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The pressure wave emitted by a pulsating bubble affects the motions of other bubbles, so in an acoustic field bubbles are in a state of coupled oscillation. In this paper, a cluster with cavitation bubbles inside is considered, and a mathematical model is developed to describe the dynamics of the bubbles of the same radius inside a spherical cluster when the effects of coupled oscillation are included. Based on this new model, the nonlinear acoustic response of cavitation bubbles is analyzed numerically. Comparison of our model with those in the literature, shows that bubbles are suppressed heavily. Because of the coupled oscillations of bubbles, the motions of a bubble are affected by more constraints in the system, which cause the decrease of natural frequency of the bubbles. The nonlinear acoustical response of bubbles is improved by the coupled oscillation in a bubble cluster. With the rise in number density of the cluster, the suppression of bubble oscillation is enhanced. For a cluster of 1 mm radius, when the bubble number is below 500, the change of bubble number may cause a sharp decrease of maximum radial displacement of the bubbles. In cavitation region, there are bubble clusters and large-sized bubble, and the moving large bubble can absorb small bubbles from the surface of bubble cluster, so the bubble numbers inside a cluster varies with time, which may change the acoustic response of coupled oscillating bubbles. The increase of the liquid static pressure can suppress the oscillation of bubbles too, and there is a sensitive region (1-2 atm) that affects remarkably the acoustical response of bubbles. Driving ultrasound can affect the motion of bubble greatly. The range of cavitation bubble size is narrowed when the wave frequency increases. The bubbles whose initial radii are close to 5 m are easy to be activated by ultrasound under given acoustic conditions, i.e. sizes of bubble cluster, surrounding liquid and inner gas. The cluster oscillation of bubbles may suppress the motion of individual bubbles, and weaken the cavition effects caused by individual bubbles. However, the collapse time of the bubbles may be delayed, and the cavitation region may become larger than that for a single bubble. As a result, cavitation effects are amplified in the cluster region.
[1] Ying C F 2007 Sci. Sin-Phys. Mech. Astron. 37 129 (in Chinese) [应崇福 2007 中国科学 37 129]
[2] Bjerknes V F K 1966 Field of Force (New York: Columbia University Press) pp45-47
[3] Wang C H, Lin S Y 2011 Acta Acustica 36 325 (in Chinese) [王成会, 林书玉 2011 声学学报 36 325]
[4] Doinikov A A, Zavtrak S T 1996 J. Acoust. Soc. Am. 99 3849
[5] An Y 2011 Phys. Rev. E 84 066313
[6] Brennen C E 1995 Cavitation and Bubble Dynamics(London: Oxford University Press) pp11-32
[7] Prosperetti A 1974 J. Acoust. Soc. Am. 56 878
[8] Prosperetti A 1975 J. Acoust. Soc. Am. 57 810
