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.

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