# Optimal Design and Operation for a No-Moving-Parts-Valve (NMPV) Micro-Pump with a Diffuser Width of 500 µm

^{1}

^{2}

^{*}

## Abstract

**:**

_{D}, ranging from 20 to 75, and expansion valve angles ranging from 30° < θ

_{1}< 57° and 110° < θ

_{2}< 120°. The D

^{p},

_{i}value, 1.02 < D

^{p},

_{i}< 1.14, is larger within the proposed range of the expansion valve angles. A flow channel structure with a depth of 500 micron is manufactured using yellow light lithography in this study. From prior analyses and experiments, it is found that piezoelectric films work better at a buzz driving frequency of f < 30Hz and the best operating frequency is at a driving frequency of f = 10Hz because it produces the largest net flow. In addition, the expansion angles θ

_{1}= 30° and θ

_{2}= 120° are the best expansion angles because they produce the largest net flow. These related results are very helpful for the actual design of no-moving-parts-valve micro-pump.

## 1. Introduction

## 2. Problem Research and Discussion

_{D}= 75, 50, 20, 10, 5. When fluid flows through the valve, the fluid flowing in the forward direction experiences an unequal resistance from that flowing in the reverse direction, causing a different degree of pressure drop at the entrance/exit ends of the flow channel; a net pressure is produced as a result. The greater the pressure drop is, the larger the bipolarity of the valve; otherwise stated, the stronger the uni-directional property of the valve.

_{ave}is the characteristic speed (the average speed at the nozzle mouthpiece), D is the characteristic width (the width of the valve nozzle), and μ is the coefficient of viscosity of the liquid.

^{p},

_{i}in name of mass flow rate addressed by Anders Olsson [14] is defined as the bi-polarity of the pressure drop valve at the entrance/exit ends of the flow channel and its definition is shown in Equation (2):

_{1}= 20°, θ

_{2}= 90°, and θ

_{1}= 30°, θ

_{2}= 120°, respectively.

## 3. Numerical Experimentation Methods

_{ref}is 998.2 kg/m

^{3}and its liquid viscosity coefficient μ

_{ref}is 1.02×10

^{-3}N s/m

^{2}.

## 4. Results and Discussion

_{1}, θ

_{2}) and D

^{p},

_{i}better, analyses using optimization theory were carried out in this study: First, the boundary conditions are set to 20° < θ

_{1}< 80° and 30° < θ

_{2}< 140° and simulation nodes are generated using Design of Experiments (DOE) [17]. Then, Response Surface Modeling (RSM) [18] is utilized to find out the best recommended range. At the beginning of optimization, ten samples of (θ

_{1}, θ

_{2}) boundary conditions were selected arbitrarily as initial conditions for producing the D

^{p},

_{i}for representing the amount of mass flow rate. Then, three samples were added to predict the D

^{p},

_{i}for each cycle and one of Reynolds number Re

_{D}. A total of 10 cycles were applied and tested for the studied cases of Re

_{D}. Hence, in this study forty calculations were conducted to determine a response surface for finding the optimal (θ

_{1}, θ

_{2}, D

^{p},

_{i}).

^{p},

_{i}exhibits a relatively irregular distribution at Reynolds number, Re

_{D}= 5. When it is increased to Re

_{D}= 20, it shows that there exists a larger D

^{p},

_{i}area on the contour line map from Figure 4. Similarly, there also exists a larger D

^{p},

_{i}area in the same direction at Re

_{D}= 50 and Re

_{D}= 75.

_{D}= 20, Re

_{D}= 50 and Re

_{D}= 75 are overlapped to find a better common area through image processing in Figure 5. The region within 20 < Re

_{D}< 75, 30° < θ

_{1}< 57° and 110° < θ

_{2}< 120° is the recommended area for the expansion valve angles with 1.02 < D

^{p},

_{i}< 1.14. The optimal region between the θ

_{1}, θ

_{2}and D

^{p},

_{i}for D = 500 μm at 20 < Re

_{D}< 75, also confirmed by a numerical analysis software CFDRC version 2009 whose numerical accuracy of 10

^{-5}makes it suitable for physical analysis.

_{1}= 20°, θ

_{2}= 90° and θ

_{1}= 30°, θ

_{2}= 120°.

## 5. Manufacturing Processes and Experimental Equipments

^{2}). Figure 8 shows the SU-8 structure with a height of 500 μm which was manufactured successfully using this process.

## 6. Conclusions

- There exists a better operating area, 1.02 < D
^{p},_{i}< 1.14, with D = 500 μm for the expansion mouthpiece, 20 < Re_{D}< 75 for Reynolds number, and 30° < θ_{1}< 57°,110° < θ_{2}< 120°. - Piezoelectric buzz films work better at a driving frequency of f < 30 Hz. They will produce the greatest net flow at a driving frequency of f = 10 Hz,
- The produced net flow is largest when the expansion valve is D = 500 μm and its expansion valve angles are θ
_{1}= 30° and θ_{2}= 120°, which are also the best angles.

## Acknowledgments

## References and Notes

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**Figure 5.**Chart for the relationship between θ

_{1}, θ

_{2}and D

^{p},

_{i}with D = 500 μm and 20 < Re

_{D}< 75.

**Figure 6.**Chart of different driving pressures with θ

_{1}= 20°, θ

_{2}= 90° and θ

_{1}= 30°, θ

_{2}= 120°.

**Figure 7.**Diagrams for the manufacturing processes for the flow channel of the NMPV micro-pump system.

**Figure 11.**The bubble moving positions at different frequencies with an expansion valve angles of θ

_{1}= 30° and θ

_{2}= 120° and a driving voltage of 150 Vp-p.

**Figure 12.**The net flow comparison chart for different driving voltages and driving frequencies with expansion valve angles of the θ

_{1}= 30°, θ

_{2}= 120° and θ

_{1}= 20°, θ

_{2}= 90°.

**Figure 13.**Experimental and simulation analysis comparison chart with expansion valve angles of θ

_{1}= 30° and θ

_{2}= 120°.

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Wang, C.-T.; Leu, T.-S.; Sun, J.-M.
Optimal Design and Operation for a No-Moving-Parts-Valve (NMPV) Micro-Pump with a Diffuser Width of 500 µm. *Sensors* **2009**, *9*, 3666-3678.
https://doi.org/10.3390/s90503666

**AMA Style**

Wang C-T, Leu T-S, Sun J-M.
Optimal Design and Operation for a No-Moving-Parts-Valve (NMPV) Micro-Pump with a Diffuser Width of 500 µm. *Sensors*. 2009; 9(5):3666-3678.
https://doi.org/10.3390/s90503666

**Chicago/Turabian Style**

Wang, Chin-Tsan, Tzong-Shyng Leu, and Jia-Ming Sun.
2009. "Optimal Design and Operation for a No-Moving-Parts-Valve (NMPV) Micro-Pump with a Diffuser Width of 500 µm" *Sensors* 9, no. 5: 3666-3678.
https://doi.org/10.3390/s90503666