本研究針對微型擴散器泵，以數值模擬在壓力為時間之正弦函數的暫態邊界條件下，探討不同的變動參數，半角 (θ為5°至55°)、流道深度 (D為100 μm至400 μm)和擴散器長度 (L為400 μm至1200 μm) 與作動頻率 (f為1 Hz至1000 Hz) 對擴散器效能之影響，以便得到最佳化的參數。
分析中得知，當給予壓力振幅為200 Pa時，所求得的Re皆小於25。在微型擴散器泵入口給予正弦壓力，由正向變負向或由負向變正向時，無論是在哪一種變動參數下，都會在擴散器壁面產生流體分離的現象，造成迴流。在小半角的微型擴散器泵 (θ < 10°) 中，迴流產生在擴散器靠近出口處;而當擴散器的半角越大，開始產生迴流的時間越早，出現的位置也越往喉部移動。當半角在5°至35°時，淨流率隨著半角的擴張而增加，當角度大於35&ordm;時，淨流率的變化小於5%。此外，微型擴散器深度越深或長度越短，可以得到更高的淨流率。而微型擴散器在低頻 ( f < 25 Hz) 時，流體指向性較佳。
本研究也針對微型擴散器的每一個變動參數，作無因次化分析，並探討壓力損失係數分析對於暫態作動的適用性。其中針對作動頻率可利用Ro (Roshko number)，分為三個區域：穩態分析區 (frequency independent zone, Ro < 0.25)、過渡區 (transition zone, 0.25 < Ro < 2) 和暫態分析區 (frequency dependent, Ro > 2)。
此外，在微型擴散器中加入兩條導翼，使單一的微型擴散器分為三個子微型擴散器，並針對導翼與擴散器側壁半角的改變，以便得到最佳化的翼型微擴散器。由數值模擬分析得知，當外部半角控制在36°至39°，而內部半角約為外部半角之三分之一時，為翼型微擴散器最佳之幾何形狀。此外，由加翼與未加翼微型擴散器的比較得知，未加翼半角27°的擴散器 (Re = 167.4) 為效率最高的擴散器。

In this study, a numerical investigation is presented to characterize the geometry effects on the transient behaviors of a micro diffuser pump. Four parameters of the dynamic diffuser pump, half-angle (θ= 5° to 55°), depth (D = 100 μm to 400 μm), length (L = 400 μm to 1200 μm), and excitation frequency (f = 1 Hz to 1000 Hz), are considered. A time-dependent sinusoidal pressure with fixed pressure amplitude (200 Pa) is applied at the inlet as the boundary condition. The results from the numerical analysis are quantified in terms of average volumetric flow rate. Despite the corresponding low Reynolds numbers (Re < 25), circulation is observed for all tested half-angles. When the direction of pressure gradient switches, fluid flows against the pressure gradient and triggers flow separation near wall. The vortex then migrates from wall toward the center of diffuser. For 5° ≤ θ ≤ 35°, diffusers with larger half angles show better rectification effects. For θ > 35°, the net flow rate is nearly independent of half angle. Shorter or deeper diffuser results in a larger net flow rate regardless of its half-angle. The increase of the excitation frequency diminishes the flow rectification in micro diffuser.
In the nondimensional analysis, the role of excitation frequency is classified into three different regimes by Roshko number: frequency independent regime (Ro < 0.25), transition regime (0.25 < Ro < 2), and frequency dependent regime (Ro > 2). In addition, the concepts of pressure loss coefficient are explored to validate its applicability to dynamic micro diffuser pump.
Vane type diffusers are also studied. Long, thin vanes are added to separate the diffuser into three sub-diffusers. The outer angle (θ) is defined as the angle between the micro diffuser wall and the symmetric axis, while the inner angle (φ) is defined as the angle between vane and the symmetric axis. Best flow rectification effects are found for θ = 36° to 39° when the outer angle is fixed at the three folds of the inner angle, i.e. the diffuser is evenly divided by vanes.

[1] N.-T. Nguyen, X. Huang, and T. K. Chuan, "MEMS-Micropumps: A Review," Journal of Fluids Engineering, vol. 124, pp. 384-392, 2002.
[2] L. Jiang, J.-M. Koo, S. Zeng, J. C. Mikkelsen, L. Zhang, P. Zhou, J. G. Santiago, T. W. Kenny, K. E. Goodson, J. G. Maveety, and Q. A. Tran, "Two-phase microchannel heat sinks for an electrokinetic VLSI chip cooling system," presented at Semiconductor Thermal Measurement and Management, Seventeenth Annual IEEE Symposium, 2001.
