臺灣博碩士論文加值系統

無閥流體驅動的研究始於約半世紀之前對於心血管系統方面的研究。而近年來在微流體及生醫系統的應用方面(例如在藥物輸送，生醫檢測晶片與微流體混合上)，無閥流體驅動也成為一個重要的議題。在本文中我們了建構一組U型開迴路無閥流體驅動之一維數學模型，藉此分析各種不同非線性對系統的影響，同時也對我們的非線性系統求出漸近解與數值解。在我們的理論模型中，不對稱性與非線性是產生驅動效果的關鍵，存在適當位置的非線性能造成驅動效果，而較不對稱的幾何配置與較大的非線性會有較佳的驅動效果。

The original objective of the research on valveless pumping was to understand the important part it plays in blood transport in cardiovascular systems. Recently, it has also found important applications in micro-fluidic and biomedical systems, and thus revived vigorous research activities.
In this thesis, we construct a lumped model for a U-shape open-loop valveless pump built by our collaborators in a previous experimental study. Based upon such a model, first we clarify the contributions of the material, kinematic, and dynamic nonlinearities to the pumping effect as characterized by the temporal mean of the pressure head established in the open-loop fluid system. It turns out that, while the kinematic and dynamic nonlinearities are essential to producing a mean pumping effect, the material nonlinearity plays a minor role in valveless pumping.
Moreover, asymptotic and numerical solutions of the mathematical model are obtained, so as to carry out a systematic parameter study. The results indicate that, while the mean pumping effect generally increases with the asymmetry (characterized by the geometrical setup and excitation site of the system) and nonlinearity (increasing with the excitation frequency) of the system, the maximum pumping effect is not necessarily produced when the system is excited at the most asymmetric site. This finding implies that the difference between the excitation frequency and the natural frequency of the system also affects the pumping effect.

摘要 Ⅰ
英文摘要 Ⅱ
誌謝 III
目錄 V
表目錄 VII
圖目錄 VIII
符號說明 X
第一章 緒論 1
1.1無閥流體驅動之必要性與應用 1
1.2研究目的 2
1.3無閥流體驅動之歷史回顧與近代發展 4
1.4小結 9
第二章 理論模型 10
2.1 一維U型開迴路無閥流體驅動模型系統 10
2.2 質量守恆與動量平衡 13
2.3 非線性效應的分析與討論 17
2.4 系統參數計算 21
2.4.1 柔度的計算 21
2.4.2 流體慣性與流體阻力的計算 23
第三章 非線性系統動態之漸近分析 26
3.1 漸近分析 27
3.2 零階解 29
3.3 第一階解 33
第四章 漸近解與數值解的分析討論 39
4.1 參數設定 39
4.2 收斂測試 39
4.3 分析與討論 42
4.3.1 漸近解的適用性 42
4.3.2 非線性參數、頻率及擠壓位置對驅動的影響 50
第五章 結論與未來工作 56
5.1 結論 56
5.2 未來工作與展望 57
參考文獻 59

[1]E. Jung, C. S. Peskin, 2-D Simulations of Valveless pumping using the Immersed Boundary Method. SIAM Journal of Scientific Computing 23, 19–45, 2001.
[2]D. H. Doan, Study on a two-dimensional valveless impedance pump. 大葉大學機械所碩士論文，中華民國95年
[3]G. Propst, Pumping effects in models of periodically forced flow configurations, PHYSICA D 217 : 193–201,2006.
[4]J. T. Ottesen, Valveless pumping in a fluid-filled closed elastic tube system : one-dimensional theory with experimental validation, J. Math.Biol. 46, 309–332 ,2003.
[5]G. Liebau, Über ein Ventilloses Pumpprinzip, Naturwissenschsften 41 327–328, 1954.
[6]G. Liebau, Die Stromungsprinzipien des Kreislaufforschung 44,667-684,1955.
[7]G. Liebau, Die Bedeutung der Tragheitskrafte für die Dynamik des Blutkreislaufs, Zs. Kreislaufforschung 46,428–438, 1957.
[8]J. T. Ottesen, A. Noordergraap, ” Donders vs Harvey” Proc IEEE 26th Ann. Northeast. Bioeng. Conf. Enderle and Macfarlane editors. pp. 43–44, 2000.
[9]O.Mahrenholtz, Ein Beitrag zum Förderprinzip periodisch arbeitender, ventilloser Pumpen, Forsch. Ingenieurwes:29, 47,1963.
[10]O.Mahrenholtz, Untersuchungen zum Liebauschen Strömungsprinzip, Verh. Dtsch. Ges. Kreislaufforsch. 29: 155 ,1963.
[11]H. J. Bredow,Untersuchung eines ventillosen pumpprinzips,Fortschr.-Ber. VDIReihe 6:7:1,1968.
[12]H. J. Bredow, Untersuchungen über ein vom menschlichen Kreislauf abgeleitetes, ventilloses Strömungsprinzip, Verh. Dtsch. Ges. Kreislaufforsch34: 296, 1968
[13]H. Thomann, A simple pumping mechanism in a valveless tube. Z Angew Math Phys 29:169–177 ,1978
[14]M. Moser, J. W. Huang, G. S. Schwarz, T. Kenner, A. Noordergraaf. Impedance defined flow - generalisation of William Harvey’s concept of the circulation - 370 years later. Internation J Cardiovascular Medicine and Science,1:205-211, 1998.
[15]E. Jung, A Mathematical Model of Valveless Pumping: A Lumped Model with Time- Dependent Compliance, Resistance, and Inertia, Bulletin of Mathematical Biology 69:2181-2198, 2007.
[16]A. Borzi, G. Propst, Numerical investigation of the Liebau phenomenon. Z. angew. Math. Phys., 54: 1050-1072, 2003.
[17]C. Manopoulos, D. S. Mathioulakis, S. G. Tsangaris, One-dimensional model of valveless pumping in a closed loop and a numerical solution, PHYSICS OF FLUIDS 18: 017106 ,2006.
[18]D. Auerbach, W. Moehring, M. Moser , An analytical approach to the Liebau problem of valveless pumping, Cardiovasc. Engng: Intl J. 4 :2: 201–207,2004.
[19]C. G. Manopoulos, S. Tsangaris, Modelling of the Blood Flow Circulation in the Human Foetus by the End of the Third Week of Gestation , Cardiovascular Engineering: An International Journal, Vol. 5, No. 1, March 2005.
[20]A. I. Hickerson, M. Gharib, On the resonance of a pliant tube as a mechanism for valveless pumping , J. Fluid Mech. (2006), vol. 555, pp. 141–148.
[21]D. J. Laser, J. G. Santiago, A review of micropumps, J. Micromech. Microeng. 14,R35–R64,2004.
[22]沈弘俊，李青峻，許家睿，吳咨亨，無閥門微幫浦裝置元件之介紹與其應用,http://www.stam.org.tw/Newsletter/123/2008-6RVMA.pdf
[23]王齊中,非穩態流場所激發彈性管震動量測及其生醫應用,國立成功大學碩士論文，中華民國94年七月。
[24]S. Lee, E. Jung, A two-chamber model of valveless pumping using the immersed boundary method, Applied Mathematics and Computation 206,876–884,2008.
[25]Matweb-material property data, http://www.matweb.com/index.aspx, Automation Creations, Inc.