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Linear wave propagation in the bubbly liquid

Wang Yong Lin Shu-Yu Zhang Xiao-Li

Linear wave propagation in the bubbly liquid

Wang Yong, Lin Shu-Yu, Zhang Xiao-Li
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  • 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.
    • Funds: Project supported by the Innovation Funds of Graduate Programs of Shaanxi Normal University, China (Grant No. 2012CXB014) and the National Natural Science Foundation of China (Grant No. 11174192).
    [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 物理学报 61 184302]

    [14]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 104302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 104302]

    [15]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 084302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 084302]

    [16]

    Zhang P L, Lin S Y 2009 Acta Phys. Sin. 58 7797 (in Chinese) [张鹏利, 林书玉 2009 物理学报 58 7797]

    [17]

    Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 物理学报 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

  • [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 物理学报 61 184302]

    [14]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 104302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 104302]

    [15]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 084302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 084302]

    [16]

    Zhang P L, Lin S Y 2009 Acta Phys. Sin. 58 7797 (in Chinese) [张鹏利, 林书玉 2009 物理学报 58 7797]

    [17]

    Qian Z W 1981 Acta Phys. Sin. 30 442 (in Chinese) [钱祖文 1981 物理学报 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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  • Received Date:  20 September 2012
  • Accepted Date:  10 October 2012
  • Published Online:  20 March 2013

Linear wave propagation in the bubbly liquid

  • 1. Institute of Applied Acoustics Shaanxi Normal University, Xi’an 710062, China
Fund Project:  Project supported by the Innovation Funds of Graduate Programs of Shaanxi Normal University, China (Grant No. 2012CXB014) and the National Natural Science Foundation of China (Grant No. 11174192).

Abstract: 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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