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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.
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Keywords:
- bubbles /
- nonspherical disturbances /
- shape coupled mode /
- Lagrange's equation
[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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[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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