[3] M. Schluter, U. Kampmeyer, I. Tahhan, and H.-J. Lilienhof, "A modular structured, planar micro pump with no moving part (NMP) valve for fluid handling in microanalysis systems," presented at Proceedings of the Proceedings of 2nd Annual International IEEE-EMB Special Topic Conference on Microtechnologies in Medicine & Biology (Cat. No. 02EX578), A. Dittmar, D. Beebe, eds., IEEE International, Madison, WI, USA, 2002.
[4] J.-H. Tsai and L. Lin, "A thermal-bubble-actuated micronozzle-diffuser pump," Journal of Microelectromechanical Systems, vol. 11, pp. 665-671, 2002.
[5] C.-l. Sun and A. P. Pisano, "Dynamic Modeling of a Thermally-Driven Micro Diffuser Pump," presented at ASME International Mechanical Engineering Congress & Exposition, Washington, D.C., 2003.
[6] S. Guo, J. Oohira, and T. Fukuda, "A novel type of micropump using SMA actuator for microflow application," presented at International Symposium on Micromechatronics and Human Science, Wisconsin, USA, 2003.
[7] F. K. Forster, R. L. Bardell, M. A. Afromowitz, N. R. Sharma, and A. Blanchard, "Design, fabrication and testing of fixed-valve micro-pumps," Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Nov 12-17, vol. 234, pp. 39-44, 1995.
[8] A. Olsson, G. Stemme, and E. Stemme, "Numerical and experimental studies of flat-walled diffuser elements for valve-less micropumps," Sensors and Actuators, A: Physical, vol. 84, pp. 165-175, 2000.
[9] V. Singhal, S. V. Garimella, and J. Y. Murthy, "Low Reynolds number flow through nozzle-diffuser elements in valveless micropumps," Sensors and Actuators, A: Physical, vol. 113, pp. 226-235, 2004.
[10] K.-S. Yang, I.-Y. Chen, B.-Y. Shew, and C.-C. Wang, "Investigation of the flow characteristics within a micronozzle/diffuser," Journal of Micromechanics and Microengineering, vol. 14, pp. 26-31, 2004.
[11] M. Gad-el-Hak, "Fluid mechanics of microdevices-the Freeman scholar lecture," Journal of Fluids Engineering, vol. 121, pp. 5-33, 1999.
[12] P. A. Thompson and S. M. Troian, "A general boundary condition for liquid flow at solid surfaces," Nature, vol. 389, pp. 360-2, 1997.
[13] E. W. Swokowski, Calculus with Analytic Geometry, Fourth ed: PWS KENT, 1998.
[14] C. Herschel, The Two Books on the Water Supply of the City of Rome of Sextus Julius Frontinus, 1899.
[15] R. W. Fox and A. T. McDonald, Introduction to Fluid Mechanics, fifth ed. New York: John Wiley, 1998.
[16] R. S. Azad, "Turbulent flow in a conical diffuser: A review," Experimental Thermal and Fluid Science, vol. 13, pp. 318, 1996.
[17] F. M. White, Fluid Mechanics, 3rd ed. New York: McGraw-Hill, 1994.
[18] B. Sahin, A. J. A Ward-Smith, and D. Lane, "The pressure drop and flow characteristics of wide-angle screened diffusers of large area ratio," Journal of Wind Engineering and Industrial Aerodynamics, vol. 58, pp. 33-50, 1995.
[19] T. Gerlach and H. Wurmus, "Working principle and performance of the dynamic micropump," Proceedings of the IEEE Micro Electro Mechanical Systems Conference, Jan 29-Feb 2, pp. 221-226, 1995.
[20] T. Gerlach, "Microdiffusers as dynamic passive valves for micropump applications," Sensors and Actuators, A: Physical, vol. 69, pp. 181-191, 1998.
[21] D. F. Young, B. R. Munson, and T. H. Oliishi, A brief introduction to fluid mechanics, 2nd ed. New York, 2001.
[22] J. E. Formm, "Numerical Solutions of Two-Dimensional Stall in Fluid Diffuser," The Physics of Fluids Supplement, vol. 2, pp. 113-119, 1969.
[23] H. K. Versteeg and W. MaLalasekera, An introduction to computational fluid dynamics The finite volume method, 1st ed. Malaysia: LongMan, 1995.