Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

doi:10.1088/1674-1056/19/2/026801

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 26801-026801.doi: 10.1088/1674-1056/19/2/026801

Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

张振宇¹, 王含², 杨永明², 张慧生²

(1)Department of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China; (2)Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China

收稿日期:2009-03-24 修回日期:2009-06-18 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10672043 and 10272032).

Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

Wang Han(王含)^a), Zhang Zhen-Yu(张振宇)^b), Yang Yong-Ming(杨永明)^a)^†, and Zhang Hui-Sheng(张慧生)^a)

^a Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China; ^b Department of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China

Received:2009-03-24 Revised:2009-06-18 Online:2010-02-15 Published:2010-02-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10672043 and 10272032).

摘要/Abstract

摘要： In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid (VOF) method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We₁,~We₂,~We₃ and We₄, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We >We₂, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.

Abstract: In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid (VOF) method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We₁, We₂, We₃ and We₄, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We≤We₂, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We >We₂, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.

Key words: rising bubble, surface tension, buoyancy, volume of fluid (VOF) method

中图分类号: (Surface tension and related phenomena)

68.03.Cd

47.55.D- (Drops and bubbles)

王含, 张振宇, 杨永明, 张慧生. Surface tension effects on the behaviour of a rising bubble driven by buoyancy force[J]. 中国物理B, 2010, 19(2): 26801-026801.

Wang Han(王含), Zhang Zhen-Yu(张振宇), Yang Yong-Ming(杨永明), and Zhang Hui-Sheng(张慧生). Surface tension effects on the behaviour of a rising bubble driven by buoyancy force[J]. Chin. Phys. B, 2010, 19(2): 26801-026801.

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Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

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