[9] Huang W, Chen W Z, Liu Y N, Gao X X 2006 Ultrasonics 22 e407
[10] Van der Kroon I, Quinto-Su P A, Li F, Ohl C 2010 Phys. Rev. E 82 066311
[11] Gaitan D F, Crum L A, Church C C, Roy R A 1992 J. Acoust. Soc. Am. 91 3166
[12] Hiller R A, Putterman S J, Weninger K R 1998 Phys. Rev. Lett. 80 1090
[13] Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A 2008 Phys. Rev. E 77 016609
[14] Rezaee N, Sadighi-Bonabi R, Mirheydari M, Ebrahimi H 2011 Chin. Phys. B 20 087804
[15] Ida M 2009 Phys. Rev. E79 016037
[16] Zhang Y L, Zheng H R, Tang M X, Zhang D 2011 Chin. Phys. B 20 114302
[17] Jiang L, Liu F, Chen H S, Wang J D, Chen D R 2012 Phys. Rev. E 85 036312
[18] Brotchie A, Grieser F, Ashokkumar M 2009 Phys. Rev. L. 102 084302
[19] Birkin P R, Offin D G, Vian C J B, Leighton T G, Maksimov A O 2011 J. Acoust. Soc. Am. 130 3297
[20] Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 75 046304
[21] Wang C H, Cheng J C 2013 Sci. China. Ser. G 56 1246
[22] Wang C H, Cheng J C 2014 Acta. Phys. Sin.63 1343013 (in Chinese) [王成会, 程建春 2014 62 134303]
[23] An Y 2012 Phys. Rev. E 85 016305
[24] Hu J, Lin S Y, Wang C H, Li J 2013 Acta. Phys. Sin.62 1343033 (in Chinese) [胡静, 林书玉, 王成会, 李锦 2013 62 134303]
[25] Wang C H, Cheng J C 2013 Chin. Phys. B 22 014304
[26] Nasibullaeva E S, Akhatov I S 2013 J. Acoust. Soc. Am. 133 3727
[27] Oma R 1987 J. Acoust. Soc. Am. 82 1018
[28] Shen Z Z, Wu S Y 2012 Acta Phys. Sin. 61 244301 (in Chinese) [沈壮志, 吴胜举 2012 61 244301]
[29] Yasui K, Towata A, Tuziuti T, Kozuka T, Kato K 2011 J. Acoust. Soc. Am. 130 3233
[30] Wang C H, Hu J, Cao H, Lin S Y, An S 2015 Sci. Sin-Phys. Mech. Astron. 45 064301 (in Chinese) [王成会, 胡静, 曹辉, 林书玉, 安帅 2015 中国科学: 物理学力学天文学 45 064301]
[31] Van der Kroon I, Quinto-Su P A, Li F, Ohl C 2010 Phys. Rev. E 82 066311
[32] Toytman I, Silbergleit A, Simanovski D, Palanker D 2010 Phys. Rev. E 82 046313
[33] Cai M, Zhao S, Liang H 2010 Desalination 263 133
[34] Brujan E A, Ikeda T, Yoshinaka K, Matsumoto Y 2011 Ultrason. Sonochem. 18 59
[35] Kanthale P M, Gogate P R, Pandit A B, Wilhelm A M 2003 Ultrason. Sonochem. 10 181
[36] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
[37] Ohl C D, Kurz Thomas, Geisler R, Lindau O, Lauterborn W 1999 Phil. Trans. R Soc. Lond. 357 269
[38] Gao X X, Chen W Z, Huang W, Xu J F, Xu X H, Liu Y N, Liang Y 2009 Chin. Sci. Bull. 54 408 (in Chinese) [高贤娴, 陈伟中, 黄威, 徐俊峰, 徐兴华, 刘亚楠, 梁越 2009 科学通报 54 408]
[39] Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[40] Wang C H, Lin S Y 2010 Acta Mech. Sinica. 42 1050 (in Chinese) [王成会, 林书玉 2010 力学学报 42 1050]
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[1] Ying C F 2007 Sci. Sin-Phys. Mech. Astron. 37 129 (in Chinese) [应崇福 2007 中国科学 37 129]
[2] Bjerknes V F K 1966 Field of Force (New York: Columbia University Press) pp45-47
[3] Wang C H, Lin S Y 2011 Acta Acustica 36 325 (in Chinese) [王成会, 林书玉 2011 声学学报 36 325]
