Theoretical Study on Bubble Rising in Liquid

• Main Authors: Wei-Ting Liao, 廖偉婷
• Other Authors: 賴君亮
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/36396190427396152455

碩士 === 國立臺灣大學 === 機械工程學研究所 === 101 === 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.