臺灣大學: 機械工程學研究所賴君亮劉士瑋Liu, Shih-WeiShih-WeiLiu2013-04-012018-06-282013-04-012018-06-282011http://ntur.lib.ntu.edu.tw//handle/246246/256344中文摘要 本論文旨在透過嚴謹的理論分析，探討長氣泡在充滿液體的圓錐管中的遷移與變形現象。 首先以簡化的物理模式，假設長氣泡在圓錐管中始終維持一極為貼近管壁的斜柱體，兩端則分別由半徑不同的兩半球所封閉。當長氣泡在圓錐管中運動時，周圍液體的流動大致可分為三個流域；分別為：半圓球狀附近流動極為緩慢的近乎停滯區(nearly stagnant region)；流經管壁及氣泡側面之間的薄液層區(thin film region)，以及連結此兩流域的過渡區(transition region)。 本文進而巧妙地以潤滑理論來模擬薄液層的流動現象，並解出其間的速度分佈以及體積流率。接著運用氣泡在遷移過程中體積維持不變以及周圍液體體積流率守恆的兩項條件，求解出長氣泡的遷移速率、長度改變以及薄液層厚度的變化等。從分析結果可知，薄液層的厚度沿管壁呈現 1⁄3 次方的成長；長氣泡的遷移速率則隨時間遞減，其長度也逐漸縮短，終至趨近於球形以符合熱力學第二定律“同體積具最小表面積”的要求。而研究結果最重要且有趣的現象是，當長氣泡以減速方式由較窄端遷移至較寬端時，其整體受力始終維持為零，此遷移現象顯然是受兩端變形量不同所致，而非如同剛體受力所產生的運動現象。本文因而稱之為“形變運動” (deformotion)！Abstract The present study is aimed at investigating theoretically the migration and deformation of a long bubble moving through a liquid-filled conical tube. A tapered cylindrical body bounded by two spherical caps with different radii is proposed as a simplified physical model for the long bubble in a conical tube. As the long bubble migrates through the conical tube, three flow regimes were defined for the surrounding liquid flow according to their flow characteristics: the nearly stagnant region near the two spherical caps, the thin film region with creeping flow between the tube wall and side surface of the bubble, and the transition region in between. The lubrication approximation is then applied to simulate the creeping flow in the thin film region. The velocity distribution and volume flow rate therein are thus derived. With the constant-volume constraint and the conservation of the bubble, the migration speed, the length change of the bubble, and the variation of the thin film thickness are computed finally. The results indicate that the thin film thickness always grows with the radial coordinate, r, to the 1⁄3 power. It is also found that as the bubble migrates, both the migration speed and length of the bubble decrease, approaching a sphere eventually as required by the second law of thermodynamics. The most important and interesting conclusion of this study is that even with a decelerating motion, the resultant force acting on the bubble always vanishes, indicating that such a migration is not the same as a rigid body motion according to the Newton’s second law. Its global migration is due to the unequal deformation of the two ends of the long bubble. Such a migration due to unequal deformation is thus named “deformotion” by the present study!844832 bytesapplication/pdfen-US氣泡圓錐管毛細壓力薄膜流遷移形變運動bubbleconical tubecapillary pressurethin-film flowmigrationdeformotionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/256344/1/ntu-100-R97522103-1.pdf