IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 60, no. 9,
September
2013
1949
Design and Manufacturing of a Piezoelectric Traveling-Wave Pumping Device Camilo Hernandez, Yves Bernard, and Adel Razek, Fellow, IEEE Abstract—In this article, we present the design and construction of a micropump exhibiting a nontraditional pumping principle whose design is achievable at very low scales. The operation is based on the action of a mechanical traveling wave deforming the bottom wall of a flexible channel containing a fluid. The paper treats for the first time the influence of the traveling wave parameters on the performance of the pump with the help of finite element simulations. The results obtained from the simulation are subsequently used for the dimensioning of the linear ultrasonic traveling wave actuator that drives the device. Finally, a very simple channel–reservoirs structure was conceived to test the device. At this point, several measurements of flow rate and back pressure were carried out to estimate the performance of the prototype for different values of wave amplitude. The article finishes with a comparison between the numerical and experimental results and a brief section of discussion and conclusions.
I. Introduction
D
uring the last two decades, the use of micropumps has reached many domains of science and technology. A huge diversity of designs, materials, and operating and actuation principles can be found in industry and the scientific literature. In spite of this significant variety, micropumps can always be identified as mechanical or nonmechanical devices [1]. Within the mechanical family, which is composed of devices requiring moving parts to function, actuation principles such as electrostatic [2], piezoelectric [3], electromagnetic [4], thermo-pneumatic [5], and pneumatic [6] are the most common. Here, many designs and architectures are possible but in general, two principal types stand out. These are reciprocating or piston-like geometries and peristaltic ones [7]. Within the nonmechanical category—devices without moving parts— electro-osmotic [8], magneto-hydrodynamic [9], and electro-hydrodynamic [10] drivers are often employed. The geometries related to nonmechanical pumps are quite simple and similar to each other. Normally, they simply consist of a linear channel connecting two reservoirs. When it comes to micropump drivers, an important list of advantages and disadvantages according to the application and operating conditions arises. Piezoelectric actuators, in particular, display a high power density (up to 1 × 104 W/cm3 according to [11]), the capability to be integrated in small-scale devices (some hundredths of
cubic micrometers [12]), and the possibility to work at ultrasonic frequencies (more than 20 kHz). To benefit from these advantages, the device described in this paper was conceived to work with piezoelectric transducers. The idea was the subject of a patent [13]. This article presents the design and manufacturing of a pump using an unconventional approach in which a mechanical traveling wave deforming the bottom wall of a flexible channel that contains a fluid is used to generate flow. The principle of acoustic streaming to pump a fluid has already been proposed. The authors of [12] and [14] presented devices that apply this concept. The actuation is performed by a piezoelectric linear ultrasonic traveling wave driver. The whole structure belongs to the mechanical category because moving parts are required for it to function. Therefore, many of the advantages of mechanical pumps are exploited in the present design. Additionally, in an effort to minimize the characteristic drawbacks of mechanical architectures, a very simple fluid-containing structure, quite similar to those typically used in nonmechanical devices, is employed. Among the most important characteristics of the pump’s design, there are the capability of producing a bidirectional flow and the possibility of pumping different types of fluids. In addition, small-scale manufacturing is achievable because of the simplicity of its geometry. The paper starts with the presentation of the structure. Then, it gives the details of the construction of a numerical model built by observing the variations of the flow rate for small changes in the parameters of the traveling wave with the help of finite element simulations. This stage is carried out to provide a starting point for the designing process. The resulting numerical data are fitted to a function describing the pumping operation in terms of the traveling wave characteristics. Using this function, the pump’s architecture is designed by adjusting the geometrical dimensions and materials used for the linear ultrasonic traveling wave actuator to obtain the highest value of flow rate for a fixed fluid-containing structure. The last part of the paper concerns the construction of the prototype and the experimental data obtained after several tests. At that point, a comparison with the numerical results is carried out, analyzed, and discussed. II. Proposed Architecture
Manuscript received May 9, 2013; accepted June 7, 2013. The authors are with the Laboratoire de Génie Electrique de Paris (LGEP)/SPEE-Labs, CNRS UMR 8507; Supélec; Université Pierre et Marie Curie Paris VI; Université Paris-Sud 11; Gif sur Yvette, France. DOI http://dx.doi.org/10.1109/TUFFC.2013.2779 0885–3010/$25.00
The pump’s architecture proposed in this paper is composed of two parts. The first is a mechanical structure employed for the device’s actuation. The second is a flu-
© 2013 IEEE
1950
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 60, no. 9,
September
2013
Fig. 1. π-like structure of a linear actuator.
id-containing arrangement whose purpose is to provide a proper enclosure for the fluid and a suitable interface with the structural unit. The mechanical component is a linear ultrasonic traveling wave actuator. It is composed of two piezoelectric transducers connected by a metallic flexural beam on which a mechanical traveling wave is induced. These elements are arranged in a π-like configuration, as shown in Fig. 1. The fluid-containing component is bonded onto the beam. It is composed of three layers of plastic forming two reservoirs connected by a channel whose base is in direct contact with the flexural beam (see Fig. 2). The objective of the device is to transfer very small quantities of a fluid from one reservoir to the other by means of the traveling wave induced on the cantilever beam and, therefore, to the base of the channel. III. Numerical Model The study of the flow generated when a fluid subjected to a traveling wave excitation was modeled by two rectangles stacked vertically, as shown in Fig. 3. Because of the simplicity of the geometry, the calculations for the flow generated by a traveling wave excitation do not require a significant calculating time, contrary to more complex 3-D models. To work with a two-dimensional model, the physical effects of the top layer of the channel were considered to be a rigid wall. This is approximation is valid only because of the significant thickness of the polydimethylsiloxane (PDMS) layer, which is 500 µm. This dimension matches that of the height of the channel; therefore, the deformations caused by the load exerted by the fluid are considered to be negligible. The top rectangle in Fig. 3 represents the fluid domain and represents the channels filled with a fluid. The bottom one, related to the structural domain, corresponds to the flexural beam. This configuration implies a structural– fluid coupling to accomplish the numerical simulations. The finite element computations of this model were performed with the help of the commercial finite element software Comsol (Comsol Inc., Burlington, MA). The
Fig. 2. (a) Channel composition and (b) cross-sectional view.
structural and fluid domains were coupled by means of an arbitrary Lagrangian Eulerian (ALE) component embedded in the program. The governing differential equation used for the structural domain is the Navier–Stokes equation accounting for Newton’s second law [15]:
ρ
∂ 2y − ∇ ⋅ c∇y = F, (1) ∂t 2
where y corresponds to displacement, c to the sound speed in the material, ρ to the density, and F to the applied forces. The fluid equation considered in the finite elements calculations corresponds to the Navier–Stokes continuity equation assuming an inviscid and irrotational flow. This expression is given by
Fig. 3. Coupled fluid–structure geometry.
