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基于磁流体管内单泡的动力学模型, 通过引入泡间次级声辐射并考虑磁流体黏度的磁场效应, 建立了管内“泡对”系统在磁声复合场中的动力学方程, 分析了磁场强度、泡对尺寸、泡间相互作用(包括次级Bjerknes力FB和磁吸引力Fm)及流体特性等对双泡振动特性的影响. 结果表明, 磁场增大了泡对的振幅, 对大泡的影响远大于对小泡的影响. 当两泡中心间距一定、两泡相对尺寸越大时, 或是当两泡尺寸一定、两泡表面间距越小时, 双泡之间的相互作用越强. 磁声复合场中, 磁场会影响FB, Fm, 磁压Pm及黏滞阻力等, 且影响程度各不相同; FB和Fm及Pm和黏滞阻力之间均存在竞争关系, 与作用在微泡上的所有力共同影响泡的运动. 通过研究“泡对”系统的动力学行为, 为实际应用中调节磁声场, 提高微泡对生物组织的靶向调控治疗效果提供了一定的理论依据.Based on the dynamic model of a single bubble in a magnetic fluid tube, the dynamic equation of a bubble pair system in a magneto-acoustic field is established by introducing the secondary sound radiation between bubbles and considering the magnetic field effect of the viscosity of the magnetic fluid. The effects of magnetic field intensity, bubble pair’s size, bubble interaction (including secondary Bjerknes force FB and magnetic attraction Fm) and fluid characteristics on the vibration characteristics of double bubbles are analyzed. The results show that magnetic field increases the amplitude of bubbles, and the influence of magnetic field on the large bubble is greater than on the small bubble. When the center distance between the two bubbles is constant and the relative size of two bubbles is larger, or when the size of the two bubbles is constant and the surface distance between two bubbles is small, the interaction between two bubbles is stronger. In the magneto-acoustic composite field, magnetic field can affect FB, Fm, magnetic pressure Pm and viscosity resistance, and the influence degrees are different. There is competition between FB and Fm and between Pm and viscosity resistance, and the forces acting on the microbubble jointly affect the movement of the bubbles. By studying the dynamic behavior of paired bubbles, it can provide a theoretical basis for improving the therapeutic effect of targeted regulation of microbubbles on biological tissues by adjusting the magneto-acoustic field in practical application.
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Keywords:
- bubble pair /
- magnetofluid /
- rigid tube /
- dynamic behavior
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图 2 泡1在不同约束条件下泡对的振动曲线 (a) 有无膜层; (b) 不同外场作用
Fig. 2. Comparison of vibration curves of bubble 1 under different constraints: (a) Layer constraint; (b) applied field constraint.
图 3 “泡对”的磁场响应(R10 = 5 μm, R20 = 3 μm, d = 20 μm) (a) 泡1; (b) 泡2
Fig. 3. Magnetic field response of fixed size bubble pairs (R10 = 5 μm, R20 = 3 μm, d = 20 μm): (a) Bubble 1; (b) bubble 2.
图 4 “泡对”的尺寸效应 (a) H = 150 kA·m–1; (b) H = 0
Fig. 4. Size effect of bubble pairs: (a) H = 150 kA·m–1; (b) H = 0.
图 5 在泡1的一个振荡周期内Fm和FB的变化规律
Fig. 5. The variation of Fm and FB during an oscillation period of bubble 1.
图 6 R1及dR1/dt对FB的影响(H = 150 kA·m–1, d = 20 μm).
Fig. 6. Influence of R1 and dR1/dt on FB (H = 150 kA·m–1, d = 20 μm).
图 7 FB-t关系 (a) H = 150 kA·m–1; (b) d = 20 μm
Fig. 7. FB-t relationship: (a) H = 150 kA·m–1; (b) d = 20 μm.
图 8 Fm-d和Fm-H变化规律 (a) H = 150 kA·m–1; (b) d = 20 μm
Fig. 8. Changes of Fm-d and Fm-H: (a) H = 150 kA·m–1; (b) d = 20 μm.
