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将非线性声波方程和改进的Rayleigh-Plesset方程联立可以描述空化环境中的声场及相应的气泡动力学特征. 用时域有限差分方法模拟了圆柱形容器内两种气泡相互混合时的空化情况. 在烧杯内的稳态背景声场形成过程中, 瓶壁耗散吸收扮演了重要的角色. 在稳态背景声场的基础上, 分析了混合气泡与声场的相互作用、气泡之间的相互作用、混合情况下的频谱特性. 结果表明: 两种气泡平衡半径都不太大时, 气泡与声场的相互作用不强, 声场及气泡的行为也比较规律; 相反, 当其中一种气泡平衡半径相对比较大时, 声场与气泡具有较强的非线性相互作用, 声场及气泡的行为表现出复杂的特性.By solving the nonlinear wave equation coupled with the modified Rayleigh-Plesset equation, the characteristics of the acoustic field and bubble motion in cavitation environment can be described. In general, the cavitation cloud consists of many kinds of bubbles with different ambient radii. For simplicity, in this work the cavitation process of the mixture of two kinds of bubbles with different ambient radii is numerically simulated, and the ratio of the mixture is adjustable. Suppose that the cavitation in water contained in a cylindrical container is stimulated by ultrasonic horn. The dissipative absorption of the container wall is taken into account, which plays an important role in forming the stationary standing wave field, otherwise, the beat signal of acoustic pressure will appear which is absent in the observation. Based on the stationary acoustic wave field, for the case of the mixed-bubble cavitation, the interactions between bubbles and acoustic field, bubbles and bubbles, as well as the spectrum of acoustic signal are analyzed. We choose the cases that the ratio of two kinds of bubble species is varying, but the total density of bubble number is fixed to be 1/mm3, and find that those results are very different. For the case that the ambient radii of two bubble species are both a few micron, revealing that the interaction between bubbles and acoustic field is usually weak. As the proportion of bigger bubble increases, the change of the acoustic pressure and the averaged radius of bubble behave regularly; for the case that the ambient radius of one of bubble specie is relatively big, for example, the ambient radius is about a few tens of microns, the interactions between bubbles and acoustic field become stronger, and the nonlinearity is more apparent. We can observe the similar trends from the frequency spectrum. For the bubble of a few microns in size, the base frequency is dominant; in contrast, for the bubble of a few tens of microns in size, the components of harmonic frequencies are far beyond the base frequency component. The interesting phenomenon is that there is the cut off frequency and the cut of frequencies for different mixture of bubbles are almost the same.
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Keywords:
- acoustic cavitation /
- bubble dynamics /
- nonlinear acoustic equation /
- cavitation of mixed bubbles
[1] Suslick K S 1990 Science 247 1439
[2] Hoff L 1996 Ultrasonics 34 591
[3] Edson P L 2001 Ph.D. Dissertation (Boston:Boston University)
[4] Manickam S, Ashokkumar M 2014 Cavitation: A Novel Energy-Efficient Technique for the Generation of Nanomaterials (Singapore: Pan Standford Publishing Pte. Ltd.) pp1-422
[5] Rayleigh L 1917 Phil. Mag. Lett. 34 94
[6] Plesset M S 1949 ASME J. Appl. Mech. 16 277
[7] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
[8] Harkin A, Kaper T J, Nadim A 2001 J. Fluid Mech. 445 377
[9] Mettin R, Akhatov I, Parlitz U, Ohl C D, Lauterborn W 1997 Phys. Rev. E 56 2924