hernandez et al.: design and manufacturing of a piezoelectric traveling-wave pumping device
1951
TABLE I. Boundary Conditions for Structural Domains According to Fig. 3 Boundary 1
Boundary 2, 6
Boundary 4
Boundary condition Displacement in y-direction (y jˆ)
Described displacement A · sin(2π ft + γx)
Free —
Free —
Displacement in x-direction (y iˆ) Force in y-direction (F jˆ)
0 —
— 0
— 0
Force in x-direction (Fiˆ)
—
0
0
A. Influence of the Traveling Wave Parameters ∂ρv T + ∇P + ρ(v ⋅ ∇)v − ∇ ⋅ [µ(∇v + (∇v ) )] = Fbody, on the Resulting Flow Rate ∂t (2) To estimate the influence of the amplitude, frequency, and wave number of the traveling wave on the resulting where v corresponds to the velocity vector, P to the presflow rate, several finite element computations were persure, μ to the viscosity, and F to the forces applied to the formed. The inputs were modified systematically and the fluid. flow rate magnitudes were recorded. First, the impacts of The boundary conditions of the sides of the rectangle each traveling wave parameter were considered separately. constituting the solid domain were left free except for the Then, their contributions were integrated in a whole exbottom side, on which a traveling wave function governing pression intended to relate the flow rate and the oscillathe displacements and, therefore, the velocity of the solid tion’s features. particles was prescribed. This function is given by
y = K ⋅ sin(γx + ωt), (3)
where K corresponds to the wave’s amplitude, γ to the wave number, ω to the angular frequency, and t to time. From (3), it is observable that three parameters completely define the dynamics of a traveling wave. These are the amplitude, the wave number, and the frequency. It is for this reason that we are interested in quantifying the resulting flow rate of the proposed pumping approach in terms of these three variables. In the case of fluid domain, three types of boundary conditions are observed. First, there are the openings or the vertical sides of the rectangle having direct contact with the reservoirs. On these lines, a constant pressure is imposed (normally zero). Second, there is the top side of the channel, in which the displacement, and consequently the velocity, of the fluid is assumed to be null. Finally, there is the bottom side, which is in direct interaction with the solid domain. At this location, the fluid particles follow the motion of the solid domain’s resulting deformation. A summary of the boundary conditions is shown in Tables I and II.
B. Impact of the Amplitude When a traveling wave of amplitude equal to the channel height is engaged in its bottom wall, a peristaltic pumping is observed. In fact, chambers of fixed volume, also called pillow volumes, are formed between two consecutive occlusion points, as is shown in Fig. 4. These chambers move at the phase velocity of the wave, transporting a defined quantity of fluid every time. Consequently, a pulsating flow is created in the direction of the traveling wave motion. The objective in this section is to determine the effect of the oscillation’s amplitude on the flow rate when the magnitude of the first is lower than the channel’s height. The height of the channel is 500 µm. The numerical simulations were performed by varying the wave’s amplitude within a range between 50 and 450 µm. A logarithmic-like response of the flow rate was found with an increasing amplitude. This suggests a maximum value of the flow rate for equal values of the traveling wave amplitude and channel height. Further descriptions of this evolution will be discussed later when considering all parameters together.
TABLE II. Boundary Conditions for Fluid Domains According to Fig. 3 Boundary condition Type Velocity in x-direction (v iˆ) Velocity in y-direction (v jˆ) Pressure (P)
Boundary 5
Boundary 3, 7
Boundary 4
Wall (no slip) Velocity 0 0
Open boundary Normal stress — —
Inlet Velocity ∂y iˆ/∂t ∂y jˆ/∂t
—
0
—
1952
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
Fig. 4. Peristaltic motion when a traveling wave is generated in the bottom wall of the channel.
C. Impact of the Wave Number This parameter has a strong influence in the shape of the oscillation observed along the channel. It determines the number of wavelengths present along the bottom wall as well as the phase velocity of the wavy motion. Similar to the amplitude, several the values of wave number were explored within a range between 50 and 300 m−1. A concave function describes the evolution of the flow rate and a maximum point was found around 100 m−1. This observation points to an optimal pumping performance near this value. D. Impact of the Frequency The same approach of the previous parameters was undertaken for the operating frequency which also defines the phase velocity of the traveling wave and the shape of the induced oscillation. The range of magnitudes considered in the frequency analysis goes from 10 to 40 kHz. This range was chosen to include the most common values of resonant frequencies found in the type of transducer used in the prototype’s construction. The flow rate response with respect to the frequency was found to follow a linear characteristic within the given range. So far, all the parameters of the traveling wave have been studied separately. However, it is of our interest to try to establish a relationship between all three and the resulting flow rate to proceed with the design process. To that end, the behavior of flow rate is observed as a function of wave amplitude and wave number at the same time for different frequencies. Fig. 5 shows the corresponding plots for 10, 20, 30, and 40 kHz. Here, it is very interesting to note that all the plots have the same shape but with different scale. This particularity confirms the linear proportionality between frequency and flow rate. The surface describing the flow rate behavior as a function of the wave amplitude and the wave number was approximated by the product of an inverse simplified quadratic function and a sigmoid function. The complete expression is given by Kγ Flow Rate(K , γ) = G(k) H (f ), a + bK + c γ + dK 2 + e γ 2 (4) where G(k) = 1/(1 + e−f (K − g)), H( f ) = 3.1 × 10−5f + 0.053, a = 1.73 × 104 s/m3, b = −1.55 × 107 s/m4, c =
vol. 60, no. 9,
September
2013
−1.31 × 102 s/m2, d = 2.16 × 106 s/m6, e = 1.17 s/m, f = 5.11 × 104 1/m, and g = 1.12 × 10−4 m. The effect of the frequency was estimated to be linear after confirming with a probabilistic approach that the slope of the curve relating flow rate and frequency is the same for all possible combinations of amplitude and wave number. To get an idea of how well the surfaces fit the values obtained from numerical methods, the average relative error for every frequency considered in the analysis has been calculated. Table III shows the results.
