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考虑了非球形气泡在声场中的形状振动，推导了非球形气泡和球形气泡之间的次Bjerknes力方程，数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力，并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明：当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时，在第一个声驱动周期内，非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大，在大小上是两个球形气泡次Bjerkens力的数倍，且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.
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关键词:
- 非球形气泡 /
- 次Bjerknes力 /
- 形状模态
The secondary Bjerknes force between bubbles in an acoustic field is a well-known acoustic phenomenon. The theoretical researches of the secondary Bjerknes force mainly focus on the case of two spherical bubbles. The secondary Bjerknes force between two spherical bubbles, calculated based on the linear equations, is very small and negligible. Therefore these theoretical researches donot give a good explanation for the phenomenon, such as “streamer formation” and multi-bubble sonoluminescence(MBSL). Experiments of sonoluminescence show that the shapes of the bubbles in a sound field are not entirely spherical. Nonspherical effects have an important influence on the secondary Bjerknes force when two bubbles come close to each other in a strong acoustic field(>1.0×105 Pa). How the shape distortion of a nonspherical bubble causes the secondary Bjerknes force between two bubbles to change, and how the secondary Bjerknes force affects the oscillations and movements of bubbles are major problems which we are to solve in the present research. The expression of the secondary Bjerknes force between a nonspherical bubble and a spherical bubble is obtained by considering the shape oscillation of a nonspherical bubble. We numerical simulate the secondary Bjerknes force between a nonspherical bubble and a spherical bubble based on the nonlinear oscillation equations of two bubbles, and compare the secondary Bjerknes force between a nonspherical bubble and a spherical bubble with the secondary Bjerknes force between two spherical bubbles in the same condition. We discuss the influence of nonspherical effects on the secondary Bjerknes force between two bubbles. The results show that when the amplitude of driving pressure is greater than the Blake threshold of a nonspherical bubble and makes the bubble oscillate stably, the secondary Bjerknes force between this nonspherical bubble and a spherical bubble is different from the secondary Bjerknes force between two spherical bubbles in direction and magnitude. The secondary Bjerknes force between a nonspherical bubble and a spherical bubble is much bigger than that between two spherical bubbles. The interactional distance of the secondary Bjerknes force between a nonspherical bubble and a spherical bubble is longer than that between two spherical bubbles. The secondary Bjerknes force between a spherical bubble and a nonspherical bubble depends on the radii of two bubbles, distance between two bubbles, shape mode of the nonspherical bubble and the amplitude of driving pressure. Our research is closer to the actual bubbles in liquid. We also prove that big mutual interaction between bubbles is the main cause for froming a stable structure between bubbles. For bubbles, big mutual interaction causing the cavitation becomes easier. These results are important for explaining the phenomenon in an acoustic field, such as “streamer formation” and MBSL.-
Keywords:
- nonspherical bubbles /
- secondary Bjerknes force /
- shape mode
[1] Anthony H, Kaper T 2001 J. Fluid Mech. 445 377
[2] Thomas J M, Sean M C 1997 J. Acoust. Soc. Am. 102 1522
[3] Rossello J M, Dellavale D, Bonetto F J 2015 Ultrason. Sonochem. 22 59
[4] Yuan L, Joseph K 2013 Phys. Fluids 25 073301
[5] Eller A 1968 J. Acoust. Soc. Am. 43 107
[6] Alexander A D 1997 J. Acoust. Soc. Am 102 747
[7] David R, Pierre T B 2011 Phys. Fluids 23 042003
[8] Mohammad A A 2011 J. Acoust. Soc. Am. 130 3321
[9] Rasoul S B, Nastaran R 2010 Phys. Rev. E 82 016316
[10] Crum L A 1975 J. Acoust. Soc. Am. 57 1363
[11] Yoshida K J, Takaaki F 2011 J. Acoust. Soc. Am 130 135
[12] Zabolotskaya E A 1984 Sov. Phys. Scoust 30 365
[13] Ida M 2007 Phys. Rev. E 76 04309
[14] Mettin R, Akhatov I, Parlitz U 1997 Phys. Rev. E 56 2924
[15] Shao W H, Chen W Z 2013 J. Acoust. Soc. Am. 133 119
[16] Prosperetti A 1977 Q. Appl. Math 34 339
[17] Bogoyavlenskiy V A 2000 Phy. Rev. E 62 2158
[18] Pelekasis N A, Tsamopouslos J A 1990 Phys. Fluids A 2 1328
[19] Xie C G, An Y 2003 Acta Phys. Sin. 52 102 （in Chinese)[谢崇国, 安宇2003 52 102]
[20] Plesset M S 1954 J. Appl. Phys. 25 96
[21] Brenner M P, Lohse D, Dupon T F 1995 Phys. Rev. Lett. 75 954
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[1] Anthony H, Kaper T 2001 J. Fluid Mech. 445 377
[2] Thomas J M, Sean M C 1997 J. Acoust. Soc. Am. 102 1522
[3] Rossello J M, Dellavale D, Bonetto F J 2015 Ultrason. Sonochem. 22 59
[4] Yuan L, Joseph K 2013 Phys. Fluids 25 073301
[5] Eller A 1968 J. Acoust. Soc. Am. 43 107
[6] Alexander A D 1997 J. Acoust. Soc. Am 102 747
[7] David R, Pierre T B 2011 Phys. Fluids 23 042003
[8] Mohammad A A 2011 J. Acoust. Soc. Am. 130 3321
[9] Rasoul S B, Nastaran R 2010 Phys. Rev. E 82 016316
[10] Crum L A 1975 J. Acoust. Soc. Am. 57 1363
[11] Yoshida K J, Takaaki F 2011 J. Acoust. Soc. Am 130 135
[12] Zabolotskaya E A 1984 Sov. Phys. Scoust 30 365
[13] Ida M 2007 Phys. Rev. E 76 04309
[14] Mettin R, Akhatov I, Parlitz U 1997 Phys. Rev. E 56 2924
[15] Shao W H, Chen W Z 2013 J. Acoust. Soc. Am. 133 119
[16] Prosperetti A 1977 Q. Appl. Math 34 339
[17] Bogoyavlenskiy V A 2000 Phy. Rev. E 62 2158
[18] Pelekasis N A, Tsamopouslos J A 1990 Phys. Fluids A 2 1328
[19] Xie C G, An Y 2003 Acta Phys. Sin. 52 102 （in Chinese)[谢崇国, 安宇2003 52 102]
[20] Plesset M S 1954 J. Appl. Phys. 25 96
[21] Brenner M P, Lohse D, Dupon T F 1995 Phys. Rev. Lett. 75 954
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