[10] Lu Y G, Wu X H 2011 Acta Phys. Sin. 60 046202 (in Chinese) [卢义刚, 吴雄慧 2011 60 046202]
[11] Jiang L, Liu F, Chen H, Chen H S, Wang J D, Chen D R 2012 Phys. Rev. E 85 36312
[12] Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 30 442]
[13] An Y 2011 Phys. Rev. E 83 66313
[14] Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A 2008 Phys. Rev.E 77 16609
[15] Zabolotskaya E A, Soluyan S I 1973 Sov. Phys. Acoust. 18 396
[16] An Y 2012 Phys. Rev. E 85 16305
[17] Vanhille C 2013 Ultrason. Sonochem. 20 963
[18] Kudryashov N A 2010 Phys. Lett. 374 2011
[19] Wang Y, Lin S Y, Zhang X L 2014 Acta Phys. Sin. 63 034301 (in Chinese) [王勇, 林书玉, 张小丽 2014 63 034301]
[20] Enflo B O, Hedberg C M 2006 Theory of Nonlinear Acoustics in Fluids (Dordrecht: Kluwer Academic Publishers) p222
[21] Desjouy C, Labelle P, Gilles B, Bera J C, Inserra C 2013 Phys. Rev. E 88 33006
[22] Jiao J J, He Y, Leong T, Kentish S E, Ashokkumar M, Manasseh R, Lee J 2013 J. Phys. Chem. B 117 12549
[23] Landau L D, Lifshitz E M (translated by Li Z) 2013 Fluid Mechanics (Beijing: Higher Education Press) pp345-348 (in Chinese) [朗道, 栗弗席兹 著 (李植 译) 2013 流体动力学 (北京:高等教育出版社) 第345–348页]
[24] Ida M 2009 Phys. Rev. E 79 16307
[25] Yasui K, Towata A, Tuziuti T, Kozuka T, Kato K 2011 J. Acoust. Soc Am. 130 3233
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[1] Suslick K S 1990 Science 247 1439
[2] Hoff L 1996 Ultrasonics 34 591
[3] Edson P L 2001 Ph.D. Dissertation (Boston:Boston University)
[4] Manickam S, Ashokkumar M 2014 Cavitation: A Novel Energy-Efficient Technique for the Generation of Nanomaterials (Singapore: Pan Standford Publishing Pte. Ltd.) pp1-422
[5] Rayleigh L 1917 Phil. Mag. Lett. 34 94
[6] Plesset M S 1949 ASME J. Appl. Mech. 16 277
[7] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
[8] Harkin A, Kaper T J, Nadim A 2001 J. Fluid Mech. 445 377
[9] Mettin R, Akhatov I, Parlitz U, Ohl C D, Lauterborn W 1997 Phys. Rev. E 56 2924
[10] Lu Y G, Wu X H 2011 Acta Phys. Sin. 60 046202 (in Chinese) [卢义刚, 吴雄慧 2011 60 046202]
[11] Jiang L, Liu F, Chen H, Chen H S, Wang J D, Chen D R 2012 Phys. Rev. E 85 36312
[12] Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 30 442]
[13] An Y 2011 Phys. Rev. E 83 66313
[14] Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A 2008 Phys. Rev.E 77 16609
[15] Zabolotskaya E A, Soluyan S I 1973 Sov. Phys. Acoust. 18 396
[16] An Y 2012 Phys. Rev. E 85 16305
[17] Vanhille C 2013 Ultrason. Sonochem. 20 963
[18] Kudryashov N A 2010 Phys. Lett. 374 2011
[19] Wang Y, Lin S Y, Zhang X L 2014 Acta Phys. Sin. 63 034301 (in Chinese) [王勇, 林书玉, 张小丽 2014 63 034301]
[20] Enflo B O, Hedberg C M 2006 Theory of Nonlinear Acoustics in Fluids (Dordrecht: Kluwer Academic Publishers) p222
[21] Desjouy C, Labelle P, Gilles B, Bera J C, Inserra C 2013 Phys. Rev. E 88 33006
[22] Jiao J J, He Y, Leong T, Kentish S E, Ashokkumar M, Manasseh R, Lee J 2013 J. Phys. Chem. B 117 12549
[23] Landau L D, Lifshitz E M (translated by Li Z) 2013 Fluid Mechanics (Beijing: Higher Education Press) pp345-348 (in Chinese) [朗道, 栗弗席兹 著 (李植 译) 2013 流体动力学 (北京:高等教育出版社) 第345–348页]
[24] Ida M 2009 Phys. Rev. E 79 16307
[25] Yasui K, Towata A, Tuziuti T, Kozuka T, Kato K 2011 J. Acoust. Soc Am. 130 3233
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