IV. Design of the Pump Langevin-type piezoelectric transducers (STC 8HS3528, Sunnytech) were employed in the manufacturing of the linear traveling wave actuator. On the top of the transducers, two metallic horns were placed to obtain a more point-like contact with the beam and to facilitate the wave propagation through the different components. A diagram of the setup is shown in Fig. 6. The maximum value of flow rate was found by performing a parametric variation of the independent variables constituting (4). Those are amplitude and frequency. The wave number, on the contrary, presents a dependence on the frequency and the physical characteristics of the beam. Therefore, the magnitudes of density, elasticity coefficient, and thickness and width of the beam become variable in the problem. In addition to the objective function, the constraints related to the bandwidth of the transducer and the materials available for construction presenting good acoustic properties have been imposed. The best configuration obtained for the given prototype using the channel’s configuration described previously, a 160 × 30 × 2.6 mm aluminum beam and two Langevin transducers is given in Table IV, for which the flow rate found was 2,31 × 10−7 m3/s. At this point, we remind the reader that by using different components, better pumping performances can be achieved. In the case of the prototype reported in this article, the resulting flow rate is closely related to the maximum vibrating amplitudes and the resonant frequency of the transducers. To obtain a vibration amplitude of 7 µm on the flexural beam at the resonant frequency of the piezoelectric transducers, an applied voltage of 80 Vpp was necessary. The power consumption of the actuator under those conditions was approximately 10 W. A. Obtaining a Traveling Wave on the Flexural Beam The technique employed to obtain a traveling wave on a finite beam, consists of exciting principally two consecutive natural modes of the beam at the same time. To accomplish this task, two forces shifted in phase by 90°, oscillating at an intermediary frequency between the two natural modes in question, are applied near the ex-
hernandez et al.: design and manufacturing of a piezoelectric traveling-wave pumping device
1953
tremities of the beam [16]. These forces must be applied in as point-like a manner as is possible at precise locations where the corresponding mode shape anti-nodes occur. If they are applied on the nodes, the shape mode will simply not be excited. The theoretical analysis is carried out based on the vibrating beam equation, which is solved by the method of modal expansion: YI
∂ 2y ∂ 4y + ρA 2 = Q f (x, t), (5) 4 ∂x ∂t
where Y, I, A, ρ, and Qf correspond to the elasticity modulus, the second moment of inertia, the cross-sectional area, the density of the beam, and the external forces acting on it, respectively. The solution to (5) for the system shown in Fig. 7 gives
y(x, t) = D1 ⋅ sin(φnx ) cos(Ωt) + D 2 ⋅ sin(φmx ) sin(Ωt)
+ D 3 ⋅ sin(φmx ) cos(Ωt) + D 4 ⋅ sin(φnx ) sin(Ωt), (6) with D1 =
K ρAΩ 2φn(l 1) K ρAΩ 2φm(l 2) = D , , 2 ω n2 − Ω 2 ωm2 − Ω 2
K ρAΩ 2φn(l 2) K ρAΩ 2φm(l 1) D3 = , , D4 = 2 2 ωm − Ω ω n2 − Ω 2
where ωi, Ω, and ϕi, correspond to angular frequency of the resonant mode i, the excitation angular frequency, and the shape of the ith resonant mode A rather well formed traveling wave appears on the beam when the constants D1, D2, D3, and D4 (which depend on the location of the applied forces l1 and l2) take values that minimize the standing wave ratio (SWR) of the oscillation created by the sum of the consecutive shape modes. In addition, one of the constants D1, D2, D3, or D4 must differ in sign from the others to obtain the desired motion on the beam. For magnitudes of l1 and l2 equal to 9 mm and 14.7 cm, respectively, a pseudo traveling wave presenting a SWR of 4.07 was obtained (values of SWR close to 1 imply a pure traveling wave). Its shape is shown in a three-dimensional plot (Fig. 8) viewed from the top, in which the x-axis corresponds to the length of the beam, the y-axis to the time, and the z-axis to the deformation amplitude. The traveling wave motion is evidenced by the diagonal stripes observed in the middle of the beam. TABLE III. Average Relative Error of the Fitted Curve for Net Flow as a Function of Frequency. Frequency (kHz)
Fig. 5. Flow rate evolution as a function of frequency.
10 20 30 40
Average relative error (%) 12.10 12.50 10.30 8.81
1954
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 60, no. 9,
September
2013
TABLE IV. Best Beam Parameters Giving the Highest Flow Rate for the Pump. Parameter Density (ρ) Elasticity modulus (Y) Wave amplitude (K) Thickness (tck) Width (w) Wave number (γ)
Fig. 6. Linear traveling wave actuator (dimensions in millimeters).
B. Channel Manufacturing The channel’s geometry was designed to be as simple as possible. As previously mentioned, it is composed of three layers. First, there is the bottom layer on which all of the structure reposes. For this prototype, it was made of a 50µm thin film of polyethylene glued directly to the beam with an epoxy substance. Above this layer, there are two more layers forming the channel and the containers. The first layer is composed of a 500-µm-thick polyester-based film (polyethylene terephthalate). Two 5-mm-diameter holes located at the extremities of the film act as containers. They are connected by a passage (channel) through which the fluid is transported. The second layer, composed of the same material used for the bottom layer, is placed on the top of the channel. Its purpose is to enclose the fluid and seal the top of the channel. The layers were assembled by means of the epoxy substance. A diagram of the structure is shown in Fig. 2.
Optimal value 2750 kg/m3 75 × 109 N/m2 5.00 × 10−4 m 0.0026 m 0.03 m 211.85 m−1
The resulting magnitudes of flow rate for different values of wave amplitude applied to the Langevin transducers are shown in Fig. 10. As expected, increments in amplitude result in increments of flow rate. At this point, it would be interesting to have an idea of the accuracy of the numerical results using the experimental data. Here, it is important to consider the fact that experimentally, it was only possible to test a very limited range of frequencies and amplitudes because of the intrinsic limitations of a Langevin transducer (low vibration amplitudes and very narrow bandwidth). For different values of amplitude applied experimentally, the observed flow rate values were compared with those predicted by (4). Fig. 10 presents the results. In this plot, some differences between the experimental and numerical results are observed. However, both the tendency and the order of magnitude of the predicted values agree at a reasonable level with the measurements. In fact, a significant relative error can be appreciated for low amplitudes. This is explained by the inaccuracies of the mathematical model for amplitudes smaller than 5 µm. For these values, the finite element simulations experience computing difficulties. Given the dimensions of the vibrating beam, the estimation of the forces and displacements that take place in the structure cannot be accurately estimated, even using a very fine meshing. This is due to the fact that the order of magnitude of the excitation (dis-
C. Flow Rate Calculation The flow rate of the prototype was calculated simply by measuring the time it takes for a droplet of definite volume of water to go from the left reservoir to the right one, as illustrated in Fig. 9.
Fig. 7. Superposition of modes approach to obtain a traveling wave on a flexural beam.
Fig. 8. Traveling wave behavior as a function of time and space.
hernandez et al.: design and manufacturing of a piezoelectric traveling-wave pumping device
1955
Fig. 9. Flow rate calculation.
placements) is far smaller than that of its physical dimensions (length and height). However, for magnitudes larger than 5 µm, the relative error decreases considerably. The average value is around 10%, suggesting an improvement in the accuracy of the proposed model. The linear dependency of the flow rate and amplitude could be explained by the proportional increase of the pillow volumes and, therefore, of the amount of liquid conveyed with the amplitude.
Fig. 11. Differential pressure manometer principle.
of the dependent variable with respect to the amplitude of the wave. It is also noticeable that numerical and experimental results differ less than those of the flow rate. The average relative error is around 11%, considering the whole range. This fact assures the validity of finite element simulations. The back pressure behavior as a function of amplitude is shown in Fig. 12.
D. Back Pressure Calculation To measure the maximum back pressure of the pump, the principle of an inclined manometer [17] was used. The mounting is depicted in Fig. 11. For this setup, the difference between pressure P0 and P1 is given by
∆P = P0 − P1 = d ρg ⋅ sin(α). (7)
To determine the maximum pressure the pump can manage, the device was systematically inclined until no pumping was observed. Because an angle α between a horizontal line and the channel is formed, the differential pressure given by (7) can be calculated. This was carried out for several levels of amplitude, as was done for the flow rate. The results are shown in Fig. 12. Similarly to the flow rate, a comparison of the expected back pressure values and the experimental ones was likewise conducted. Here, we remark a proportional increment
Fig. 10. Maximum flow rate versus amplitude.