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[1] Plesset M S, Prosperetti A 1977 Annu. Rev. Fluid Mech. 9 145
Google Scholar
[2] Rooze J, Rebrov E V, Schouten J C, Keurentjes J T 2013 Ultrason. Sonochem. 20 1
Google Scholar
[3] Maruvada S 2019 J. Acoust. Soc. Am. 146 2870
Google Scholar
[4] Brennen C E 2015 Interface. Focus 5 20150022
Google Scholar
[5] Dimcevski G, Kotopoulis S, Bjnes T, Hoem D, Schjtt J 2016 J. Control. Release 243 172
Google Scholar
[6] Kooiman K, Vos H J, Versluis M, de Jong N 2014 Adv. Drug Deliv. Rev. 72 28
Google Scholar
[7] Lentacker I, de Cock I, Deckers R, de Smedt S C 2014 Adv. Drug. Deliv. Rev. 72 49
Google Scholar
[8] Sarkar K, Shi W T, Chatterjee D, Forsberg F 2005 J. Acoust. Soc. Am. 118 539
Google Scholar
[9] Rajabi M, Mojahed A 2018 Ultrasonics 83 146
Google Scholar
[10] Zhang J, Song L, Zhang H, Zhou S 2019 ACS Omega 4 4691
Google Scholar
[11] Mobadersany N, Sarkar K 2017 J. Acoust. Soc. Am. 141 3952
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[12] De S, Carugo D, Barnsley L C, Owen J, Coussios C C, Stride E 2017 Phys. Med. Biol. 62 7451
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[13] Beata C, Robert L 2018 Theranostics 8 341
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[14] Vlaskou D, Plank C, Mykhaylyk O 2013 Methods Mol. Biol. 948 205
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[15] Saurabh D, Constantin C, Azzdine Y A, Douglas M T 2008 Ultrasound Med. Biol. 34 1421
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[16] Teng Z G, Wang R H, Zhou Y, Kolios M 2017 Biomaterials 134 43
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[18] Holm C Weis J J 2005 Curr. Opin. Colloid Interface Sci. 10 133
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Shi H M, Hu J, Wang C H, Feng F L, Mo R Y 2021 Acta Phys. Sin. 70 214303
Google Scholar
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Google Scholar
Ma Y, Lin S Y, Xian X J 2016 Acta Phys. Sin. 65 014301
Google Scholar
[23] 王德鑫, 那仁满都拉 2018 物理学报 67 037802
Google Scholar
Wang D X, Na R M D L 2018 Acta Phys. Sin. 67 037802
Google Scholar
[24] 李想, 陈勇, 封皓, 綦磊 2020 物理学报 69 184703
Google Scholar
Li X, Chen Y, Feng H, Qi L 2020 Acta Phys. Sin. 69 184703
Google Scholar
[25] 蔡晨亮, 屠娟, 郭霞生, 章东 2019 声学技术 44 772
Google Scholar
Chen C L, Tu J, Guo X S, Zhang D 2019 Acta. Acustica 44 772
Google Scholar
[26] Mukundakrishnan K, Quan S, Eckmann D M, Ayyaswamy P S 2007 Phys. Rev. E 76 036308
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[27] Howison D 1986 Proc. Roy. Soc. Edinburgh, Sect. A: Math. 102 141
Google Scholar
[28] Corapcioglu M Y, Cihan A, Drazenovic M 2004 Water Resour. Res. 40 W04214
Google Scholar
[29] Guet S, Ooms G 2006 Annu. Rev. Fluid Mech. 38 225
Google Scholar
[30] Yang Z L, Dinh T N, Nourgaliev R R, Sehgal B R 2000 Int. J. Therm. Sci. 39 1
Google Scholar
[31] Kantarci N, Borak F, Ulgen K O 2005 Process Biochem. 40 2263
Google Scholar
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Google Scholar
[33] Senapati A, Singh G, Lakkaraju R 2019 Chem. Eng. Sci. 208 115159
Google Scholar
[34] 王成会, 程建春 2013 中国科学: 物理学 力学 天文学 43 230
Google Scholar
Wang C H, Cheng J C 2013 Scientia Sinica Physica, Mechanica & Astronomica 43 230
Google Scholar
[35] Liu B, Cai J, Tao Y, Huai Xi 2017 J. Therm. Sc. 26 66
Google Scholar
[36] Kang K H, Kang I S, Lee C M 2002 Phys. Fluids 14 29
Google Scholar
[37] Ishimoto J, Okubo M, Kamiyama S, Higashitani M 1995 JSME Int. J. 38 382
Google Scholar
[38] Wakayama N I, Qi J W, Yabe A 1999 Proc. SPIE-Int. Soc. Opt. Eng. 3792 48
Google Scholar
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[40] Mettin R, Akhatov I, Parlitz U, Ohl C D, Lauterborn W B 1997 Phys. Rev. E 56 2924
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Google Scholar
[42] Bekovic M, Hamler A 2010 IEEE T. Magn. 46 552
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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