Results in Physics 18 (2020) 103166 Contents lists available at ScienceDirect Results in Physics journal homepage: www.elsevier.com/locate/rinp Design and simulation of the new ultrasonic atomizer using silicon-based with one step resonator T ⁎ Yu-Lin Songa,b, , Lavanya Bandib a b Department of Bioinformatics and Medical Engineering, Asia University, Taichung 413, Taiwan Department of Computer Science and Information Engineering, Asia University, Taichung 413, Taiwan A R T I C LE I N FO A B S T R A C T Keywords: Ultrasonic device Computer-aided design COMSOL multi-physics Space claim Surface wave Capillary-waves The design and simulation of a new generation Fourier ampliﬁer were investigated in this study. The design and characterization of 500 kHz micro fabricated silicon-based ultrasonic atomization is presented for the concept of uniform and ﬁne droplets. Ultrasonic atomizer nozzle is composed of a silicon-based resonator consisting of the Fourier-Horn., drive section and one step part. The atomization of liquid droplets is veriﬁed by using the direct modeling CAD software Space Claim and to construct a single and three Fourier-Horn Ampliﬁer model. At the same time, the multi-section geometric model is completed by the array geometry function of the CAE numerical software COMSOL and the physical characteristics of the Fourier ampliﬁer designed by the ﬁnite element analysis module. The simulation study states that the onset amplitude of single Horn ultrasonic atomizer produces to 6.8 μm droplets with a designated frequency of 492 kHz. The types and basic principles of mechanical ampliﬁers (Horn) and the reason for choosing and the designing of required Fourier ampliﬁers are explained. The simulation data ﬁt well with experimental data. Micro-droplets are steady and uniformly formed after the liquid feeding rate is optimized. This newly designed ultrasonic atomizer facilitates the development of capillary surface-wave resonance at a designated frequency and easy to form atomization of a liquid drop. There are many uses for uniform and ﬁne droplets, for example, it can be used as a precursor for making micro-sized drops, and can be used as a coating to form extremely ﬁne surfaces; it can increase the surface of droplets, increase evaporation speed and even fuel rate; can be suspended Drugs enter the lungs directly and are absorbed into the blood, treatment of inner ear diseases, nose diseases, and even eye cares can use this single Horn atomizer with a tube. Introduction Uniform and small droplets can be achieved by atomizing the liquid, and the atomization methods can be roughly divided into three methods: pressure, pressure-assisted (Pneumatic), and ultrasonic atomization [1]. The pressure atomizer is mainly atomized by pushing the liquid into the nozzle with high pressure. The atomized particles are usually large and uneven. The gas-assisted atomizer uses the kinetic energy of the gas to impact the ﬂuid to produce larger shear. The shear stress makes the liquid reach a ﬁner atomizing particle size. The ultrasonic atomizer mainly relies on ultrasonic waves to generate capillary waves or cavitation on the liquid surface to atomize the liquid, and the atomization process is kept at a low temperature and low atomization. Flow rate, atomized particles are smaller and more uniform. According to the literature [2,3], when the atomized particle size is less than 10 µm, 90 nm particles can be produced through pyrolysis, and the ⁎ requirements of drug particle size (3 ~ 5 µm), so the main purpose of this research is to design and manufacture high-frequency atomizing ampliﬁers. At low frequencies, a general shaker is suﬃcient to meet atomization requirements, but the bandwidth of the oscillator is limited and cannot meet the needs of high frequencies. Ultrasonic ampliﬁers must be used. In 1963, Eisner [4] designed the ampliﬁer in a completely diﬀerent way. First, the vibration mode of the ampliﬁer was determined, and then the shape of the ampliﬁer was determined. Eisner expanded the mode using a Fourier series, and the ampliﬁer shape can be calculated through the equation of the ampliﬁer's motion. A class ampliﬁer is called a Fourier ampliﬁer. By 20th century Ultrasonic atomizer has many practical applications and successfully applied in biomedical engineering such as food industries, chemical coating, and miniature carriers in pharmaceutical and for the fabrication of printed electronics and sensors [5]. Propagations of ultrasonic surface‐wave are of great interest in the middle of Corresponding author. E-mail address: [email protected] (Y.