V. Conclusions In this paper, the manufacturing process of the pump prototype was described and the experimental setup installed for its characterization was explained. Using an elementary structure for the channels, the pumping principle was proven. Recent technological developments in the manufacturing of micromechanical systems, especially in the domain of micro-beams [18]–[20], suggest the possibility of miniaturizing the pump presented in this paper to be subsequently integrated into a sub-centimeter- or sub-millimeter-sized device. The model described in this article suggests a better performance of the pump for a traveling wave amplitude equal to the channels height and for a high operating frequency. By reducing the size of the device, it would be
Fig. 12. Maximum back pressure versus amplitude.
1956
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
possible to attain these conditions and obtain exploitable flow rates for microfluid applications which in some cases can be as low as some picoliters per minute [21]. The most important pumping characteristics of the device were measured and compared with the proposed model employed for dimensioning purposes presented in previous sections. The results are very satisfactory because they do not differ significantly from the expectations. However, further measurements must be done to explore the device’s behavior under different frequencies and higher values of amplitude, keeping in mind that different prototypes are necessary to carry out this task. VI. References [1] F. Tay, Microfluidics and BioMEMS Applications, 1st ed., Boston, MA: Kluwer Academic Publishers, 2002, pp. 3–24. [2] M. M. Teymoori and E. Abbaspour-Sani, “Design and simulation of a novel electrostatic peristaltic micromachined pump for drug delivery applications,” Sens. Actuators A, vol. 117, no. 2, pp. 222–229, 2005. [3] H. Andersson, W. van der Wijngaart, P. Nilsson, P. Enoksson, and G. Stemme, “A valveless diffuser micropump for microfluidic analytical systems,” Sens. Actuators B, vol. 72, no. 3, pp. 259–265, 2001. [4] S. Guo, J. Wang, Q. Pan, and J. Guo, “Solenoid actuator-based novel type of micro-pump,” in IEEE Int. Conf. Robotics and Biomimetics, 2006, pp. 1281–1286. [5] J.-C. Yoo, Y. J. Choi, C. J. Kang, and Y.-S. Kim, “A novel polydimethylsiloxane microfluidic system including thermopneumatic-actuated micro-pump and paraffin-actuated microvalve,” Sens. Actuators A, vol. 139, no. 1–2, pp. 216–220, 2007. [6] K. Y. Lien, W. C. Lee, H. Y. Lei, and G. B. Lee, “Integrated reverse transcription polymerase chain reaction systems for virus detection,” Biosens. Bioelectron., vol. 22, pp. 1739–1748, Mar. 2007. [7] C. Hernandez, Y. Bernard, and A. Razek, “A global assessment of piezoelectric actuated micro-pumps,” Eur. Phys. J. Appl. Phys., vol. 51, no. 2, art. no. 20101 Aug. 2010. [8] S. Joo, T. D. Chung, and H. C. Kim, “A rapid field-free electroosmotic micropump incorporating charged microchannel surfaces,” Sens. Actuators B, vol. 123, no. 2, pp. 1161–1168, 2007. [9] A. V. Lemoff and A. P. Lee, “An ac magnetohydrodynamic micropump,” Sens. Actuators B, vol. 63, no. 3, pp. 178–185, 2000. [10] V. Singhal and S. V. Garimella, “Induction electrohydrodynamics micropump for high heat flux cooling,” Sens. Actuators A, vol. 134, no. 2, pp. 650–659, 2007. [11] J. L. Pons, Emerging Actuator Technologies: A Micromechatronic Approach. Chichester, UK: Wiley, 2005. [12] C. E. Bradley and R. M. White, “Acoustically driven flow in flexural plate wave devices: Theory and experiment,” in IEEE Ultrasonics Symp. Proc., 1994, pp. 593–597. [13] Y. Bernard, C. Hernandez, and A. Razek, “Micro pompe à onde progressive ultrasonore pour liquide,” Institut National de la Propriété Industrielle, Patent B10026WO. [14] H. Yu and E. S. Kim, “Noninvasive acoustic-wave microfluidic driver,” in IEEE Int. Micro Electro Mechanical Systems Conf., 2002, pp. 125–128. [15] COMSOL AB, COMSOL Multiphysics Modeling Guide, (version 3.2), Burlington, MA: Comsol, 2005. [16] B. G. Loh and P. I. Ro, “An object transport system using flexural ultrasonic progressive waves generated by two-mode excitation,”
vol. 60, no. 9,
September
2013
IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 47, no. 4, pp. 994–999, 2000. [17] D. Rama Durgaiah, Fluid Mechanics and Machinery. New Delhi, India: New Age International Publishers, 2006. [18] S. M. Yang and C. A. Chang, “Piezoresistive bridge-microcantilever biosensor by CMOS process for surface stress measurement,” Sens. Actuators B, vol. 145, no. 1, pp. 405–410, 2010. [19] A. M. Moulin, S. J. O’Shea, and M. E. Welland, “Microcantileverbased biosensors,” Ultramicroscopy, vol. 82, no. 1–4, pp. 23–31, 2000. [20] W. Dong, X. Lu, Y. Cui, J. Wang, and M. Liu, “Fabrication and characterization of microcantilever integrated with PZT thin film sensor and actuator,” Thin Solid Films, vol. 515, no. 24, pp. 8544– 8548, 2007. [21] D. J. Laser and J. G. Santiago, “A review of micropumps,” J. Micromech. Microeng., vol. 14, no. 6, pp. R35–R64, 2004.
Camilo Hernandez graduated in electrical engineering from the University of Los Andes, Bogota, Colombia, in 2003. He received his Ph.D. degree in sciences from the University of Paris XI, France, in September 2010 for his work on piezoelectric micropumps. He is working on piezoelectric motors in a postdoctoral position in the Laboratory of Electrical Engineering in Paris.
Yves Bernard was born in Paris, France, on January 8, 1974. He graduated from the University of Paris-Sud Orsay with a diploma in energy transformation. He received his doctoral degree in September 2000 with a thesis on the magnetic hysteresis modeling in the finite element modeling method. He has been a professor at the University of Paris-Sud Orsay since September 2012. His research activity deals with the modeling and conception of piezoelectric devices.
Adel Razek was born in Egypt. He obtained the Dipl.Eng. and M.Sc.Eng. degrees from Cairo University in Egypt in 1968 and 1971. Joining the Institut National Polytechnique de Grenoble (INPG) in 1971, he became Docteur d’État ès Sciences Physiques in 1976. In 1977, he was a postdoctoral researcher at INPG. He has been a Research Director at the Centre National de la Recherche Scientifique (CNRS) in France since 1986. He moved to the Laboratoire de Génie Électrique de Paris associated with CNRS, SUPELEC, and the University of Paris, as a research scientist at CNRS in 1978, senior research scientist in 1981, research director in 1986, and senior research director in 1997. His main current research concerns computational electromagnetics (EMC, NDT, CAD) and design of electrical drives and actuators. He is the author or co-author of more than 150 scientific papers. Dr. Razek received the André Blondel medal in 1985 for his research work. He is a Fellow of the IEEE, a Fellow of the Institution of Electrical Engineers (IEE/IET; UK), and a Membre Émérite of the Société des Ingénieurs Électriciens (SEE; France).
vol. 60, no. 9,
September
2013
1949
Design and Manufacturing of a Piezoelectric Traveling-Wave Pumping Device Camilo Hernandez, Yves Bernard, and Adel Razek, Fellow, IEEE Abstract—In this article, we present the design and construction of a micropump exhibiting a nontraditional pumping principle whose design is achievable at very low scales. The operation is based on the action of a mechanical traveling wave deforming the bottom wall of a flexible channel containing a fluid. The paper treats for the first time the influence of the traveling wave parameters on the performance of the pump with the help of finite element simulations. The results obtained from the simulation are subsequently used for the dimensioning of the linear ultrasonic traveling wave actuator that drives the device. Finally, a very simple channel–reservoirs structure was conceived to test the device. At this point, several measurements of flow rate and back pressure were carried out to estimate the performance of the prototype for different values of wave amplitude. The article finishes with a comparison between the numerical and experimental results and a brief section of discussion and conclusions.
