Oscillation behavior of bubble pair in magnetic fluid tube under magneto-acoustic complex field

Shi Hui-Min; Mo Run-Yang; Wang Cheng-Hui

doi:10.7498/aps.71.20212150

Abstract

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 F_B and magnetic attraction F_m) 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 F_B, F_m, magnetic pressure P_m and viscosity resistance, and the influence degrees are different. There is competition between F_B and F_m and between P_m 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.

Keywords:

Authors and contacts

Shaanxi Key Laboratory of Ultrasonics, Shaanxi Normal University, Xi’an 710119, China

Corresponding author: Mo Run-Yang, mmrryycn@snnu.edu.cn ; Wang Cheng-Hui, wangld001@snnu.edu.cn

Funds: Project supported by the National Science Foundation of China (Grant Nos. 12074238, 11974232, 11774212)

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References

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Cited By

图 1 柱形管内泡对几何模型

Figure 1. Geometric model of paired bubbles in cylindrical tube.

DownLoad: Full-Size Img PowerPoint

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

Figure 2. Comparison of vibration curves of bubble 1 under different constraints: (a) Layer constraint; (b) applied field constraint.

DownLoad: Full-Size Img PowerPoint

图 3 “泡对”的磁场响应(R₁₀ = 5 μm, R₂₀ = 3 μm, d = 20 μm)　(a) 泡1; (b) 泡2

Figure 3. Magnetic field response of fixed size bubble pairs (R₁₀ = 5 μm, R₂₀ = 3 μm, d = 20 μm): (a) Bubble 1; (b) bubble 2.

DownLoad: Full-Size Img PowerPoint

图 4 “泡对”的尺寸效应　(a) H = 150 kA·m^–1; (b) H = 0

Figure 4. Size effect of bubble pairs: (a) H = 150 kA·m^–1; (b) H = 0.

DownLoad: Full-Size Img PowerPoint

图 5 在泡1的一个振荡周期内F_m和F_B的变化规律

Figure 5. The variation of F_m and F_B during an oscillation period of bubble 1.

DownLoad: Full-Size Img PowerPoint

图 6 R₁及dR₁/dt对F_B的影响(H = 150 kA·m^–1, d = 20 μm).

Figure 6. Influence of R₁ and dR₁/dt on F_B (H = 150 kA·m^–1, d = 20 μm).

DownLoad: Full-Size Img PowerPoint

图 7 F_B-t关系　(a) H = 150 kA·m^–1; (b) d = 20 μm

Figure 7. F_B-t relationship: (a) H = 150 kA·m^–1; (b) d = 20 μm.

DownLoad: Full-Size Img PowerPoint

图 8 F_m-d和F_m-H变化规律　(a) H = 150 kA·m^–1; (b) d = 20 μm

Figure 8. Changes of F_m-d and F_m-H: (a) H = 150 kA·m^–1; (b) d = 20 μm.

DownLoad: Full-Size Img PowerPoint

图 9 磁场对磁流体黏度增量Δη及磁压P_m的影响

Figure 9. Effect of magnetic field on viscosity increment Δη and magnetic pressure P_m of magnetic fluid.

DownLoad: Full-Size Img PowerPoint

[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 Google Scholar
[12]	De S, Carugo D, Barnsley L C, Owen J, Coussios C C, Stride E 2017 Phys. Med. Biol. 62 7451 Google Scholar
[13]	Beata C, Robert L 2018 Theranostics 8 341 Google Scholar
[14]	Vlaskou D, Plank C, Mykhaylyk O 2013 Methods Mol. Biol. 948 205 Google Scholar
[15]	Saurabh D, Constantin C, Azzdine Y A, Douglas M T 2008 Ultrasound Med. Biol. 34 1421 Google Scholar
[16]	Teng Z G, Wang R H, Zhou Y, Kolios M 2017 Biomaterials 134 43 Google Scholar
[17]	Steven J L 2014 Phys. Fluids 26 061901 Google Scholar
[18]	Holm C Weis J J 2005 Curr. Opin. Colloid Interface Sci. 10 133 Google Scholar
[19]	Malvar S, Gontijo R G, Cunha F R 2018 J. Eng. Math. 108 143 Google Scholar
[20]	Chen J, Zhao L, Wang C, Mo R 2021 J. Magn. Magn. Mater. 538 168293 Google Scholar
[21]	史慧敏, 胡静, 王成会, 凤飞龙, 莫润阳 2021 物理学报 70 214303 Google Scholar Shi H M, Hu J, Wang C H, Feng F L, Mo R Y 2021 Acta Phys. Sin. 70 214303 Google Scholar
[22]	马艳, 林书玉, 鲜晓军 2016 物理学报 65 014301 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 Google Scholar
[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
[32]	Gui Y, Shan C, Zhao J, Wu J 2020 AIP Advances 10 105210 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
[39]	Doinikov A A, Bouakaz A 2014 J. Fluid Mech. 742 425 Google Scholar
[40]	Mettin R, Akhatov I, Parlitz U, Ohl C D, Lauterborn W B 1997 Phys. Rev. E 56 2924 Google Scholar
[41]	Rigoni C, Fresnais J, Talbot D, Massart R, Perzynski R, Bacri J C, Abou-Hassan A 2020 Langmuir 36 5048 Google Scholar
[42]	Bekovic M, Hamler A 2010 IEEE T. Magn. 46 552 Google Scholar
[43]	Sharman S, Singh U, Katiyar V K 2015 J. Magn. Magn. Mater. 377 395 Google Scholar
[44]	STRIDE E 2008 Phil. Trans. R. Soc. A 366 2103 Google Scholar
[45]	Cunha F R, Sousa A J, Morais P C 2002 J. Magn. Magn. Mater. 252 271 Google Scholar
[46]	Hilgenfeldt S, Grossmann S, Lohse D 1999 Phys. Fluids 11 1318 Google Scholar
[47]	Lee W K, Scardovelli R, Trubatch A D, Yecko P 2010 Phys. Rev. E 82 016302 Google Scholar

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