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匀强磁场对水中气泡运动的影响

莫润阳 吴临燕 詹思楠 张引红

引用本文:
Citation:

匀强磁场对水中气泡运动的影响

莫润阳, 吴临燕, 詹思楠, 张引红

Effect of magnetic field on single-bubble in water

Mo Run-Yang, Wu Lin-Yan, Zhan Si-Nan, Zhang Yin-Hong
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  • 基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.
    In this paper, we extend the Rayleigh-Plesset model by considering the effect of a magnetic field on the nonlinear response of an oscillating spherical air bubble in water. Water molecules in motion, derived by a time varying ultrasound pressure field, suffer a torque from the magnetic field by Lorentz force. The rotational energy and the translational energy together constitute the kinetic energy of the water molecule. The work done by the pressure during the contraction and expansion of bubble is equal to the total kinetic energy of the water molecule in liquid. According to energy conservation, we establish a modified control equation of the bubble motion under the action of an applied external magnetic field. The integration of the nonlinear differential equation governing the bubble motion is performed analytically by using a regular expansion, and is solved numerically by using a fourth-order Runge-Kutta method. It is shown that the variation of ambient pressure changes the bubble dynamics when the magnetic field is off. The ambient pressure is increased due to the effect of external magnetic field. The pressure induced by magnetic field increases linearly with the increase of magnetic field intensity and the coefficient is about 103 times. The bubble expansion rate, maximum radius, and the velocity of the collapsing bubble decrease as the magnetic field increases. It is predicted that the applying of a magnetic field can widen the pressure range and modify bubble dynamics.
    • 基金项目: 国家自然科学基金(批准号:11274216)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274216).
    [1]

    Oh J M, Kim P J, Kang I S 2001 Phys. Fluids 13 2820

    [2]

    Dong W, Li R Y, Yu H L, Huang X 2004 J. Eng. Thermophys. 25 439 (in Chinese) [董伟, 李瑞阳, 郁鸿凌, 黄煊 2004 工程热物理学报 25 439]

    [3]

    Shen Z Z, Wu S J 2012 Acta Phys. Sin. 61 124301 (in Chinese) [沈壮志, 吴胜举 2012 物理学报 61 124301]

    [4]

    Shalnev K K, Shalobasov I A 1970 Trans. IAHR Symposium Paper H1

    [5]

    Shalobasov I A, Shalnev K K 1971 Heat Transfer-Soviet Research 3 141

    [6]

    Hammitt F G 1974 Report No. UMICH 01357-30-I

    [7]

    Young J B, Schmiedel T, Kang W 1996 Phys. Rev. Lett. 77 4816

    [8]

    Yasui K 1999 Phys. Rev. E 60 1759

    [9]

    Ding C F, Xing D 2004 Sci. China: Phys. Mech. Astron. 34 257 (in Chinese) [丁春峰, 邢达 2004 中国科学: 物理学 力学 天文学 34 257]

    [10]

    Li C H, An Y 2009 Sci. China: Phys. Mech. Astron. 52 593

    [11]

    Leighton T G 1994 The Acoustic Bubble (London: Academic Press) p85

    [12]

    Kondic L, Yuan C, Chan C K 1998 Phys. Rev. E 57 R32

    [13]

    Liu H J, An Y 2004 Acta Phys. Sin. 53 1406 (in Chinese) [刘海军, 安宇 2004 物理学报 53 1406]

    [14]

    Liu H J, An Y 2003 Acta Phys. Sin. 52 620 (in Chinese) [刘海军, 安宇 2003 物理学报 52 620]

    [15]

    Chen W Z, Huang W, Liu Y N, Gao X X 2006 Sci China: Phys. Mech. Astron. 36 113 (in Chinese) [陈伟中, 黄威, 刘亚楠, 高贤娴 2006 中国科学: 物理学 力学 天文学 36 113]

    [16]

    Chen W Z, Wei R J, Wang B R 1996 Acta Phys. Sin. (Oversea Ed.) 5 620

    [17]

    Toegel R, Lohse D 2003 J. Chem. Phys. 118 1863

    [18]

    Matula T J, Crum L A 1998 Phys. Rev. Lett. 80 865

  • [1]

    Oh J M, Kim P J, Kang I S 2001 Phys. Fluids 13 2820

    [2]

    Dong W, Li R Y, Yu H L, Huang X 2004 J. Eng. Thermophys. 25 439 (in Chinese) [董伟, 李瑞阳, 郁鸿凌, 黄煊 2004 工程热物理学报 25 439]

    [3]

    Shen Z Z, Wu S J 2012 Acta Phys. Sin. 61 124301 (in Chinese) [沈壮志, 吴胜举 2012 物理学报 61 124301]

    [4]

    Shalnev K K, Shalobasov I A 1970 Trans. IAHR Symposium Paper H1

    [5]

    Shalobasov I A, Shalnev K K 1971 Heat Transfer-Soviet Research 3 141

    [6]

    Hammitt F G 1974 Report No. UMICH 01357-30-I

    [7]

    Young J B, Schmiedel T, Kang W 1996 Phys. Rev. Lett. 77 4816

    [8]

    Yasui K 1999 Phys. Rev. E 60 1759

    [9]

    Ding C F, Xing D 2004 Sci. China: Phys. Mech. Astron. 34 257 (in Chinese) [丁春峰, 邢达 2004 中国科学: 物理学 力学 天文学 34 257]

    [10]

    Li C H, An Y 2009 Sci. China: Phys. Mech. Astron. 52 593

    [11]

    Leighton T G 1994 The Acoustic Bubble (London: Academic Press) p85

    [12]

    Kondic L, Yuan C, Chan C K 1998 Phys. Rev. E 57 R32

    [13]

    Liu H J, An Y 2004 Acta Phys. Sin. 53 1406 (in Chinese) [刘海军, 安宇 2004 物理学报 53 1406]

    [14]

    Liu H J, An Y 2003 Acta Phys. Sin. 52 620 (in Chinese) [刘海军, 安宇 2003 物理学报 52 620]

    [15]

    Chen W Z, Huang W, Liu Y N, Gao X X 2006 Sci China: Phys. Mech. Astron. 36 113 (in Chinese) [陈伟中, 黄威, 刘亚楠, 高贤娴 2006 中国科学: 物理学 力学 天文学 36 113]

    [16]

    Chen W Z, Wei R J, Wang B R 1996 Acta Phys. Sin. (Oversea Ed.) 5 620

    [17]

    Toegel R, Lohse D 2003 J. Chem. Phys. 118 1863

    [18]

    Matula T J, Crum L A 1998 Phys. Rev. Lett. 80 865

计量
  • 文章访问数:  2675
  • PDF下载量:  3975
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-10-22
  • 修回日期:  2014-12-17
  • 刊出日期:  2015-06-05

匀强磁场对水中气泡运动的影响

  • 1. 陕西师范大学物理学与信息技术学院, 陕西省超声学重点实验室, 西安 710119
    基金项目: 

    国家自然科学基金(批准号:11274216)资助的课题.

摘要: 基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.

English Abstract

参考文献 (18)

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