I. Introduction
D
uring the last two decades, the use of micropumps has reached many domains of science and technology. A huge diversity of designs, materials, and operating and actuation principles can be found in industry and the scientific literature. In spite of this significant variety, micropumps can always be identified as mechanical or nonmechanical devices [1]. Within the mechanical family, which is composed of devices requiring moving parts to function, actuation principles such as electrostatic [2], piezoelectric [3], electromagnetic [4], thermo-pneumatic [5], and pneumatic [6] are the most common. Here, many designs and architectures are possible but in general, two principal types stand out. These are reciprocating or piston-like geometries and peristaltic ones [7]. Within the nonmechanical category—devices without moving parts— electro-osmotic [8], magneto-hydrodynamic [9], and electro-hydrodynamic [10] drivers are often employed. The geometries related to nonmechanical pumps are quite simple and similar to each other. Normally, they simply consist of a linear channel connecting two reservoirs. When it comes to micropump drivers, an important list of advantages and disadvantages according to the application and operating conditions arises. Piezoelectric actuators, in particular, display a high power density (up to 1 × 104 W/cm3 according to [11]), the capability to be integrated in small-scale devices (some hundredths of
cubic micrometers [12]), and the possibility to work at ultrasonic frequencies (more than 20 kHz). To benefit from these advantages, the device described in this paper was conceived to work with piezoelectric transducers. The idea was the subject of a patent [13]. This article presents the design and manufacturing of a pump using an unconventional approach in which a mechanical traveling wave deforming the bottom wall of a flexible channel that contains a fluid is used to generate flow. The principle of acoustic streaming to pump a fluid has already been proposed. The authors of [12] and [14] presented devices that apply this concept. The actuation is performed by a piezoelectric linear ultrasonic traveling wave driver. The whole structure belongs to the mechanical category because moving parts are required for it to function. Therefore, many of the advantages of mechanical pumps are exploited in the present design. Additionally, in an effort to minimize the characteristic drawbacks of mechanical architectures, a very simple fluid-containing structure, quite similar to those typically used in nonmechanical devices, is employed. Among the most important characteristics of the pump’s design, there are the capability of producing a bidirectional flow and the possibility of pumping different types of fluids. In addition, small-scale manufacturing is achievable because of the simplicity of its geometry. The paper starts with the presentation of the structure. Then, it gives the details of the construction of a numerical model built by observing the variations of the flow rate for small changes in the parameters of the traveling wave with the help of finite element simulations. This stage is carried out to provide a starting point for the designing process. The resulting numerical data are fitted to a function describing the pumping operation in terms of the traveling wave characteristics. Using this function, the pump’s architecture is designed by adjusting the geometrical dimensions and materials used for the linear ultrasonic traveling wave actuator to obtain the highest value of flow rate for a fixed fluid-containing structure. The last part of the paper concerns the construction of the prototype and the experimental data obtained after several tests. At that point, a comparison with the numerical results is carried out, analyzed, and discussed. II. Proposed Architecture
Manuscript received May 9, 2013; accepted June 7, 2013. The authors are with the Laboratoire de Génie Electrique de Paris (LGEP)/SPEE-Labs, CNRS UMR 8507; Supélec; Université Pierre et Marie Curie Paris VI; Université Paris-Sud 11; Gif sur Yvette, France. DOI http://dx.doi.org/10.1109/TUFFC.2013.2779 0885–3010/$25.00
The pump’s architecture proposed in this paper is composed of two parts. The first is a mechanical structure employed for the device’s actuation. The second is a flu-
© 2013 IEEE
1950
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 60, no. 9,
September
2013
Fig. 1. π-like structure of a linear actuator.
id-containing arrangement whose purpose is to provide a proper enclosure for the fluid and a suitable interface with the structural unit. The mechanical component is a linear ultrasonic traveling wave actuator. It is composed of two piezoelectric transducers connected by a metallic flexural beam on which a mechanical traveling wave is induced. These elements are arranged in a π-like configuration, as shown in Fig. 1. The fluid-containing component is bonded onto the beam. It is composed of three layers of plastic forming two reservoirs connected by a channel whose base is in direct contact with the flexural beam (see Fig. 2). The objective of the device is to transfer very small quantities of a fluid from one reservoir to the other by means of the traveling wave induced on the cantilever beam and, therefore, to the base of the channel. III. Numerical Model The study of the flow generated when a fluid subjected to a traveling wave excitation was modeled by two rectangles stacked vertically, as shown in Fig. 3. Because of the simplicity of the geometry, the calculations for the flow generated by a traveling wave excitation do not require a significant calculating time, contrary to more complex 3-D models. To work with a two-dimensional model, the physical effects of the top layer of the channel were considered to be a rigid wall. This is approximation is valid only because of the significant thickness of the polydimethylsiloxane (PDMS) layer, which is 500 µm. This dimension matches that of the height of the channel; therefore, the deformations caused by the load exerted by the fluid are considered to be negligible. The top rectangle in Fig. 3 represents the fluid domain and represents the channels filled with a fluid. The bottom one, related to the structural domain, corresponds to the flexural beam. This configuration implies a structural– fluid coupling to accomplish the numerical simulations. The finite element computations of this model were performed with the help of the commercial finite element software Comsol (Comsol Inc., Burlington, MA). The
Fig. 2. (a) Channel composition and (b) cross-sectional view.
structural and fluid domains were coupled by means of an arbitrary Lagrangian Eulerian (ALE) component embedded in the program. The governing differential equation used for the structural domain is the Navier–Stokes equation accounting for Newton’s second law [15]:
ρ
∂ 2y − ∇ ⋅ c∇y = F, (1) ∂t 2
where y corresponds to displacement, c to the sound speed in the material, ρ to the density, and F to the applied forces. The fluid equation considered in the finite elements calculations corresponds to the Navier–Stokes continuity equation assuming an inviscid and irrotational flow. This expression is given by
Fig. 3. Coupled fluid–structure geometry.
