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Dynamical behaviors of cavitation bubble under acoustic standing wave field

Shen Zhuang-Zhi

Dynamical behaviors of cavitation bubble under acoustic standing wave field

Shen Zhuang-Zhi
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  • Considering the compressibility of liquid, we investigate the dynamical behaviors of a cavitation bubble in an acoustic standing wave field by regarding water as a work medium. The motion state of the cavitation bubble at each position is simulated in the standing wave field, the influences of the primary Bjerknes force on the motion direction of the cavitation bubble at each position are also simulated with different relevant parameters. The results show that in the standing wave field, the motion state of the cavitation bubble is divided into three aspects: the cavitation bubble is of steady-state cavitation near the pressure antinode; the cavitation bubble is of transient cavitation at the position deviating from the pressure antinode; in the vicinity of the acoustic pressure node, the cavitation bubble has been moving to the acoustic pressure node due to the primary Bjerknes force, so the phenomenon of cavitation does not occur. In the standing wave field, when the acoustic pressure amplitude exceeds its upper limit, the primary Bjerknes force makes the cavitation bubble move to pressure node, it is not conducive to the occurrence of cavitation. When the acoustic frequency is smaller than the bubble resonant frequency, the primary Bjerknes force will make more cavitation bubbles move to acoustic pressure node with the increase of the acoustic pressure, so this is not conducive to the occurrence of cavitation. Especially, the height of the liquid level should not be a quarter of acoustic wavelength. For a given acoustic frequency, the larger the initial radius of cavitation bubble, the more favorable the occurrence of cavitation is. But when the initial radius of cavitation bubble exceeds the resonant radius of acoustic frequency, the bubble will be pushed to pressure node. That is to say, the acoustic pressure amplitude, the acoustic frequency, and the initial radius of cavitation bubble each have a corresponding limit. Moreover, the lower limit is conducive to the occurrence of the phenomenon of cavitation.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11174191).
    [1]

    Kumar P S, Kumar M S, Pandit A B 2000 Chem. Eng. Sci. 55 1633

    [2]

    Wang S K, Wang J G, Guo P Q, Guo W L, Li G L 2008 Ultrason. Sonchem. 15 357

    [3]

    Zong S G, Wang J A, Ma Z G 2010 Chin. J. Laser 37 1000 (in Chinese) [宗思光, 王江安, 马治国 2010 中国激光 37 1000]

    [4]

    Brujan E A, Nahen K, Schmidt P 2001 J. Fluid Mech. 433 251

    [5]

    Lang P S, Ching W K, Willberg D M 1998 Environ. Sci. Technol. 32 3142

    [6]

    Ye Q Z, Qi J, Gu W G, Li J 2004 High Volt. Eng. 20 110 (in Chinese) [叶齐政, 齐军, 顾温国, 李劲 2004 高电压技术 20 110]

    [7]

    Sikney Clement J 1987 IEEE Trans Ind. Appl. 23 224

    [8]

    Ishimoto J, Okubo M, Kamiyama S 1995 JSME Int. J. Ser. B 38 382

    [9]

    Cunha F R, Sousa A J, Morais P C 2002 J. Magnet. Magnet. Mater. 252 271

    [10]

    Mason T J 1993 Chem. Ind. 18 50

    [11]

    Feng R, Li H M 1992 Sonchemistry and Its Application (Anhui: Anhui Science and Technology Press) (in Chinese) p174 [冯若, 李化茂 1992 声化学及其应用 (安徽: 安徽科学技术出版社) 第174页]

    [12]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 084302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 084302]

    [13]

    Lin S Y, Zhang F C, Guo X W 1993 Appl. Acoust. 12 34 (in Chinese) [林书玉, 张福成, 郭孝武 1993 应用声学 12 34]

    [14]

    Zhang J C 1993 Techn. Acoust. 12 28 (in Chinese) [张镜澄 1993 声学技术 12 28]

    [15]

    Shen Z Z, Shang Z Y 1999 Appl. Acoust. 18 41 (in Chinese) [沈壮志, 尚志远 1999 应用声学 18 41]

    [16]

    Zhu C P, Feng R, Yang Y, Xu Y 2000 Techn. Acoust. 19 125 (in Chinese) [朱昌平, 冯若, 杨勇, 徐勇 2000 声学技术 19 125]

    [17]

    Prosperetti A 1984 Ultrasonics 22 69

    [18]

    Keller B, Miksis M 1980 J. Acoust. Soc. Am. 68 628

    [19]

    Du G H, Zhu Z M, Gong X F 1981 Acoustics Foundation (Shanghai: Shanghai Science Technology Press) p180 (in Chinese) [杜功焕, 朱哲民, 龚秀芬 1981 声学基础 (上海: 上海科学技术出版社) 第180页]

    [20]

    Fu J X 1988 J. Qufu Nor. Univ. 14 88 (in Chinese) [付吉孝 1988 曲阜师范大学学报 14 88]

    [21]

    Lauterborn W, Parlitz U 1988 J. Acoust. Soc. Am. 84 1975

    [22]

    Blake F G 1949 J. Acoust. Soc. Am. 21 551

    [23]

    Eller A 1968 J. Acoust. Soc. Am. 43 170

    [24]

    Akhatov I, Mettin R, Ohi C D, Parlitz U, Lauterborn W 1997 Phys. Rev. E 55 3747

    [25]

    Robert M, Alexander A D 2009 Appl. Acoust. 70 1330

  • [1]

