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为了探讨含气泡液体对声波传播的影响, 研究了声波在含气泡液体中的线性传播. 在建立含气泡液体的声学模型时引入气泡含量的影响,建立气泡模型时引用 Keller的气泡振动模型并同时考虑气泡间的声相互作用,得到了经过修正的气泡振动方程. 通过对含气泡液体的声传播方程和气泡振动方程联立并线性化求解,在满足 (ω R0)/c << 1 的前提下,得到了描述含气泡液体对声波传播的衰减系数和传播速度. 通过数值分析发现,在驱动声场频率一定的情况下,气泡含量的增加及气泡的变小均会导致衰减系数增加和声速减小;气泡的体积分数和大小一定时, 驱动声场频率在远小于气泡谐振频率的情况下,声速会随驱动频率的增加而减小; 气泡间的声相互作用对声波传播速度及含气泡液体衰减系数的影响不明显.最终认为气泡的大小、 数量和驱动声场频率是影响声波在含气泡液体中线性传播的主要因素.In order to get the factor of influence of bubbly liquid on the acoustic wave propagation, the linear wave propagation in bubbly liquid is studied. The influence of bubbles is taken into account when the acoustic model of bubbly liquid is established, and we can get the corrected oscillation equation of the bubble when the interaction of bubbles is taken into the Keller's model. One can get the acoustic attenuation coefficient and the sound speed of the bubbly liquid through solving the linearized equation of wave propagation of bubbly liquids and the oscillation equation of bubbles when (ωR0)/c << 1. After the numerical analysis, we find that the acoustic attenuation coefficient increases and the sound speed will turn smaller as the numbers of bubbles increases and the bubbles gets smaller when the driving frequency of sound field keeps constant; when the driving frequency is far bellow the resonance frequency of bubble and both the volume fraction and the size of bubbles are kept constant, the sound speed will changes in a way contrary to the case of driving frequency of sound field; it is not evident that the bubble interaction influences the acoustic attenuation coefficient and the sound speed. Finally, we deem that the volume concentration, the size of bubble and the driving frequency of sound field are the important parameters which determine the deviations of the sound speed and the attenuation from those of bubble-free water.
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Keywords:
- bubbly liquids /
- linear acoustic wave /
- acoustic attenuation coefficient /
- wave speed
[1] Mallock A 1911 Proc. R. Soc. Lond. A 84 391
[2] Wijngaarden L V 1972 Ann. Rev. Fluid Mech. 4 369
[3] Caflisch R E, Miksis M J, Papanicolaou G C, Ting L 1985 J. Fluid Mech. 160 1
[4] Caflisch R E, Miksis M J, Papanicolaou G C, Ting L 1985 J. Fluid Mech. 153 259
[5] Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732
[6] Prosperetti A, Crum L A, Commander K W 1988 J. Acoust. Soc. Am. 83 502
[7] Li F X, Sun J C, Huang J Q 1998 J. Northwestern Polytech. Univ. 16 241 (in Chinese) [李福新, 孙进才, 黄景泉 1998 西北工业大学学报 16 241]
[8] Kudryashov N A, Sinelshchikov D I 2010 Phys. Lett. A 374 2011
[9] Kudryashov N A, Sinelshchikov D I 2010 Appl. Math. Comput. 217 414
[10] Vanhille C, Campos-Pozuelo C 2009 Ultrason. Sonochem. 16 669
[11] Vanhille C, Campos-Pozuelo C 2011 Ultrason. Sonochem. 18 679
[12] Louisnard O 2012 Ultrason. Sonochem. 19 56
[13] Zhang J, Zeng X W, Chen D, Zhang Z F 2012 Acta Phys. Sin. 61 184302 (in Chinese) [张军, 曾新吾, 陈聃, 张振福 2012 61 184302]
[14] Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 104302 (in Chinese) [沈壮志, 林书玉 2011 60 104302]
[15] Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 084302 (in Chinese) [沈壮志, 林书玉 2011 60 084302]
[16] Zhang P L, Lin S Y 2009 Acta Phys. Sin. 58 7797 (in Chinese) [张鹏利, 林书玉 2009 58 7797]
[17] Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 30 442]
[18] Prosperetti A, Lezzi A 1986 J. Fluid Mech. 168 457
[19] Foldy L L 1945 Phys. Rev. 67 107
[20] Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732
[21] Prosperetti A 1984 Ultrasonics 22 115
[22] Prosperetti A 1977 J. Acoust. Soc. Am. 61 17
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[1] Mallock A 1911 Proc. R. Soc. Lond. A 84 391
[2] Wijngaarden L V 1972 Ann. Rev. Fluid Mech. 4 369
[3] Caflisch R E, Miksis M J, Papanicolaou G C, Ting L 1985 J. Fluid Mech. 160 1
[4] Caflisch R E, Miksis M J, Papanicolaou G C, Ting L 1985 J. Fluid Mech. 153 259
[5] Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732
[6] Prosperetti A, Crum L A, Commander K W 1988 J. Acoust. Soc. Am. 83 502
[7] Li F X, Sun J C, Huang J Q 1998 J. Northwestern Polytech. Univ. 16 241 (in Chinese) [李福新, 孙进才, 黄景泉 1998 西北工业大学学报 16 241]
[8] Kudryashov N A, Sinelshchikov D I 2010 Phys. Lett. A 374 2011
[9] Kudryashov N A, Sinelshchikov D I 2010 Appl. Math. Comput. 217 414
[10] Vanhille C, Campos-Pozuelo C 2009 Ultrason. Sonochem. 16 669
[11] Vanhille C, Campos-Pozuelo C 2011 Ultrason. Sonochem. 18 679
[12] Louisnard O 2012 Ultrason. Sonochem. 19 56
[13] Zhang J, Zeng X W, Chen D, Zhang Z F 2012 Acta Phys. Sin. 61 184302 (in Chinese) [张军, 曾新吾, 陈聃, 张振福 2012 61 184302]
[14] Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 104302 (in Chinese) [沈壮志, 林书玉 2011 60 104302]
[15] Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 084302 (in Chinese) [沈壮志, 林书玉 2011 60 084302]
[16] Zhang P L, Lin S Y 2009 Acta Phys. Sin. 58 7797 (in Chinese) [张鹏利, 林书玉 2009 58 7797]
[17] Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 30 442]
[18] Prosperetti A, Lezzi A 1986 J. Fluid Mech. 168 457
[19] Foldy L L 1945 Phys. Rev. 67 107
[20] Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732
[21] Prosperetti A 1984 Ultrasonics 22 115
[22] Prosperetti A 1977 J. Acoust. Soc. Am. 61 17
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