肥皂泡是許多人童年中的回憶，從沖澡到洗碗，生活中隨處可見。肥皂泡在拉
伸時，我們分析肥皂泡的變細的過程。相較於已被廣被研究的肥皂膜塌縮，
我們專注在體積守恆的肥皂泡。這份研究發現自相似現象的出現在以前探討
中的primary necking。藉由cosine-similarity去區分肥皂膜與肥皂泡的字相似程
度。V是灌氣量的體積，R是泡泡環的半徑。當V/R3 = constant時，不同半徑
的primary necking 區間會有相同的輪廓。上述的結果顯示出我們的肥皂泡具有
普適性。在這篇論文中，也探討了不同灌氣量與不同拉伸速度對肥皂泡頸縮造
成的影響。先前的研究討論到，泡泡膜塌縮的不可逆區分成許多不同的區間。
肥皂膜與肥皂泡之間，有著需多相似與不同之處。最後，這份研究也探討了，
灌氣量如何影響泡泡膜最後分離時的距離。

All children enjoy blowing soap bubbles that also show up in our bath and when we wash dishes. We analyze the thinning of soap bubble neck when it is stretched. To contrast with the collapsing of an open film that has been widely studied before, we concentrate on volume- conserved bubble. Self-similarity is newly found in the regime of primary necking. By using cosine-similarity, we can distinguish the level of self-similarity between open and closed systems. Contours in primary necking have same curvature when V/R3 =constant where V is pumping volume and R is the radius of rings. This result shows soap bubble has universal property. This thesis also discusses how volume and pulling speed affect the properties in soap bubble necking. Previous research found there are several parts in the irreversible regime of soap film collapsing. Soap bubble collapsing have similar and different parts in irreversible regime compare to soap films. After breaking, the separating length of soap bubbles relates to pumping volume.

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