hernandez et al.: design and manufacturing of a piezoelectric traveling-wave pumping device
1951
TABLE I. Boundary Conditions for Structural Domains According to Fig. 3 Boundary 1
Boundary 2, 6
Boundary 4
Boundary condition Displacement in y-direction (y jˆ)
Described displacement A · sin(2π ft + γx)
Free —
Free —
Displacement in x-direction (y iˆ) Force in y-direction (F jˆ)
0 —
— 0
— 0
Force in x-direction (Fiˆ)
—
0
0
A. Influence of the Traveling Wave Parameters ∂ρv T + ∇P + ρ(v ⋅ ∇)v − ∇ ⋅ [µ(∇v + (∇v ) )] = Fbody, on the Resulting Flow Rate ∂t (2) To estimate the influence of the amplitude, frequency, and wave number of the traveling wave on the resulting where v corresponds to the velocity vector, P to the presflow rate, several finite element computations were persure, μ to the viscosity, and F to the forces applied to the formed. The inputs were modified systematically and the fluid. flow rate magnitudes were recorded. First, the impacts of The boundary conditions of the sides of the rectangle each traveling wave parameter were considered separately. constituting the solid domain were left free except for the Then, their contributions were integrated in a whole exbottom side, on which a traveling wave function governing pression intended to relate the flow rate and the oscillathe displacements and, therefore, the velocity of the solid tion’s features. particles was prescribed. This function is given by
y = K ⋅ sin(γx + ωt), (3)
where K corresponds to the wave’s amplitude, γ to the wave number, ω to the angular frequency, and t to time. From (3), it is observable that three parameters completely define the dynamics of a traveling wave. These are the amplitude, the wave number, and the frequency. It is for this reason that we are interested in quantifying the resulting flow rate of the proposed pumping approach in terms of these three variables. In the case of fluid domain, three types of boundary conditions are observed. First, there are the openings or the vertical sides of the rectangle having direct contact with the reservoirs. On these lines, a constant pressure is imposed (normally zero). Second, there is the top side of the channel, in which the displacement, and consequently the velocity, of the fluid is assumed to be null. Finally, there is the bottom side, which is in direct interaction with the solid domain. At this location, the fluid particles follow the motion of the solid domain’s resulting deformation. A summary of the boundary conditions is shown in Tables I and II.
B. Impact of the Amplitude When a traveling wave of amplitude equal to the channel height is engaged in its bottom wall, a peristaltic pumping is observed. In fact, chambers of fixed volume, also called pillow volumes, are formed between two consecutive occlusion points, as is shown in Fig. 4. These chambers move at the phase velocity of the wave, transporting a defined quantity of fluid every time. Consequently, a pulsating flow is created in the direction of the traveling wave motion. The objective in this section is to determine the effect of the oscillation’s amplitude on the flow rate when the magnitude of the first is lower than the channel’s height. The height of the channel is 500 µm. The numerical simulations were performed by varying the wave’s amplitude within a range between 50 and 450 µm. A logarithmic-like response of the flow rate was found with an increasing amplitude. This suggests a maximum value of the flow rate for equal values of the traveling wave amplitude and channel height. Further descriptions of this evolution will be discussed later when considering all parameters together.
TABLE II. Boundary Conditions for Fluid Domains According to Fig. 3 Boundary condition Type Velocity in x-direction (v iˆ) Velocity in y-direction (v jˆ) Pressure (P)
Boundary 5
Boundary 3, 7
Boundary 4
Wall (no slip) Velocity 0 0
Open boundary Normal stress — —
Inlet Velocity ∂y iˆ/∂t ∂y jˆ/∂t
—
0
—
1952
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
Fig. 4. Peristaltic motion when a traveling wave is generated in the bottom wall of the channel.
C. Impact of the Wave Number This parameter has a strong influence in the shape of the oscillation observed along the channel. It determines the number of wavelengths present along the bottom wall as well as the phase velocity of the wavy motion. Similar to the amplitude, several the values of wave number were explored within a range between 50 and 300 m−1. A concave function describes the evolution of the flow rate and a maximum point was found around 100 m−1. This observation points to an optimal pumping performance near this value. D. Impact of the Frequency The same approach of the previous parameters was undertaken for the operating frequency which also defines the phase velocity of the traveling wave and the shape of the induced oscillation. The range of magnitudes considered in the frequency analysis goes from 10 to 40 kHz. This range was chosen to include the most common values of resonant frequencies found in the type of transducer used in the prototype’s construction. The flow rate response with respect to the frequency was found to follow a linear characteristic within the given range. So far, all the parameters of the traveling wave have been studied separately. However, it is of our interest to try to establish a relationship between all three and the resulting flow rate to proceed with the design process. To that end, the behavior of flow rate is observed as a function of wave amplitude and wave number at the same time for different frequencies. Fig. 5 shows the corresponding plots for 10, 20, 30, and 40 kHz. Here, it is very interesting to note that all the plots have the same shape but with different scale. This particularity confirms the linear proportionality between frequency and flow rate. The surface describing the flow rate behavior as a function of the wave amplitude and the wave number was approximated by the product of an inverse simplified quadratic function and a sigmoid function. The complete expression is given by Kγ Flow Rate(K , γ) = G(k) H (f ), a + bK + c γ + dK 2 + e γ 2 (4) where G(k) = 1/(1 + e−f (K − g)), H( f ) = 3.1 × 10−5f + 0.053, a = 1.73 × 104 s/m3, b = −1.55 × 107 s/m4, c =
vol. 60, no. 9,
September
2013
−1.31 × 102 s/m2, d = 2.16 × 106 s/m6, e = 1.17 s/m, f = 5.11 × 104 1/m, and g = 1.12 × 10−4 m. The effect of the frequency was estimated to be linear after confirming with a probabilistic approach that the slope of the curve relating flow rate and frequency is the same for all possible combinations of amplitude and wave number. To get an idea of how well the surfaces fit the values obtained from numerical methods, the average relative error for every frequency considered in the analysis has been calculated. Table III shows the results.
