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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.
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Keywords:
- the secondary Bjerknes force /
- volume amplitude /
- pulsation phase /
- scattering
[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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[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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