摘要
有關氣泡在液體中上浮運動的現象，本論文分兩部分來進行理論分 析與研究。第一部分主要在於探討氣泡上升過程中，其體積膨脹、所 受浮力與阻力、以及運動本身之間的耦合現象。第二部分則著重於探 討當氣泡上浮至非常接近自由液面或一固體平面時，邊界效應對氣泡 上浮運動的影響。 在第一部分的研究中，本文利用解析的技巧有系統地分析了小氣泡 與大氣泡在液體中的上浮運動。研究發現，由於小氣泡內的壓力主要 由表面張力所決定，因此在上浮過程中其體積的膨脹與上浮速度的改 變非常有限。而大氣泡內的壓力則主要來自周遭液體的靜壓力，因此 在上浮過程中，其體積的膨脹與速度的改變顯得明顯且重要。然而當 氣泡接近液面時，由於大氣壓成為主要壓力的來源，氣泡有可能維持 在一固定的平衡半徑，並以終端速度持續上升。 在第二部分的研究中，當氣泡上浮至非常接近界面時， 由於氣泡 與液面或固體邊界間的間隙非常狹小，本文於是利用薄液膜和潤滑理 論以解析的技巧分別探討了自由液面與固體邊界對氣泡上浮運動的影 響。研究發現當氣泡接近自由液面時，所產生的阻力是氣泡上浮速度 的函數，此阻力可能大於也或許小於氣泡所受的浮力， 但無論何種情 形，氣泡接近自由液面的速度終將趨於一定植，且此一終端速度與周 遭液體的性質無關。研究的結果亦發現，由於無滑動邊界條件的效 應，當氣泡接近固體邊界時，其上浮運動受阻而趨緩的現象較之於其 接近自由液面時更為明顯， 且上浮速度呈單調遞減直至趨近於零，並 無終端速度的存在。
並列摘要
Two parts of the bubble rising in a liquid are theoretically studied in this thesis. The first part is on the coupling among the volume expansion, acting forces, i.e., the buoyancy and drag, and the motion itself during the rising of the bubble. The second part emphasizes on the boundary effect on the bubble motion when the bubble is approaching very close to, or impinging on, the free surface or a plane solid boundary on top. In the first part, two limiting situations, i.e., the small bubble limit and the large bubble limit, are studied analytically and systematically. The results indicate that, in the small bubble limit, since the bubble pressure is mainly balanced by the surface tension, the bubble expansion and the variation of the rising velocity become quite limited. In the large bubble limit, the bubble pressure is nearly equal to the hydrostatic pressure of the surrounding liquid. As a result, the volume expansion and the variation of the rising velocity become appreciable as the bubble ascends. However, when the bubble moves close to the free surface, the atmospheric pressure becomes dominant over the liquid hydrostatic pressure. The bubble may retain the constant equilibrium radius, and rises with the terminal velocity. In the second part, because there exists a very small gap between the boundary and the bubble surface during impinging, the thin film and lubrication approximations are applied to solve the problem analytically. The effects on the impinging motion of the bubble due respectively to the free surface and solid boundary are studied. The results indicate that the induced drag on the bubble motion due to the existence of the free surface is a function of the impinging velocity. It may or may not be large enough to suppress the bubble motion. Nonetheless, the bubble seems to approach finally a constant terminal velocity which is independent of the liquid properties. It is also shown by the analysis that owing to the no-slip condition, the retardation on the impinging motion of the bubble by the solid boundary is more than that by the free surface. The impinging velocity keeps decreasing until it diminishes to zero asymptotically; there exists no terminal velocity in this situation.
並列關鍵字
bubble rising ； coupling ； no-slip condition ； terminal velocity ； thin-liquid film ； lubrication參考文獻
延伸閱讀
- 簡碩廷（2014）。液滴撞擊有邊界液面所產生大氣泡之研究〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2014.10275
- 黃柏毅（2006）。浮力於微垂直管中推動氣泡之流場研究〔碩士論文，國立清華大學〕。華藝線上圖書館。https://doi.org/10.6843/NTHU.2006.00594
- 田文斌（2007）。氣泡於水平板面成長與脫離之研究〔碩士論文，國立清華大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0016-1411200715111876
- Liu, S. W. (2011). 長氣泡在圓錐管內的運動 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2011.00910
- 張清泉（2010）。The Effect of Fluid Properties on the Evolution of a Long Bubble in a Circular Tube〔博士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/cycu201000703