次Bjerknes力作用下气泡的体积振动和散射声场

马艳; 林书玉; 鲜晓军

doi:10.7498/aps.65.014301

摘要

利用Lagrange方程得到了次Bjerknes力作用下气泡的体积振动方程, 并探讨了次Bjerknes力作用下不同参数对气泡体积振动振幅和振动初相位的影响, 研究了振动初相位差为和0的气泡对在液体中形成的散射声场特征. 结果表明: 次Bjerknes作用力下, 相邻气泡半径、气泡间距、多方指数均能影响气泡的体积振动振幅, 气泡对的均衡半径、气泡间距和驱动频率则对气泡振动初相位产生明显影响; 相距很近、相位相差为的两个气泡的散射声压与气泡体积振动振幅、气泡间距、驱动频率和振动初相位有关, 随声场距离成反比减小, 与声场位置有关, 其平均散射声功率是单个孤立气泡的1/6 (kd12)2; 半径相同、相距很近、相位相同的两个气泡的散射声压与气泡振动初相位、体积振动振幅、气泡间距、驱动频率有关, 随声场距离成反比减小, 其平均散射声功率是单个孤立气泡的4倍.

关键词:

Abstract

The interaction of bubbles must be taken into consideration in the investigation of sound wave in the liquid containing gas bubbles, particularly in the case where the gas content is high. The force between two air bubbles due to the secondary sound fields radiated by the bubbles is called the secondary Bjerknes force, which makes the dynamics and scattering of bubbles different from a single bubble's. In order to investigate the influence of secondary Bjerknes force on bubbles' pulsation and scattering, we obtain the universal expression of bubbles' pulsation under the secondary Bjerknes force by Lagrange's equation. The influences on volume amplitude and initial phase of different parameter under the second Bjerknes force are discussed, and the scattering of bubbles with phase differences of and 0 is studied. The results show that the radius of neighbouring bubble, distance between two bubbles, polytropic coefficient and the phase can change the volume amplitude of pulsation under the secondary Bjerknes force. The mean radius of bubbles, distance and the frequency of sound have a significant effect on initial phase; the scattering of two bubbles of small distance and phase difference of is directional and decreases with distance r, which is related to the volume amplitude, initial phase and distance between two bubbles. The mean scattering power of bubble pairs of phase difference is 1/6(kd12)2 of single bubble's. The scattering of two bubbles with small distance and same phase also decreases with the distance r and relates to the volume amplitude, initial phase and distance between two bubbles. The mean scattering power of bubble pairs of same phase is 4 times as bigger as the mean scattering power of single bubble. It is expected that the mean radiuses, driving frequency and distance between bubbles can be used to change the scattering of bubbles.

Keywords:

作者及机构信息

1.
陕西师范大学, 陕西省超声学重点实验室, 西安 710062;

2.
宁夏师范学院物理与信息技术学院, 固原 756000

通信作者: 林书玉, sylin@snnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11174192, 11374200, 11474192)资助的课题.

Authors and contacts

1.
Shaanxi Key Laboratory of Ultrasonics, Shaanxi Normal University, Xi'an 710062, China;

2.
School of Physics and Information Technology, Ningxia Normal University, Guyuan 756000, China

Corresponding author: Lin Shu-Yu, sylin@snnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11174192, 11374200, 11474192).