[4] Doinikov A A, Zavtrak S T 1996 J. Acoust. Soc. Am. 99 3849
[5] An Y 2011 Phys. Rev. E 84 066313
[6] Brennen C E 1995 Cavitation and Bubble Dynamics(London: Oxford University Press) pp11-32
[7] Prosperetti A 1974 J. Acoust. Soc. Am. 56 878
[8] Prosperetti A 1975 J. Acoust. Soc. Am. 57 810
[9] Huang W, Chen W Z, Liu Y N, Gao X X 2006 Ultrasonics 22 e407
[10] Van der Kroon I, Quinto-Su P A, Li F, Ohl C 2010 Phys. Rev. E 82 066311
[11] Gaitan D F, Crum L A, Church C C, Roy R A 1992 J. Acoust. Soc. Am. 91 3166
[12] Hiller R A, Putterman S J, Weninger K R 1998 Phys. Rev. Lett. 80 1090
[13] Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A 2008 Phys. Rev. E 77 016609
[14] Rezaee N, Sadighi-Bonabi R, Mirheydari M, Ebrahimi H 2011 Chin. Phys. B 20 087804
[15] Ida M 2009 Phys. Rev. E79 016037
[16] Zhang Y L, Zheng H R, Tang M X, Zhang D 2011 Chin. Phys. B 20 114302
[17] Jiang L, Liu F, Chen H S, Wang J D, Chen D R 2012 Phys. Rev. E 85 036312
[18] Brotchie A, Grieser F, Ashokkumar M 2009 Phys. Rev. L. 102 084302
[19] Birkin P R, Offin D G, Vian C J B, Leighton T G, Maksimov A O 2011 J. Acoust. Soc. Am. 130 3297
[20] Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 75 046304
[21] Wang C H, Cheng J C 2013 Sci. China. Ser. G 56 1246
[22] Wang C H, Cheng J C 2014 Acta. Phys. Sin.63 1343013 (in Chinese) [王成会, 程建春 2014 62 134303]
[23] An Y 2012 Phys. Rev. E 85 016305
[24] Hu J, Lin S Y, Wang C H, Li J 2013 Acta. Phys. Sin.62 1343033 (in Chinese) [胡静, 林书玉, 王成会, 李锦 2013 62 134303]
[25] Wang C H, Cheng J C 2013 Chin. Phys. B 22 014304
[26] Nasibullaeva E S, Akhatov I S 2013 J. Acoust. Soc. Am. 133 3727
[27] Oma R 1987 J. Acoust. Soc. Am. 82 1018
[28] Shen Z Z, Wu S Y 2012 Acta Phys. Sin. 61 244301 (in Chinese) [沈壮志, 吴胜举 2012 61 244301]
[29] Yasui K, Towata A, Tuziuti T, Kozuka T, Kato K 2011 J. Acoust. Soc. Am. 130 3233
[30] Wang C H, Hu J, Cao H, Lin S Y, An S 2015 Sci. Sin-Phys. Mech. Astron. 45 064301 (in Chinese) [王成会, 胡静, 曹辉, 林书玉, 安帅 2015 中国科学: 物理学力学天文学 45 064301]
[31] Van der Kroon I, Quinto-Su P A, Li F, Ohl C 2010 Phys. Rev. E 82 066311
[32] Toytman I, Silbergleit A, Simanovski D, Palanker D 2010 Phys. Rev. E 82 046313
[33] Cai M, Zhao S, Liang H 2010 Desalination 263 133
[34] Brujan E A, Ikeda T, Yoshinaka K, Matsumoto Y 2011 Ultrason. Sonochem. 18 59
[35] Kanthale P M, Gogate P R, Pandit A B, Wilhelm A M 2003 Ultrason. Sonochem. 10 181
[36] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
[37] Ohl C D, Kurz Thomas, Geisler R, Lindau O, Lauterborn W 1999 Phil. Trans. R Soc. Lond. 357 269
[38] Gao X X, Chen W Z, Huang W, Xu J F, Xu X H, Liu Y N, Liang Y 2009 Chin. Sci. Bull. 54 408 (in Chinese) [高贤娴, 陈伟中, 黄威, 徐俊峰, 徐兴华, 刘亚楠, 梁越 2009 科学通报 54 408]
[39] Ida M, Naoe T, Futakawa M 2007 Phys. Rev. E 76 046309
[40] Wang C H, Lin S Y 2010 Acta Mech. Sinica. 42 1050 (in Chinese) [王成会, 林书玉 2010 力学学报 42 1050]
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