-L. Song). https://doi.org/10.1016/j.rinp.2020.103166 Received 29 March 2020; Received in revised form 11 May 2020; Accepted 13 May 2020 Available online 25 May 2020 2211-3797/ © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Results in Physics 18 (2020) 103166 Y.-L. Song and L. Bandi Design of Fourier Horn the 20th century, as it has enabled atomization of incompressible frictionless ﬂuid and has often known in a compact, atomized liquid droplets [6]. The control of the atomized droplet process and the characterization of the vaporized droplet size are important issues to obtain good physical properties and repeatability. In 2018, M L Hakim [7] states that the spreading factor decreases with the increasing of surface roughness at 140 degreesC due to incomplete wetting of droplet on the surface, the maximum spreading factor is relatively independent to the change of surface roughness. In 2019, Wang and Junlei proposed a cross-coupled dual beam structure [8] with various incoming directions. The upper and bottom piezoelectric beams can generate a maximum power output of 6.77 µW and 56.64 µW. This research focuses on the development of a new generation of ultrasonic atomizers. The main function is to serve as an eﬃcient drugcovered component device. During this time, the optimized atomizer structure will be designed by COMSOL software modeling. It meets the required particle size and particle size, and then the micro-electromechanical process technology [9] is used to complete this component mechanical device to design a new generation of an ultrasonic atomizer. The advantages of the early design of the ultrasonic atomizer design and the general commercial atomization are mainly that the atomization particle size generated is quite uniform and mostly 7 μm (80%), while the traditional commercial atomizers are 20 μm to 150 μm, the distribution is quite uneven. And the energy required is high, about 23.5 W. The Fourier Ultrasonic Atomizer of this study only needs 0.65 W to produce very uniform particles. However, although there are so many advantages in the practical application, when used clinically device exhibits tolerance. It is mainly the size of the nozzle head, which causes a lot of drug loss and inconvenience of the device when it is used for drug coating [10]. Because of the above-mentioned shortcomings, this research will develop a full-ﬂedged Fourier ultrasonic atomizer, minimizing the components and devices for drug delivery, and making its nozzle size only 100 μm × 100 μm (the previous design nozzle size is 1.06 mm × 1.25 mm, it is easy to produce wetting throughout the nozzle and cannot be materialized.) The design shape is shown in Fig. 1. This newly added half-wavelength silicon tube greatly reduces the original wetting at the tip end, which can improve its working performance. The ampliﬁer is a 3D vibrating body. When it is free to vibrate, the input and output ends are not stressed, and the amplitude of the output end (Tip end) is greater than the input end (Base end). Since a 3D vibrating body cannot be directly analyzed using a mathematical model, the following conditions must be assumed to simplify the original 3D model into one dimension: (1) The ampliﬁer material is uniform; the purpose is to make the entire ampliﬁer have a uniform density. (2) The vibration on the cross-section of the center axis of the ampliﬁer is the same. Here, the center axis is located on the x-axis of the Cartesian coordinate (the axis represents the normal vector of the cross-section). This condition means that the cross-section vibration is independent of y, z. (3) Displacement and velocity are continuous in the ampliﬁer. Equation of motion From the above conditions, the equation of motion of the ampliﬁer can be simpliﬁed as: 1 ∂ ∂2u¯ (x , t ) [σxx A (x )] = ρs A (x ) ∂x ∂t 2 (1) Where A(x): cross-sectional area of the ampliﬁer,σxx: stress,ρs : ampliﬁer density,ū(x,t): longitudinal amplitude. When the ampliﬁer is in harmonic vibration, the