本文將進行二維細流道充填過程的噴泉流研究以及分別探討主導流場的幾個無因次參數的變化對充填過程中自由液面形狀和速度壓力場造成的影響，其中包括雷諾數、毛細數及接觸角，對於噴泉流這類的問題，因為在液氣交界面上，力平衡方程式的表面張力項和交界面形狀曲率相關，然而過去對於自由液面的曲率計算並沒有一個簡單有效的計算方法，而對於細流道的噴泉流，充填過程自由液面可將其視為近似球面形狀，因此本文提出以最小平方誤差法去計算自由液面曲率，透過此數值方法，在充填過程的每一個時間去重新計算一通過自由液面的圓，並將其曲率提供給力平衡方程式的表面張力項，進而得到兩相壓力差，藉此數值方法得到一均勻分布的自由液面壓力。

Two-dimensional fountain flow in the filling process inside a small channel is studied in this thesis. In addition, variation of a group of dimensionless parameters which dominate the free surface meniscus and flow field in the filling process are discussed respectively as well, including Reynold number, Capillary number, and the Contact angle. For a fountain flow problem, the surface tension term in force balance equation is highly related to the free surface curvature on liquid-air interface, however, there isn’t a simple and effective method for the curvature calculation on free surface in the past. For a fountain flow inside a channel, free surface shape can be approximately regarded as a circle, thus, a least square method is proposed in this thesis to handle the curvature calculation on free surface. By this numerical method, a best fitting circle is calculated according to the present free surface shape in filling process at every time step. After that, it provides a curvature to surface tension term in force balance equation, and then we get the two-phase pressure difference between liquid-air interface. Lastly, a uniform free surface pressure is properly estimated through this numerical method.

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