sheet actuator on the system, the flow rate is calculated wafer (step 4), cured, and then will be separated (step by FEM simulations. Figure 12 shows the flow rate of 5). The PDMS piece containing the inverse of the the micropump. As can be seen from this figure, the 8 2 molded feature, which includes the micropump cham- maximum flow rate reaches up to 22:93 10 m =s , ber and microflaps, is then attached to the second and which is suitable for pumping biological samples, such third wafer to form enclosed chamber (step 6). Finally, as blood. The result reveals that this flow rate is 14.7 the optimized double-PZT-sheet actuator will be placed times higher than a single layer PZT-sheet actuator. In on the top of the second substrate in step 6. addition, it is obvious from Figure 13 that with this new compliant microflap, the flow leakage will reach zero. The comparison of multiple conventional micro- Experimental results pumps with our proposed device is summarized in Table 5. Our device is featured by its small footprint After designing the microflap, the double-PZT-sheet but a decent level of flow rate. actuator micropump has been modeled in COMSOL 10 Advances in Mechanical Engineering Conclusion In this paper, we designed and optimized a PZT layer as an actuator in addition to microvalve for the micro- pump. The analytic analysis of the PZT-layer-based actuator was first conducted and then verified by using FEM simulations and experimental measurement. The comparison between the analytic computation and COMSOL Multiphysics simulation reveals the high accuracy of our proposed analytic solution, whose error is less than 2% for the first natural frequency. This is valuable since the designers can efficiently esti- mate the natural frequencies and mode shapes of a new configuration with different dimensions and further design the microflaps by using our proposed analytic solution without depending on any computationally expensive FEM simulations. Moreover, an experimen- tal setup was established to measure the maximum dis- placement for a comparison with the FEM simulation. The results show that the difference between our experimental measurement and FEM simulation is less than 4%. Furthermore, the optimized actuator was applied to a typical micropump to evaluate its function- ality. The comparison between a regular micropump with a single-PZT-sheet actuator and the same micro- pump with our optimized double-PZT-sheet actuator Figure 10. Process for fabricating microfluid pump with one- reveals that the flow rate could be increased up to 14.7 way compliant microflaps using PDMS. Figure 11. The FEM modeling of the micropump with the double-PZT-sheet actuator: (a) the suction mode and (b) the pump mode. Parsi et al. 11 Table 5. Comparison among various conventional micropumps and our proposed device. Ref Actuation mechanism Valves type Chamber size Pressure Flow rate Fluid Wang et al. PZT Passive F20 mm 56.7 kpa 186.8 mL/min Gas Cazorla et al. PZT Active F7:5 mm 32 mbar 3.5mL/min Water Ma et al. PZT Active F10 mm – 9.1 mL/min Water Le and Hegab PZT Passive F20 mm 2x 18 kpa 32 cm/min Gas Cheng et al. PZT Active – 2.35 kpa 0.24 mL/min Air Dong et al. PZT Passive F7:8 mm 2.18 kpa 218.7 mL/min Air Haldkar et al. PZT – F9 mm – 1.256 mL/s Blood Our Device PZT Active zero leakage F 50 mm 0.46 kpa 13.74 mL/min Water Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial sup- port for the research, authorship, and/or publication of this article: This work was supported partially by the Natural Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation, the Research and Development Corporation of Newfoundland and Labrador through the Industrial Research and Innovation Fund and Figure 12. The outlet and inlet flow rates of the micropump Arctic TECH R&D Award, and the Memorial University of with the optimized double-PZT-sheet actuator. Newfoundland. ORCID iD Behzad Parsi https://orcid.org/0000-0002-2417-107X References 1. Song Y, Cheng D and Zhao L. Microfluidics: fundamen- tals, devices, and applications. Hoboken, NJ: John Wiley & Sons, 2018. 2. Gravesen P, Branebjerg J and Jensen OS. Microfluidics-a review. J Micromech Microeng 1993; 3: 168–182. 3. Cunneen J, Lin YC, Caraffini S, et al. A positive displa- cement micropump for microdialysis. Mechatronics 1998; 8: 561–583. Figure 13. Inlet and outlet velocity of the micropump with our 4. Chen Z, Wang P and Chang HC. An electro-osmotic optimized double-PZT-sheet actuator. micro-pump based on monolithic silica for micro-flow analyses and electro-sprays. Anal Bioanal Chem 2005; 382: 817–824. times in addition to zero leakage. The future research 5. Jeong OC and Konishi S. Fabrication and drive test of work includes the optimization of the entire micro- pneumatic PDMS micro pump. Sens Actuators A 2007; pump as well as the validation of the micropump 135: 849–856. advanced fabrication process. 