IV. Design of the Pump Langevin-type piezoelectric transducers (STC 8HS3528, Sunnytech) were employed in the manufacturing of the linear traveling wave actuator. On the top of the transducers, two metallic horns were placed to obtain a more point-like contact with the beam and to facilitate the wave propagation through the different components. A diagram of the setup is shown in Fig. 6. The maximum value of flow rate was found by performing a parametric variation of the independent variables constituting (4). Those are amplitude and frequency. The wave number, on the contrary, presents a dependence on the frequency and the physical characteristics of the beam. Therefore, the magnitudes of density, elasticity coefficient, and thickness and width of the beam become variable in the problem. In addition to the objective function, the constraints related to the bandwidth of the transducer and the materials available for construction presenting good acoustic properties have been imposed. The best configuration obtained for the given prototype using the channel’s configuration described previously, a 160 × 30 × 2.6 mm aluminum beam and two Langevin transducers is given in Table IV, for which the flow rate found was 2,31 × 10−7 m3/s. At this point, we remind the reader that by using different components, better pumping performances can be achieved. In the case of the prototype reported in this article, the resulting flow rate is closely related to the maximum vibrating amplitudes and the resonant frequency of the transducers. To obtain a vibration amplitude of 7 µm on the flexural beam at the resonant frequency of the piezoelectric transducers, an applied voltage of 80 Vpp was necessary. The power consumption of the actuator under those conditions was approximately 10 W. A. Obtaining a Traveling Wave on the Flexural Beam The technique employed to obtain a traveling wave on a finite beam, consists of exciting principally two consecutive natural modes of the beam at the same time. To accomplish this task, two forces shifted in phase by 90°, oscillating at an intermediary frequency between the two natural modes in question, are applied near the ex-
hernandez et al.: design and manufacturing of a piezoelectric traveling-wave pumping device
1953
tremities of the beam [16]. These forces must be applied in as point-like a manner as is possible at precise locations where the corresponding mode shape anti-nodes occur. If they are applied on the nodes, the shape mode will simply not be excited. The theoretical analysis is carried out based on the vibrating beam equation, which is solved by the method of modal expansion: YI
∂ 2y ∂ 4y + ρA 2 = Q f (x, t), (5) 4 ∂x ∂t
where Y, I, A, ρ, and Qf correspond to the elasticity modulus, the second moment of inertia, the cross-sectional area, the density of the beam, and the external forces acting on it, respectively. The solution to (5) for the system shown in Fig. 7 gives
y(x, t) = D1 ⋅ sin(φnx ) cos(Ωt) + D 2 ⋅ sin(φmx ) sin(Ωt)
+ D 3 ⋅ sin(φmx ) cos(Ωt) + D 4 ⋅ sin(φnx ) sin(Ωt), (6) with D1 =
K ρAΩ 2φn(l 1) K ρAΩ 2φm(l 2) = D , , 2 ω n2 − Ω 2 ωm2 − Ω 2
K ρAΩ 2φn(l 2) K ρAΩ 2φm(l 1) D3 = , , D4 = 2 2 ωm − Ω ω n2 − Ω 2
where ωi, Ω, and ϕi, correspond to angular frequency of the resonant mode i, the excitation angular frequency, and the shape of the ith resonant mode A rather well formed traveling wave appears on the beam when the constants D1, D2, D3, and D4 (which depend on the location of the applied forces l1 and l2) take values that minimize the standing wave ratio (SWR) of the oscillation created by the sum of the consecutive shape modes. In addition, one of the constants D1, D2, D3, or D4 must differ in sign from the others to obtain the desired motion on the beam. For magnitudes of l1 and l2 equal to 9 mm and 14.7 cm, respectively, a pseudo traveling wave presenting a SWR of 4.07 was obtained (values of SWR close to 1 imply a pure traveling wave). Its shape is shown in a three-dimensional plot (Fig. 8) viewed from the top, in which the x-axis corresponds to the length of the beam, the y-axis to the time, and the z-axis to the deformation amplitude. The traveling wave motion is evidenced by the diagonal stripes observed in the middle of the beam. TABLE III. Average Relative Error of the Fitted Curve for Net Flow as a Function of Frequency. Frequency (kHz)
Fig. 5. Flow rate evolution as a function of frequency.
10 20 30 40
Average relative error (%) 12.10 12.50 10.30 8.81
1954
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 60, no. 9,
September
2013
TABLE IV. Best Beam Parameters Giving the Highest Flow Rate for the Pump. Parameter Density (ρ) Elasticity modulus (Y) Wave amplitude (K) Thickness (tck) Width (w) Wave number (γ)
Fig. 6. Linear traveling wave actuator (dimensions in millimeters).
B. Channel Manufacturing The channel’s geometry was designed to be as simple as possible. As previously mentioned, it is composed of three layers. First, there is the bottom layer on which all of the structure reposes. For this prototype, it was made of a 50µm thin film of polyethylene glued directly to the beam with an epoxy substance. Above this layer, there are two more layers forming the channel and the containers. The first layer is composed of a 500-µm-thick polyester-based film (polyethylene terephthalate). Two 5-mm-diameter holes located at the extremities of the film act as containers. They are connected by a passage (channel) through which the fluid is transported. The second layer, composed of the same material used for the bottom layer, is placed on the top of the channel. Its purpose is to enclose the fluid and seal the top of the channel. The layers were assembled by means of the epoxy substance. A diagram of the structure is shown in Fig. 2.
Optimal value 2750 kg/m3 75 × 109 N/m2 5.00 × 10−4 m 0.0026 m 0.03 m 211.85 m−1
The resulting magnitudes of flow rate for different values of wave amplitude applied to the Langevin transducers are shown in Fig. 10. As expected, increments in amplitude result in increments of flow rate. At this point, it would be interesting to have an idea of the accuracy of the numerical results using the experimental data. Here, it is important to consider the fact that experimentally, it was only possible to test a very limited range of frequencies and amplitudes because of the intrinsic limitations of a Langevin transducer (low vibration amplitudes and very narrow bandwidth). For different values of amplitude applied experimentally, the observed flow rate values were compared with those predicted by (4). Fig. 10 presents the results. In this plot, some differences between the experimental and numerical results are observed. However, both the tendency and the order of magnitude of the predicted values agree at a reasonable level with the measurements. In fact, a significant relative error can be appreciated for low amplitudes. This is explained by the inaccuracies of the mathematical model for amplitudes smaller than 5 µm. For these values, the finite element simulations experience computing difficulties. Given the dimensions of the vibrating beam, the estimation of the forces and displacements that take place in the structure cannot be accurately estimated, even using a very fine meshing. This is due to the fact that the order of magnitude of the excitation (dis-
C. Flow Rate Calculation The flow rate of the prototype was calculated simply by measuring the time it takes for a droplet of definite volume of water to go from the left reservoir to the right one, as illustrated in Fig. 9.
Fig. 7. Superposition of modes approach to obtain a traveling wave on a flexural beam.
Fig. 8. Traveling wave behavior as a function of time and space.
hernandez et al.: design and manufacturing of a piezoelectric traveling-wave pumping device
1955
Fig. 9. Flow rate calculation.
placements) is far smaller than that of its physical dimensions (length and height). However, for magnitudes larger than 5 µm, the relative error decreases considerably. The average value is around 10%, suggesting an improvement in the accuracy of the proposed model. The linear dependency of the flow rate and amplitude could be explained by the proportional increase of the pillow volumes and, therefore, of the amount of liquid conveyed with the amplitude.
Fig. 11. Differential pressure manometer principle.
of the dependent variable with respect to the amplitude of the wave. It is also noticeable that numerical and experimental results differ less than those of the flow rate. The average relative error is around 11%, considering the whole range. This fact assures the validity of finite element simulations. The back pressure behavior as a function of amplitude is shown in Fig. 12.
D. Back Pressure Calculation To measure the maximum back pressure of the pump, the principle of an inclined manometer [17] was used. The mounting is depicted in Fig. 11. For this setup, the difference between pressure P0 and P1 is given by
∆P = P0 − P1 = d ρg ⋅ sin(α). (7)
To determine the maximum pressure the pump can manage, the device was systematically inclined until no pumping was observed. Because an angle α between a horizontal line and the channel is formed, the differential pressure given by (7) can be calculated. This was carried out for several levels of amplitude, as was done for the flow rate. The results are shown in Fig. 12. Similarly to the flow rate, a comparison of the expected back pressure values and the experimental ones was likewise conducted. Here, we remark a proportional increment
Fig. 10. Maximum flow rate versus amplitude.