    Kumar P S, Kumar M S, Pandit A B 2000 Chem. Eng. Sci. 55 1633

    [2]

    Wang S K, Wang J G, Guo P Q, Guo W L, Li G L 2008 Ultrason. Sonchem. 15 357

    [3]

    Zong S G, Wang J A, Ma Z G 2010 Chin. J. Laser 37 1000 (in Chinese) [宗思光, 王江安, 马治国 2010 中国激光 37 1000]

    [4]

    Brujan E A, Nahen K, Schmidt P 2001 J. Fluid Mech. 433 251

    [5]

    Lang P S, Ching W K, Willberg D M 1998 Environ. Sci. Technol. 32 3142

    [6]

    Ye Q Z, Qi J, Gu W G, Li J 2004 High Volt. Eng. 20 110 (in Chinese) [叶齐政, 齐军, 顾温国, 李劲 2004 高电压技术 20 110]

    [7]

    Sikney Clement J 1987 IEEE Trans Ind. Appl. 23 224

    [8]

    Ishimoto J, Okubo M, Kamiyama S 1995 JSME Int. J. Ser. B 38 382

    [9]

    Cunha F R, Sousa A J, Morais P C 2002 J. Magnet. Magnet. Mater. 252 271

    [10]

    Mason T J 1993 Chem. Ind. 18 50

    [11]

    Feng R, Li H M 1992 Sonchemistry and Its Application (Anhui: Anhui Science and Technology Press) (in Chinese) p174 [冯若, 李化茂 1992 声化学及其应用 (安徽: 安徽科学技术出版社) 第174页]

    [12]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 084302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 084302]

    [13]

    Lin S Y, Zhang F C, Guo X W 1993 Appl. Acoust. 12 34 (in Chinese) [林书玉, 张福成, 郭孝武 1993 应用声学 12 34]

    [14]

    Zhang J C 1993 Techn. Acoust. 12 28 (in Chinese) [张镜澄 1993 声学技术 12 28]

    [15]

    Shen Z Z, Shang Z Y 1999 Appl. Acoust. 18 41 (in Chinese) [沈壮志, 尚志远 1999 应用声学 18 41]

    [16]

    Zhu C P, Feng R, Yang Y, Xu Y 2000 Techn. Acoust. 19 125 (in Chinese) [朱昌平, 冯若, 杨勇, 徐勇 2000 声学技术 19 125]

    [17]

    Prosperetti A 1984 Ultrasonics 22 69

    [18]

    Keller B, Miksis M 1980 J. Acoust. Soc. Am. 68 628

    [19]

    Du G H, Zhu Z M, Gong X F 1981 Acoustics Foundation (Shanghai: Shanghai Science Technology Press) p180 (in Chinese) [杜功焕, 朱哲民, 龚秀芬 1981 声学基础 (上海: 上海科学技术出版社) 第180页]

    [20]

    Fu J X 1988 J. Qufu Nor. Univ. 14 88 (in Chinese) [付吉孝 1988 曲阜师范大学学报 14 88]

    [21]

    Lauterborn W, Parlitz U 1988 J. Acoust. Soc. Am. 84 1975

    [22]

    Blake F G 1949 J. Acoust. Soc. Am. 21 551

    [23]

    Eller A 1968 J. Acoust. Soc. Am. 43 170

    [24]

    Akhatov I, Mettin R, Ohi C D, Parlitz U, Lauterborn W 1997 Phys. Rev. E 55 3747

    [25]

    Robert M, Alexander A D 2009 Appl. Acoust. 70 1330

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  • Received Date:  13 November 2014
  • Accepted Date:  15 December 2014
  • Published Online:  05 June 2015

Dynamical behaviors of cavitation bubble under acoustic standing wave field

  • 1. Shaanxi Key Laboratory of Ultrasonics, Institude of Applied Acoustics, Shaanxi Normal University, Xi’an 710119, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11174191).

Abstract: Considering the compressibility of liquid, we investigate the dynamical behaviors of a cavitation bubble in an acoustic standing wave field by regarding water as a work medium. The motion state of the cavitation bubble at each position is simulated in the standing wave field, the influences of the primary Bjerknes force on the motion direction of the cavitation bubble at each position are also simulated with different relevant parameters. The results show that in the standing wave field, the motion state of the cavitation bubble is divided into three aspects: the cavitation bubble is of steady-state cavitation near the pressure antinode; the cavitation bubble is of transient cavitation at the position deviating from the pressure antinode; in the vicinity of the acoustic pressure node, the cavitation bubble has been moving to the acoustic pressure node due to the primary Bjerknes force, so the phenomenon of cavitation does not occur. In the standing wave field, when the acoustic pressure amplitude exceeds its upper limit, the primary Bjerknes force makes the cavitation bubble move to pressure node, it is not conducive to the occurrence of cavitation. When the acoustic frequency is smaller than the bubble resonant frequency, the primary Bjerknes force will make more cavitation bubbles move to acoustic pressure node with the increase of the acoustic pressure, so this is not conducive to the occurrence of cavitation. Especially, the height of the liquid level should not be a quarter of acoustic wavelength. For a given acoustic frequency, the larger the initial radius of cavitation bubble, the more favorable the occurrence of cavitation is. But when the initial radius of cavitation bubble exceeds the resonant radius of acoustic frequency, the bubble will be pushed to pressure node. That is to say, the acoustic pressure amplitude, the acoustic frequency, and the initial radius of cavitation bubble each have a corresponding limit. Moreover, the lower limit is conducive to the occurrence of the phenomenon of cavitation.

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