声场中空化气泡的耦合振动及形状不稳定性的研究

马艳; 林书玉; 徐洁

doi:10.7498/aps.67.20171573

摘要

计算了两个具有非球形扰动的气泡所组成系统的能量，并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程，研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种：形状耦合模式和径向耦合模式，气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅，具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.

关键词:

Abstract

Based on the Lagrange's equation, the dynamic equations and shape mode equations of two bubbles with nonspherical distortion are obtained. The radial oscillations and shape instabilities of two bubbles with nonspherical distortion in an acoustic field are numerically investigated. The numerical results show that there are two coupled modes between two nonspherical bubbles: shape coupled mode and radial coupled mode. The coupled modes between two nonspherical bubbles depend on the shape modes of two bubbles. When the shape mode of the first bubble is equal to that of the second bubble (n=m), the shape coupled mode and radial coupled mode both exist. The interaction force between bubbles is caused by these two coupled modes. If the two bubbles have different shape mode orders (n m), there is a radially coupled mode between two bubbles. The interaction force between two bubbles is caused by radially coupled mode. The interaction caused by the radial coupling and shape coupling has an influence on the instability of gas bubble. The influencing factors depend on the shape mode, the equilibrium radius of neighboring bubble, and the driving acoustic field. The results demonstrate that the shape coupling can change the severity of the collapse of a gas bubble, and increase the ability of a gas bubble to resist distortion under a certain condition. The nonspherical disturbance of a real bubble in an acoustic field is not a single shape mode, but the coupling of different shape modes, so the shape coupling has an obvious influence on the shape instability of a real bubble. These may be the reason why bubbles can form some stable structures and keep stable oscillations in an acoustic field.

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电子信息工程学院, 纳米结构及功能材料工程技术研究中心, 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：11374200，11674206）、宁夏自然科学基金（批准号：NZ17254）和宁夏高等学校一流学科建设（教育学学科）资助项目（批准号：NXYLXK2017B11）资助的课题.

Authors and contacts

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

2.
Engineering Research Center of Nanostructure and Functional Materials, College of Physics and Electronic Information Engineering, 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. 11374200, 11674206), the Natural Science Foundation of Ningxia, China (Grant No. NZ17254), and the Top Discipline Construction (Pedagogy) Foundation of Colleges and Universities of Ning Xia, China (Grant No. NXYLXK2017B11).

参考文献

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[19]	Lu Y, Katz J, Prosperetti A 2013 Phys. Fluids 25 073301
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[22]	Hens A, Biswas G, De S 2014 Phys. Fluids 26 012105

施引文献

[1]	Crum L A 1994 J. Acoust. Soc. Am. 95 559
[2]	Gaitan D F, Crum L A, Church C C, Roy R A 1992 J. Acoust. Soc. Am. 91 3166
[3]	Holot R G, Gaitan D F 1996 Phys. Rev. Lett. 77 3791
[4]	Zhang S G, Duncan J H 1994 Phys. Fluids 6 2352
[5]	Leong T, Yasui K, Kato K, Harvie D, Ashokkumar M, Kentish S 2014 Phys. Rev. E 89 043007
[6]	Pelekasis N A, Tsamopouslos J A 1990 Phys. Fluids A 2 1328
[7]	Feng Z C, Leal L G 1997 Annu. Rev. Fluid Mech. 29 201
[8]	Reddy A J, Szeri A J 2002 Phys. Fluids 14 2216
[9]	Harkin A A, Kaper T J, Nadim A 2013 Phys. Fluids 25 062101
[10]	Plesset M S 1954 J. Appl. Phys. 25 96
[11]	Brenner M P, Lohse D, Dupont T F 1995 Phys. Rev. Lett. 75 954
[12]	Bogoyavlenskiy V A 2000 Phys. Rev. E 62 2158
[13]	Wang W J, Chen W Z 2003 J. Acoust. Soc. Am. 114 1898
[14]	Liu H J, An Y 2003 Acta Phys. Sin. 52 620 (in Chinese) [刘海军, 安宇 2003 52 620]
[15]	Qian M L, Cheng Q, Ge C Y 2002 Acta Acust. 27 289 (in Chinese) [钱梦騄, 程茜, 葛曹燕 2002 声学学报 27 289]
[16]	Hilgenfeldt S, Lohse D, Brenner M P 1996 Phys. Fluids 8 2808
[17]	Godinez F A, Navarrete M 2011 Phys. Rev. E 84 016312
[18]	Ueno I, Ando J, Koiwa Y, Saiki T, Kaneko T 2015 Eur. Phys. J. Special Topics 224 415
[19]	Lu Y, Katz J, Prosperetti A 2013 Phys. Fluids 25 073301
[20]	Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[21]	Zhang W J, An Y 2013 Phys. Rev. E 87 053023
[22]	Hens A, Biswas G, De S 2014 Phys. Fluids 26 012105

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