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

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

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.

Keywords: rising bubble surface tension buoyancy volume of fluid (VOF) method

Received: 24 March 2009
Revised: 18 June 2009
Accepted manuscript online:

PACS:	68.03.Cd	(Surface tension and related phenomena)
	47.55.D-	(Drops and bubbles)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10672043 and 10272032).

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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 2010 Chin. Phys. B 19 026801

[1]	Moore D W 1959 J. Fluid Mech. 6 113
[2]	Taylor T D and Acrivos A 1964 J. Fluid Mech. 18 466
[3]	Davies R M and Taylor F I 1950 Proc. R. Soc. Lond. A 200 375
[4]	Walters J K and Davidson J F 1962 J. Fluid Mech. 12 408
[5]	Walters J K and Davidson J F 1963 J. Fluid Mech. 17 321
[6]	Hnat J G and Buckmaster J D 1976 Phys. Fluids 19 182
[7]	Bhaga D and Weber M E 1981 J. Fluid Mech. 105 61
[8]	Zhang Y L, Yeo K S, Khoo B C and Wang C 2001 J. Comp. Phys. 166 336
[9]	Ryskin G and Leal L G 1984 J. Fluid Mech. 148 19
[10]	Unverdi S O and Tryggvason G 1992 J. Comp. Phys. 100 25
[11]	Hua J S and Jing L 2007 J. Comp. Phys. 2 22 769
[12]	Liu R X and Shu C W 2003 Some New Methods in Computational Fluid Dynamics (Beijing: Science Press) (in Chinese)
[13]	Sussman M and Smereka P 1997 J. Fluid Mech. 341 269
[14]	Hirt C W and Nichols B D 1981 J. Comp. Phys. 39 201
[15]	Rider W J and Kothe D B 1998 J. Comp. Phys. 141 112
[16]	Zou J F, Huang Y Q, Ying X Y and Ren A L 2002 China Ocean Engnrg. 16 525
[17]	Chen L and Suresh V 1999 J. Fluid Mech. 387 61
[18]	Wan D C 1998 Chinese J. Comp. Phys. 15 655
[19]	Sussman M 2003 J. Comp. Phys. 187 110
[20]	Wang H, Zhang Z Y, Yang Y M, Hu Y and Zhang H S 2008 Chin. Phys. B 17 3847
[21]	Zhang Z Y and Zhang H S 2004 Phys. Rev. E 70 056310
[22]	Zhang Z Y and Zhang H S 2005 Phys. Rev. E 71 066302
[23]	Sussman M, Smith K M, Hussaini M Y, Ohta M and Zhi-Wei R 2007 J. Comp. Phys. 221 469
[24]	Batchelor G K 1967 An Introduction to Fluid Dynamics (Cambrndge: Cambridge University Press) Section 1.9, 5.14, 6.4, 6.6

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

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