displacement can be expressed as: From Hook’s law [11]: ∂u¯ σxx = E¯ ∂x (2) Putting formula (2) into formula (1), we get ∂ 2ū 1 dA ∂ū 1 ∂ 2ū = −2 2 A dx ∂x c0 ∂t + ∂x 2 (3) Where, − − c0 = E / ρs − E : Young's coeﬃcient [12]. When that the ampliﬁer is in harmonic vibration, the displacement can be expressed [13] as Design and production of ampliﬁer Using the characteristics of the mechanical ampliﬁer, the vibration displacement generated at the input end is ampliﬁed at the output end, and the liquid at the output end is atomized. This chapter ﬁrst introduces the types and basic principles of mechanical ampliﬁers (Horn) and explains the reasons for choosing Fourier ampliﬁers. Second, the Fourier ampliﬁers required for the experiment are designed and simulated by the ﬁnite element method (FEM). − u (x , t ) = us (x ) eiωt (4) Substituting Eq. (4) into (3) gives d 2u s dx 2 + 1 dA dus = β¯2us = 0 A dx dx (5) Where − β = ω − c0 Dimensionless formula (5) gives the following formula: u'' + u' dlnA + Ω̄2U = 0 dX (6) Based on the 1-D model for longitudinal particle displacement u x of the horn with varying cross section area A(x) at coordinate x in Eq. (6). Since A(x) is ﬁnite, d [lnA(x )] ~ A′ (x ) dx x Where, X = l′ U= Fig. 1. Space Claim constructed Fourier ampliﬁer. 2 us l′ A (x ) Results in Physics 18 (2020) 103166 Y.-L. Song and L. Bandi − − Ω = βl are the length of the ampliﬁer, U ' = dU and the Eq. (6) is recombined to obtain X = us α1 = 1 − (M − 1)[3α52 − 4(4 − γ 2)] U0 32 dX (22) − d ln A U ′ ′ + Ω̄2U =− dX U′ α2 = (7) 1 (M + 1)(9 − γ 2) U0 16 (23) 1 − α3 = − (M − 1)(α52 + γ 2) U0 8 Horn boundary conditions (24) − α4 = (1) If there is no stress at both ends of the ampliﬁer, then U ' (0) = 0 (8) U ' (1) = 0 (9) 1 (M + 1)(γ 2 − 1) U0 16 32 α5 , ¯ −1 U0 M Ω̄ π (25) l λ/2 γ= = Where, α52 = Substituting the above Eqs. (23)–(25) into Eq. (7), the calculation can be obtained: 1− A (X ) = A (0) e ∫0 (2) The amplitude ratio at both ends is − M̄ , M̄ which the amplitude ampliﬁcation factor is. The negative sign is because the vibration phases at both ends are 180 degrees apart. f (α52, γ , X ) d (cosπX ) (26) Where, − f (α52, γ , X ) − (10) U (0) = U0 = − (11) U (1) = −MU0 (3) If the change in area is to be limited, dA/ dx ≠ ∞ use this relationship and Eqs. (7)–(9) to know −2 −2 U '' (1) = −Ω U (1) Fourier Horn simulation discussion (13) After determining the values, the shape of the Fourier ampliﬁer can be calculated. Under the premise of constant thickness, the three-dimensional structure of the ampliﬁer can be obtained. The ﬁnite element method is used to establish a grid [18] for simulation. The required vibration frequency of the ampliﬁer designed in this research is about 300 kHz to 1 MHz. It can be known from the literature [19] that when the ultrasonic wave is transmitted through the ampliﬁer, the maximum particle velocity, the ultrasonic wave transmission speed, and the maximum strain of the ampliﬁer have the following relationship: X →1 theL' Hospital rule [14], we get −2 −2 d U '' + Ω U U ''' + Ω U ' lnA = − lim = − lim =0 ' X → 0 dX X →0 X →0 U U '' lim (14) In Eq. (14), since it is ﬁnite [15], it is necessary to satisfy ''' (15) U (0) = 0 vm =Kεm c Similarly U ''' (1) = 0 − μ (3 − γ 2) − 2(γ 2 + 2α52)cosπX + 3μ (γ 2 − 1)cos2 πX + 4α52cos3 πX (12) (4) Make the area change rate of the input and output terminals d d zero, lim dX lnA = 0 and lim dX lnA = 0 . Then formula (7) and using X →0 − ¯ + 1)/(M ¯ − 1) [11,17] from the above derivation, the bigμ¯ = (M gest diﬀerence between the Fourier ampliﬁer and other types of ampliﬁers is that the form of vibration is determined ﬁrst, and then the shape is calculated. The shape of the other types of ampliﬁers is determined after the shape is calculated. Here X = 0 is the big-endian position and X = 1 little-endian. U '' (0) = −Ω U (0) (4 − γ 2)(γ 2 + α52) − μ (9 − γ 2)(γ 2 − 1)cosπX − (16 − γ 2) α52cos2 πX (27) Where K is constant that is only related to the shape of the ampliﬁer.And εm c are related to the material of the ampliﬁer. Under the same ampliﬁer shape, it is known that silicon has a higher value than ordinary metals and εm c can withstand higher frequency vibration. Therefore, this design uses silicon as the ampliﬁer substrate. This Fourier ampliﬁer is divided into two