参考文献

[1]	Carstensen E L, Foldy L L 1947 J. Acoust. Soc. Am. 19 481
[2]	Devin C J R 1959 J. Acoust. Soc. Am. 31 1654
[3]	Himmelblau D M 1964 Chem. Rev. 64 527
[4]	Kapodistrias G, Dahl P H 2001 J. Acoust. Soc. Am. 110 1271
[5]	Kohanvosky A A 2004 Am. J. Phys. 72 258
[6]	Cai L W 2004 J. Acoust. Soc. Am. 115 986
[7]	Kapodistrias G, Dahl P H 2000 J. Acoust. Soc. Am. 107 3006
[8]	Farmer D M, Deane G B 2001 IEEE J. Oceanic Eng. 26 113
[9]	Flynn H G 1975 J. Acoust. Soc. Am. 57 1379
[10]	Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 30 442]
[11]	Wang Y, Lin S Y 2014 Acta Phys. Sin. 63 034301 (in Chinese) [王勇, 林书玉 2014 63 034301]
[12]	Wang C H, Cheng J C 2014 Acta Phys. Sin. 63 134301 (in Chinese) [王成会, 程建春 2014 63 134301]
[13]	Wu J, Fan T B 2014 Chin. Phys. B 23 104302
[14]	Wang L, Tu J 2014 Chin. Phys. B 23 124302
[15]	Ye Z 1996 J. Acoust. Soc. Am. 100 2011
[16]	Sadighi-Bonabi R, Rezaee N, Ebrahimi H, Mirheydari M 2010 Phys. Rev. E 82 016316
[17]	Gaunaurd G C, Huang H S 2000 J. Acoust. Soc. Am. 107 95
[18]	Kapodistrias G, Dahl P H 2012 J. Acoust. Soc. Am. 131 4243
[19]	Church C C 1995 J. Acoust. Soc. Am. 97 1510
[20]	Zabolotskaya E A 1984 Sov. Phys. Acoust 30 365
[21]	Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[22]	Yuan L, Katz J 2013 Phys. Fluids 25 073301
[23]	Alibakhshi M A 2011 J. Acoust. Soc. Am. 130 3321
[24]	Mettin R, Akhatov I, Parlitz U, Oho C D 1997 Phys. Rev. E 56 2924

施引文献

[1]	Carstensen E L, Foldy L L 1947 J. Acoust. Soc. Am. 19 481
[2]	Devin C J R 1959 J. Acoust. Soc. Am. 31 1654
[3]	Himmelblau D M 1964 Chem. Rev. 64 527
[4]	Kapodistrias G, Dahl P H 2001 J. Acoust. Soc. Am. 110 1271
[5]	Kohanvosky A A 2004 Am. J. Phys. 72 258
[6]	Cai L W 2004 J. Acoust. Soc. Am. 115 986
[7]	Kapodistrias G, Dahl P H 2000 J. Acoust. Soc. Am. 107 3006
[8]	Farmer D M, Deane G B 2001 IEEE J. Oceanic Eng. 26 113
[9]	Flynn H G 1975 J. Acoust. Soc. Am. 57 1379
[10]	Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 30 442]
[11]	Wang Y, Lin S Y 2014 Acta Phys. Sin. 63 034301 (in Chinese) [王勇, 林书玉 2014 63 034301]
[12]	Wang C H, Cheng J C 2014 Acta Phys. Sin. 63 134301 (in Chinese) [王成会, 程建春 2014 63 134301]
[13]	Wu J, Fan T B 2014 Chin. Phys. B 23 104302
[14]	Wang L, Tu J 2014 Chin. Phys. B 23 124302
[15]	Ye Z 1996 J. Acoust. Soc. Am. 100 2011
[16]	Sadighi-Bonabi R, Rezaee N, Ebrahimi H, Mirheydari M 2010 Phys. Rev. E 82 016316
[17]	Gaunaurd G C, Huang H S 2000 J. Acoust. Soc. Am. 107 95
[18]	Kapodistrias G, Dahl P H 2012 J. Acoust. Soc. Am. 131 4243
[19]	Church C C 1995 J. Acoust. Soc. Am. 97 1510
[20]	Zabolotskaya E A 1984 Sov. Phys. Acoust 30 365
[21]	Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[22]	Yuan L, Katz J 2013 Phys. Fluids 25 073301
[23]	Alibakhshi M A 2011 J. Acoust. Soc. Am. 130 3321
[24]	Mettin R, Akhatov I, Parlitz U, Oho C D 1997 Phys. Rev. E 56 2924

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