無閥幫浦系統由於無閥門，設計簡單，較無損壞的問題，所以被廣泛運用在工程或者生醫方面。其原理是利用系統中各組件交界阻抗不對等的特性去驅動流體，但何種的驅動頻率或者擠壓方式為最有效率，許多學者眾說紛紜，沒有定論。本研究團隊發現文獻中許多研究皆忽略了無閥幫浦中，擠壓器和受壓之彈性組件之間的動態衝擊行為，所以便設計了一個由兩條硬管連接兩彈性球所組成的模型系統，其中擠壓器為系統動力來源，持續地碰撞彈性球去驅動流體。先前的研究發現，當擠壓頻率超過門檻頻率時，擠壓器會和彈性球分開，因此產生淨流量。由於其模型為預壓式閉迴路無閥幫浦系統，所以系統靜止時，擠壓器掐著彈性球。因此，我們提出了疑問，如果擠壓器一開始就沒有和彈性球接觸會產生甚麼樣的情形。所以我們將模型作改變，並試著討論預壓和無預壓的差異性。在本文中，我們比較漸近解和數值解的結果非常吻合，因此確信數值解的可信度；同時，也利用數值解去分析擠壓器和彈性球之間的各種碰撞模式。在無預壓式閉迴路無閥幫浦系統中，我們將各種不同的動態響應作分類，並利用體積隨時間的關係圖和相位圖讓我們對各種碰撞情形之間的轉換有更深一層的了解。發現無預壓式無閥幫浦系統的碰撞模式更為複雜，此外，也對流量和系統複雜響應區作討論，希望能夠對閉迴路無閥幫浦系統有更進一步的貢獻。

Valveless pumping systems have been widely used in engineering and biomedical applications, because they do not require a moving valve to regulate the flow direction, which greatly simplifies the system design and increases the system robustness. One important physical mechanism for the working of valveless pumping systems is the impedance mismatch between their constituent components. But, since there are other mechanisms that also play a significant part, such as the interaction between the actuator and the pliant part of a valveless pumping system, the system dynamics indeed is complicated and remains incompletely understood. It is therefore not a straightforward task to optimize the system performance and produce a maximized flow rate. Indeed, in this work we aim to investigate the aforementioned interaction between the actuator and the pliant part of a valveless pumping system, which oftentimes is overlooked in previous studies.
To that end, here we consider a model system consisting of two distensible reservoirs connected by two rigid tubes of different sizes. In addition, an actuator periodically compresses one of the distensible reservoirs to drive the fluid in the closed loop. A mathematical model accounting for mass and momentum balance in such a system also is constructed. It has been shown in previous studies that even if the above model system is pre-compressed ― i.e., with the maximum volume of the compressed distensible reservoir set by the actuator being less than its free volume ― the actuator still would separate from the distensible reservoir when the driving frequency exceeds a certain threshold frequency, resulting a net flow rate in the loop. The emphasis of the present work therefore is on the case without pre-compression, and the purpose is to clarify the dynamical difference between systems with and without pre-compression.
Through asymptotic calculations and numerical computations, we discover that the interaction modes of the compressed reservoir with the actuator are more complex for the system without pre-compression, as one might have expected. Specifically, compared with pre-compressed systems, the dynamical response of the system without pre-compression exhibits many more new types. In this thesis, the temporal evolutions of the distensible reservoirs are closely monitored, and phase diagrams of such new system responses are systematically examined, so as to bring about a deeper understanding of the system dynamics of the valveless pumping system. Moreover, the dependence of the net flow rate on the system modes also is discussed here.

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