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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.
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Keywords:
- uniform magnetic field /
- water medium /
- single bubble /
- ambient pressure
[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
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[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
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