6. Kaviani S, Bahrami M, Esfahani AM, et al. A modeling and vibration analysis of a piezoelectric micro-pump dia- Acknowledgement phragm. C R Mec 2014; 342: 692–699. The authors would like to thank Prof. A. Fisher, Dr. V. 7. Loth A and Fo¨ rster R. Disposable high pressure peristal- Masek and Dr. A. Nasiri for helping enable the associated tic micro pump for standalone and on-chip applications. laboratory case study in the Faculty of Engineering and In: 2016 IEEE 11th annual international conference on Applied Science at the Memorial University of nano/micro engineered and molecular systems (NEMS), Newfoundland. April 2016, pp.29–33. New York: IEEE. 12 Advances in Mechanical Engineering 8. Mi S, Pu H, Xia S, et al. A minimized valveless electro- 20. Gong J, Wang Q, Liu B, et al. A novel on-chip liquid- magnetic micropump for microfluidic actuation on organ metal-enabled microvalve. Micromachines 2021; 12: 1051. chips. Sens Actuators A 2020; 301: 111704. 21. Harris NR, Hill M, Torah R, et al. A multilayer thick- 9. Alvarez-Bran˜ a Y, Etxebarria-Elezgarai J, Ruiz de, Larri- film PZT actuator for MEMs applications. Sens Actua- naga-Vicente L, et al. Modular micropumps fabricated tors A 2006; 132: 311–316. by 3D printed technologies for polymeric microfluidic 22. Haldkar RK, Khalatkar A, Gupta VK, et al. New piezo- device applications. Sens Actuators A 2021; 342: 129991. electric actuator design for enhance the micropump flow. 10. Qi C and Shinshi T. A disposable bidirectional micro- Mater Today Proc 2021; 44: 776–781. pump with three diaphragms driven by a rotating multi- 23. Liu YZ, Hao ZW, Yu JX, et al. A high-performance soft pole magnet. In: 2021 IEEE 30th international symposium actuator based on a poly(vinylidene fluoride) piezoelectric on industrial electronics (ISIE), 2021. New York: IEEE. bimorph. Smart Mater Struct 2019; 28: 055011. 11. Sravani KG, Ramakrishna D, Chandh P, et al. Design of 24. Zhang L and Kleine U. A genetic approach to analog micropump with two stacked ring type piezoelectric module placement with simulated annealing. In: 2002 actuators for drug delivery. J Micro-Bio Robot 2021; 17: IEEE international symposium on circuits and systems. 69–78. proceedings (Cat. No. 02CH37353), May 2002, vol. 1, 12. Nishikata K, Nakamura M, Arai Y, et al. An integrated pp.345–348. New York: IEEE. pulsation-free, backflow-free micropump using the ana- 25. Howell LL. Compliant mechanisms. In: McCarthy J log waveform-driven Braille actuator. Micromachines (ed.) 21st century kinematics. London: Springer, 2013, 2022; 13: 294. 189–216. 13. Arik M, Zurn SM, Bar-Cohen A, et al. Design, fabrica- 26. Parsi B, Zhang L and Masek V. Disposable off-chip tion, and characterization of thin film PZT membranes micro-dispenser for accurate droplet transportation. for high flux electronics cooling applications. Smart IEEE Sens J 2019; 19: 575–586. Mater Struct 2005; 14: 1239–1249. 27. Wang J, Liu Y, Shen Y, et al. A resonant piezoelectric 14. Hu Y, Liang X and Wang W. A theoretical solution of diaphragm pump transferring gas with compact struc- resonant circular diaphragm-type piezoactuators with ture. Micromachines 2016; 7: 219. added mass loads. Sens Actuators A 2017; 258: 74–87. 28. Cazorla PH, Fuchs O, Cochet M, et al. A low voltage sili- 15. Mo C, Wright R, Slaughter WS, et al. Behaviour of a con micro-pump based on piezoelectric thin films. Sens unimorph circular piezoelectric actuator. Smart Mater Actuators A 2016; 250: 35–39. Struct 2006; 15: 1094–1102. 29. Ma HK, Chen RH, Yu NS, et al. A miniature circular 16. Monemian Esfahani A and Bahrami M. Vibration analy- pump with a piezoelectric bimorph and a disposable sis of a circular thin polymeric piezoelectric diaphragm chamber for biomedical applications. Sens Actuators A with fluid interaction. Int J Mech Mater Des 2016; 12: 2016; 251: 108–118. 401–411. 30. Le S and Hegab H. Investigation of a multistage micro 17. Gunda A, Ozkayar G, Tichem M, et al. Proportional gas compressor cascaded in series for increase pressure microvalve using a unimorph piezoelectric microactuator. rise. Sens Actuators A 2017; 256: 66–76. Micromachines 2020; 11: 130. 31. Cheng CH, Yang AS, Lin CJ, et al. Characteristic studies 18. Bamido A, Thyagarajan A, Shettigar N, et al. A ther- of a novel piezoelectric impedance micropump. Microsyst mally actuated microvalve for irrigation in precision agri- Technol 2017; 23: 1709–1717. culture applications. In: ASME 2020 heat transfer 32. Dong JS, Liu RG, Liu WS, et al. Design of a piezoelectric summer conference, 2020. ASME. pump with dual vibrators. Sens Actuators A 2017; 257: 19. Amnache A, Laguna G, Leveille E, et al. Fabrication and 165–172. demonstration of a self-adaptive microvalve array for dis- 33. Haldkar RK, Gupta VK, Sheorey T, et al. Design, mod- tributed liquid cooling in microelectronic interposers. J eling, and analysis of piezoelectric-actuated device for Microelectromech Syst 2020; 29: 769–775. blood sampling. Appl Sci 2021; 11: 8449.
Advances in Mechanical Engineering – SAGE
Published: May 1, 2023
Keywords: Mechanical micropumps; compliant mechanism; microflap; piezoelectric material; genetic algorithm; FEM simulations; and micropumps
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.