氣泡在液體內的運動行為普遍的出現在自然界與實際的工程問題中。為了解決諸多工程實際問題，探討氣泡在液體內的上升運動為近幾十年來學者不斷研究的重要問題。

本研究利用邊界元素法模擬三維軸對稱氣泡在無限液體內的初始上升運動與在上升的過程中所發生的變形行為，並且討論表面張力效應對氣泡上升運動與變形行為的影響。

由數值模擬的結果可發現，氣泡在浮力的推動下會以兩倍重力加速度的初始加速度作等加速度上升運動，此結果與Walters and Davidson(1963)的理論結果相吻合。因為氣泡下表面的靜水壓力大於氣泡上表面的靜水壓力，此壓力差會導致氣泡下方產生一個方向與重力方向相反的向上液體射流。液體射流會從下方開始推擠氣泡使氣泡發生變形，隨著時間的增加，液體射流會更進一步的推擠氣泡使氣泡下表面產生凹陷，之後氣泡的下表面逐漸往氣泡的上表面接近。最後氣泡的下表面會碰撞到氣泡的上表面，此時液體射流會穿透氣泡的上表面，
使氣泡發生破裂變形為環形氣泡。另外，當表面張力太大時，氣泡最終不會破裂變形為環形氣泡而是變形為球帽型氣泡。

The behaviors of gas bubbles in a liquid appear frequently in nature and engineering. In order to solve many engineering problems, the study of the rising motion of a gas bubble in a liquid is of great interest to many researchers.

In this study we use the boundary element method to simulate the rising motion and deformation of a three-dimensional, axisymmetric gas bubble in an infinite domain of inviscid and incompressible fluid. The effect of surface tension on the rising motion and deformation of the gas bubble will be investigated.

The results suggest that the initial acceleration of the gas bubble is 2g owing to buoyancy which is consistent with the prediction of Walters and Davidson(1963). Because the hydrostatic pressure at the bottom surface of the gas bubble is higher than that at the top surface, the difference of the hydrostatic pressure induces the formation of a liquid jet which pushes into the gas bubble from below. As time progresses, the liquid jet further penetrates into the gas bubble, which leads to the bottom surface approaching the top surface of the gas bubble. Eventually, the impact of the liquid jet results in the bottom surface piercing through the top surface of the gas bubble then the gas bubble breaks up into a toroidal bubble. If the effect of surface tension is strong enough, the gas bubble forms a spherical-cap bubble without breaking into a toroidal bubble.

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