parts: (16) Determine the appearance of the Fourier ampliﬁer If the amplitude is expanded using the Fourier series to: N U (X ) = ∑ αn cos[(n − 1) πX ] 1. The driving part (Piezoelectric Actuator) of piezoelectric material PZT. 2. Fourier ampliﬁer with half-wavelength design at double magniﬁcation (17) n=1 Due to the characteristics of the cosine function, Eqs. (8), (9), (15), and (16) can be satisﬁed by themselves, and there are four remaining conditions [16], so undetermined coeﬃcients N = 4 can be obtained atαn . But in order to increase the ﬂexibility of the appearance design, we add one more variable, that is N = 5. Substituting (17) into four boundary conditions (10)–(13) gives: Its structure is shown in Fig. 1. There is a ﬁrst-rate channel in the middle. The channel that mainly provides liquid from the input end to the output end, can also be used as a cooling device. The large and small ends ratio of area can be reduced [20]. (18) α1 + α2 + α3 + α4 + α5 = U0 COMSOL simulation − (19) α1 − α2 + α3 − α4 + α5 = −MU0 −2 π 2α2 + 4π 2α3 + 9π 2α4 + 16π 2α5 = Ω U0 (20) ¯ 2U0 π 2α2 − 4π 2α3 + 9π 2α4 − 16π 2α5 = MΩ (21) PZT and monocrystalline silicon are both anisotropic materials, the material parameters must be set according to the lattice direction of the material parameters in the simulation to obtain the true results. This simulation uses COMSOL to set the coordinate axis according to the simulated material orientation settings. Diﬀerent coordinate systems, and then setting these materials in these coordinate systems, you can α5 are optional parameters. From formulas (18) to (21), the following formulas can be solved: 3 Results in Physics 18 (2020) 103166 Y.-L. Song and L. Bandi give a material that can simulate non-isotropic materials with diﬀerent orientations, and when changing ampliﬁers with diﬀerent magniﬁcations, in the past, it was necessary to continuously modify the geometry through CAD software. Then import CAE software to have a way to simulate. COMSOL can use the array method. This method not only arrays the geometry, but also sets the material along with the set material and boundary conditions [17,21]. Ampliﬁers with diﬀerent magniﬁcations can be adjusted quickly, which can greatly reduce the simulation time. The ﬁnite element method COMSOL 3D simulation program is used to seek the resonance frequency of pure longitudinal vibration (Longitudinal Vibration). In addition to the ampliﬁer itself and PZT, there is also a driving section at one end of the magniﬁcation, which is mainly used to connect the PZT piezoelectric plates on the left and right sides. It is a device that converts input energy into mechanical energy. The simulation program calculates the shape of the ampliﬁer following the previous calculation, establishes a grid, performs ampliﬁer simulation, and adjusts the better sum obtained previously to make the simulation frequency and ampliﬁcation meet the design requirements. After a series of simulations to ﬁnd twice the ampliﬁcation, seek to meet design requirements as well. Taking 500 kHz as an example, the frequency of the single-mode longitudinal vibration mode in Fig. 2 is 491.95 kHz and the magniﬁcation is 2.013. Secondly, ﬁnd the size of the PZT sheet, get the length of this PZT sheet according to the design frequency, and then continuously adjust the length to make the PZT sheet’s pure longitudinal vibration modal frequency and the single-cell ampliﬁer frequency the same. The same method is used to make the driving section plus PZT longitudinal vibration frequency equal to the frequency of the singlesegment ampliﬁer. The above is to determine the size of the siliconbased ampliﬁer. Finally, after combining the ampliﬁer, driving section, and PZT, ﬁnd the ampliﬁer section line position and add Upper ﬁxed end. The simulation substrate is a silicon wafer. The longitudinal vibration is in the direction of the wafer (1 1 0). Si anisotropic element is used [22]. The piezoelectric plate should use PZT-5H. Finally, the size of each unit of the Fourier ampliﬁer is shown in Fig. 3. ANSYS Mechanical ﬁnite element analysis software is utilized to Fig. 3. Single 500 kHz Fourier Horn longitudinal vibration mode. reproduce PC models of structures, hardware, or machine parts for breaking down quality, durability, versatility, temperature