V. Conclusions In this paper, the manufacturing process of the pump prototype was described and the experimental setup installed for its characterization was explained. Using an elementary structure for the channels, the pumping principle was proven. Recent technological developments in the manufacturing of micromechanical systems, especially in the domain of micro-beams [18]–[20], suggest the possibility of miniaturizing the pump presented in this paper to be subsequently integrated into a sub-centimeter- or sub-millimeter-sized device. The model described in this article suggests a better performance of the pump for a traveling wave amplitude equal to the channels height and for a high operating frequency. By reducing the size of the device, it would be
Fig. 12. Maximum back pressure versus amplitude.
1956
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
possible to attain these conditions and obtain exploitable flow rates for microfluid applications which in some cases can be as low as some picoliters per minute [21]. The most important pumping characteristics of the device were measured and compared with the proposed model employed for dimensioning purposes presented in previous sections. The results are very satisfactory because they do not differ significantly from the expectations. However, further measurements must be done to explore the device’s behavior under different frequencies and higher values of amplitude, keeping in mind that different prototypes are necessary to carry out this task. VI. References [1] F. Tay, Microfluidics and BioMEMS Applications, 1st ed., Boston, MA: Kluwer Academic Publishers, 2002, pp. 3–24. [2] M. M. Teymoori and E. Abbaspour-Sani, “Design and simulation of a novel electrostatic peristaltic micromachined pump for drug delivery applications,” Sens. Actuators A, vol. 117, no. 2, pp. 222–229, 2005. [3] H. Andersson, W. van der Wijngaart, P. Nilsson, P. Enoksson, and G. Stemme, “A valveless diffuser micropump for microfluidic analytical systems,” Sens. Actuators B, vol. 72, no. 3, pp. 259–265, 2001. [4] S. Guo, J. Wang, Q. Pan, and J. Guo, “Solenoid actuator-based novel type of micro-pump,” in IEEE Int. Conf. Robotics and Biomimetics, 2006, pp. 1281–1286. [5] J.-C. Yoo, Y. J. Choi, C. J. Kang, and Y.-S. Kim, “A novel polydimethylsiloxane microfluidic system including thermopneumatic-actuated micro-pump and paraffin-actuated microvalve,” Sens. Actuators A, vol. 139, no. 1–2, pp. 216–220, 2007. [6] K. Y. Lien, W. C. Lee, H. Y. Lei, and G. B. Lee, “Integrated reverse transcription polymerase chain reaction systems for virus detection,” Biosens. Bioelectron., vol. 22, pp. 1739–1748, Mar. 2007. [7] C. Hernandez, Y. Bernard, and A. Razek, “A global assessment of piezoelectric actuated micro-pumps,” Eur. Phys. J. Appl. Phys., vol. 51, no. 2, art. no. 20101 Aug. 2010. [8] S. Joo, T. D. Chung, and H. C. Kim, “A rapid field-free electroosmotic micropump incorporating charged microchannel surfaces,” Sens. Actuators B, vol. 123, no. 2, pp. 1161–1168, 2007. [9] A. V. Lemoff and A. P. Lee, “An ac magnetohydrodynamic micropump,” Sens. Actuators B, vol. 63, no. 3, pp. 178–185, 2000. [10] V. Singhal and S. V. Garimella, “Induction electrohydrodynamics micropump for high heat flux cooling,” Sens. Actuators A, vol. 134, no. 2, pp. 650–659, 2007. [11] J. L. Pons, Emerging Actuator Technologies: A Micromechatronic Approach. Chichester, UK: Wiley, 2005. [12] C. E. Bradley and R. M. White, “Acoustically driven flow in flexural plate wave devices: Theory and experiment,” in IEEE Ultrasonics Symp. Proc., 1994, pp. 593–597. [13] Y. Bernard, C. Hernandez, and A. Razek, “Micro pompe à onde progressive ultrasonore pour liquide,” Institut National de la Propriété Industrielle, Patent B10026WO. [14] H. Yu and E. S. Kim, “Noninvasive acoustic-wave microfluidic driver,” in IEEE Int. Micro Electro Mechanical Systems Conf., 2002, pp. 125–128. [15] COMSOL AB, COMSOL Multiphysics Modeling Guide, (version 3.2), Burlington, MA: Comsol, 2005. [16] B. G. Loh and P. I. Ro, “An object transport system using flexural ultrasonic progressive waves generated by two-mode excitation,”
vol. 60, no. 9,
September
2013
IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 47, no. 4, pp. 994–999, 2000. [17] D. Rama Durgaiah, Fluid Mechanics and Machinery. New Delhi, India: New Age International Publishers, 2006. [18] S. M. Yang and C. A. Chang, “Piezoresistive bridge-microcantilever biosensor by CMOS process for surface stress measurement,” Sens. Actuators B, vol. 145, no. 1, pp. 405–410, 2010. [19] A. M. Moulin, S. J. O’Shea, and M. E. Welland, “Microcantileverbased biosensors,” Ultramicroscopy, vol. 82, no. 1–4, pp. 23–31, 2000. [20] W. Dong, X. Lu, Y. Cui, J. Wang, and M. Liu, “Fabrication and characterization of microcantilever integrated with PZT thin film sensor and actuator,” Thin Solid Films, vol. 515, no. 24, pp. 8544– 8548, 2007. [21] D. J. Laser and J. G. Santiago, “A review of micropumps,” J. Micromech. Microeng., vol. 14, no. 6, pp. R35–R64, 2004.
Camilo Hernandez graduated in electrical engineering from the University of Los Andes, Bogota, Colombia, in 2003. He received his Ph.D. degree in sciences from the University of Paris XI, France, in September 2010 for his work on piezoelectric micropumps. He is working on piezoelectric motors in a postdoctoral position in the Laboratory of Electrical Engineering in Paris.
Yves Bernard was born in Paris, France, on January 8, 1974. He graduated from the University of Paris-Sud Orsay with a diploma in energy transformation. He received his doctoral degree in September 2000 with a thesis on the magnetic hysteresis modeling in the finite element modeling method. He has been a professor at the University of Paris-Sud Orsay since September 2012. His research activity deals with the modeling and conception of piezoelectric devices.
Adel Razek was born in Egypt. He obtained the Dipl.Eng. and M.Sc.Eng. degrees from Cairo University in Egypt in 1968 and 1971. Joining the Institut National Polytechnique de Grenoble (INPG) in 1971, he became Docteur d’État ès Sciences Physiques in 1976. In 1977, he was a postdoctoral researcher at INPG. He has been a Research Director at the Centre National de la Recherche Scientifique (CNRS) in France since 1986. He moved to the Laboratoire de Génie Électrique de Paris associated with CNRS, SUPELEC, and the University of Paris, as a research scientist at CNRS in 1978, senior research scientist in 1981, research director in 1986, and senior research director in 1997. His main current research concerns computational electromagnetics (EMC, NDT, CAD) and design of electrical drives and actuators. He is the author or co-author of more than 150 scientific papers. Dr. Razek received the André Blondel medal in 1985 for his research work. He is a Fellow of the IEEE, a Fellow of the Institution of Electrical Engineers (IEE/IET; UK), and a Membre Émérite of the Société des Ingénieurs Électriciens (SEE; France).