distribution, electromagnetism, ﬂuid ﬂow, and diﬀerent traits [23]. Fig. 3a explains the Fourier Horn longitudinal vibration at diﬀerent position. The mode of longitudinal vibration is also shown and the displacement of single 500 kHz in longitudinal vibrational mode is shown in Fig. 3a. To verify that the designed ampliﬁer can generate this mode when the voltage is applied, through COMSOL's frequency sweep function, ground on one side and the other side of the applied voltage PZT [24]. The analog frequency range is 450 kHz ~ 550 kHz. The impedance analysis diagram of this section is shown in Fig. 3b. From the results obtained by the pattern, the lowest impedance value is the frequency of the desired operating mode. Simulation discussion for 3Horn-1Step The above method is to complete the design and simulation of a Fig. 2. 500 kHz Fourier's pure longitudinal vibration mode. 4 Results in Physics 18 (2020) 103166 Y.-L. Song and L. Bandi Fig. 3a. Single 500 kHz Fourier Horn longitudinal vibration mode and displacement with X-axis, Y-axis, and Z-axis at 492 kHz. The longitudinal vibration mode of 3-Horn 1-Step with vibrational frequency of 493 kHz is shown in Fig. 4a. And the displacement of 3section 500 kHz in longitudinal vibrational mode, the impedance analysis diagram of this section is also shown in Fig. 4a. From the results obtained by the pattern, the lowest impedance value is the frequency of the desired operating mode. 3-Horn atomizer consume high frequency compared to single Horn ultrasonic atomizer. Two types of spray nozzles are recommended in industries: air-driven sprays, which are produced by atomizer nozzles (present research), and pressure sprays which are produced by pressure nozzles [27,28]. This research shows that single Horn design will be longitudinal wave mode, which is called working mode. Previous mode and Last mode of frequency vibration does not belong to longitudinal wave mode. Using the same process can get the design size of the frequency, the results are shown in Table 1 for 500 kHz simulation results. Fourier Horn measurement results Fig. 3b. 1-section 500 kHz Fourier Horn analog impedance analysis diagram. Fourier Horn electrical characteristics analysis single double-time Fourier ampliﬁer. There are two ways to design a higher magniﬁcation ampliﬁer: The One-Step Fourier Horn atomizer obtained by the micro-electromechanical process is shown in Fig. 5. The size of the one-step device and the three-stage One-Step Fourier Horn atomizer are 27.5 mm and 67.5 mm, respectively. The impedance results obtained by putting the ﬁnished product in an impedance analysis instrument (HP_4294A_16047A Test Fixture) are shown in Fig. 6. Comparing the results with the results of the COMSOL simulation (Fig. 3b), it can be found that the data are quite consistent, and it can be judged that if the longitudinal vibration [29] (Longitudinal Vibration) is between 490 and 492 kHz, the simulation and actual atomizer results can be seen Anastomosis. In the meantime, add the signal and energy ampliﬁer to this atomizer, ﬁnd its resonance atomization frequency, and get a good resonance frequency of 491 kHz. It can be known from this that the simulation system matches the real ﬁnished product quite well and is reliable [30]. In the supporting materials S1 shows the simulation results of single horn with one step atomizer. The S1 present resonated frequency at 492 kHz. The S2 was shown that simulation results of 3-Horn with one step atomizer resonate at 493 kHz. The atomization experimental results of a single Horn with one step are shown in S3 and 3-Horn with one step are shown in S4 supporting materials. (1) Like the design of the double magniﬁcation process, after determining the magniﬁcation, ﬁnd a better sum and then engage in three-dimensional simulation to determine the size of the ampliﬁer. However, when this magniﬁcation is large, the length of the big end will be longer than the ampliﬁer longitudinal length [25]. In this case, the pure longitudinal vibration mode cannot be accurately obtained during the simulation process, and the cross-section vibrations are related, i.e. the assumptions of the original derivation of the ampliﬁer are no longer applicable. (2) As shown in Fig. 4, three separate Fourier ampliﬁers are connected in series into one, and the ampliﬁcation eﬀect of the ampliﬁer can be known from the design. The magniﬁcation obtained by this design can be changed to 3 sections to obtain 8 times magniﬁcation [26]. Fourier Horn atomization analysis Based on the research and development results of this research, the atomizing droplet size of this atomizer is determined by the resonance frequency of the atomizer. Compared with the previous research journals [17,22], we can know that λ = [8πT /(ρ f02 )]1/3 it is multiplied by 0.34 to estimate its droplet size to be 6.8 μm. Particle size analysis instrument (Malvern Particle Sizer) obtained three distribution indicators of particle size analysis: MMD: 7.77 μm Fig. 4. 3-section 500 kHz Fourier Horn longitudinal vibration mode. 5 Results in Physics 18 (2020) 103166 Y.-L. Song and L. Bandi Fig. 4a. 3-section 500 kHz Fourier Horn longitudinal vibration mode at resonated frequency with displacement and analog impedance analysis diagram. Table 1 Simulation results of 500 kHz by varying no. of Horns. No. of Horns Previous mode Working mode Last mode 1 3 480 460 492 493 510 539 VMD: 7.48 μm and SMD: 7.48 μm, as shown in Fig. 7. Note that MMD, VMD and SMD are inset designated droplet mass mean diameter, volume droplet means diameters and surface area droplet mean diameters, respectively. The distribution phase is concentrated at 7 μm. It is in good agreement with the theoretical predictions. The multiple One-Step design is mainly because when there is no such designs before, often because the viscosity of the precursor and the silicon wafer atomize its front surface contact, it is easy to form water droplets, which causes the resonance frequency of the atomizer to shift, causing stop atomization [31]. When using the One-Step design, the contact area is relatively small (0.1 mm × 0.1 mm ≪ 1.06 mm × 1.25 mm). Therefore, reducing its contact area can avoid the atomization interruption caused by the accumulation of liquid beads at the front of the atomizer. In addition, it can take advantage of the needle-like characteristics of the front end, which can bring the atomized liquid beads into the tiny holes. For example, when engaged in otitis media drug delivery, this nebulizer can ﬁrst enter the middle ear cavity in the eardrum. The medicine is atomized and sent to achieve an eﬀective drug treatment mode. Fig. 6. 1-section 500 kHz Fourier Horn impedance analysis chart. veriﬁcation, the novel ultrasonic atomizer using single horn can be obtained, which will have the advantages and eﬀectiveness of its previous design. The simulation study states that the onset amplitude of single horn ultrasonic atomizer is 6.8um with a designated frequency of 491 kHz. The simulated droplet size is in good agreement with that predicted by the capillary wave atomization machine. This ﬁnding represents the ultrasonic atomizer designed in this new study can make a section atomizer atomization (previously only three or four sections Conclusion Based on previous discussions, simulation results and experimental Fig. 5. 1-section and 3-section 500 kHz Fourier Horn ﬁnished products. 6 Results in Physics 18 (2020) 103166 Y.-L. Song and L. Bandi https://doi.org/10.1063/1.5031505. [6] Wei L-J, Oxley CH. Carbon based resistive strain gauge sensor fabricated on titanium using micro-dispensing direct write technology. 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CRediT authorship contribution statement Yu-Lin Song: Conceptualization, Methodology, Software, Investigation, Writing - review & editing, Validation, Supervision. Lavanya Bandi: Data curation, Writing - original draft, Software, Investigation. Declaration of Competing Interest 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. Acknowledgments This work was supported in part by the Ministry of Science and Technology, Taiwan, through grant MOST 106-2221-E-468-015. The authors are grateful to the Prof. Y. F. Chou with the Department of mechanical engineering, National Taiwan University, Taipei, Taiwan, for his technical support and valuable suggestion in numerical simulation. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.rinp.2020.103166. References [1] Lefebvre Arthur Henry. Atomization and sprays. 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