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为探究外层弹性介质对液体腔内气泡和粒子相互作用的影响, 从速度势分布理论出发, 结合拉格朗日方程得到了腔内气泡和粒子的运动方程, 分析了气泡的共振频率及声波作用下粒子和气泡间的相互作用对其平动行为的影响. 结果表明, 介质弹性和密度等特性均可改变腔内气泡的共振频率, 表现为气泡的共振频率随着球腔的半径增大有先减小后增大的变化趋势, 且逐渐趋于无界液体中单泡的共振频率. 气泡和粒子在球形液体腔中的平动受到声场参数、外层弹性介质特性、气泡和粒子本身特征等因素的影响, 总体特征表现为粒子有向腔壁运动的趋势, 气泡的平动与气泡和粒子间相互作用特征密切相关.A theory is developed to model the dynamic of bubble and particle inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim of this work is to study how the outer elastic medium affects the interaction between bubble and particle. Starting from the theory of velocity potential distribution, combined with Lagrangian equations, the motion equations of bubbles and particles in the cavity are obtained. The resonance frequency of the bubbles and influence of the interaction between particle and bubble on the translational behavior under the action of sound waves are analyzed. The results show that the properties of medium elasticity and density can change the resonance frequency of the bubble in the cavity. As the radius of the spherical cavity increases, the resonance frequency of the bubble has a tendency to first decrease and then increase, and gradually tends to the resonance frequency of a single bubble in an unbounded liquid. The translation of bubble and particle in the spherical liquid cavity is affected by factors such as acoustic field parameters, the characteristics of the outer elastic medium, and the characteristics of the bubble and particle themselves. The overall characteristic is that the particle has a tendency to move to the cavity wall, and the translation of bubble is closely related to the interaction characteristics between bubble and particle.
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Keywords:
- bubble /
- particle /
- radial vibration and translation /
- spherical liquid cavity
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图 2 相对频率随空腔半径与气泡半径比值的变化
Fig. 2. The relative frequency changes with the ratio of cavity radius to bubble radius.
图 3 气泡初始半径对气泡和粒子的平动的影响
Fig. 3. The effect of initial radius of bubble on the translation of bubble and particle.
图 4 驱动声波频率对气泡和粒子的平动的影响
Fig. 4. The influence of driving sound frequency on the translation of bubble and particle.
图 5 驱动声压幅值对气泡和粒子的平动的影响
Fig. 5. The influence of sound pressure amplitude on the translation of bubble and particle.
图 6 腔体大小对气泡和粒子平动的影响
Fig. 6. The influence of cavity size on the translation of bubble and particle.
图 7 粒子密度对气泡和粒子平动的影响
Fig. 7. The influence of particle density on the translation of bubble and particle.
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[1] Roedder E, Bodnar R J 1980 Annu. Rev. Earth Planet Sci. 8 263
Google Scholar
[2] Stroock A D, Pagay VV, Zwieniecki M A, Michele H N 2013 Annu. Rev. Fluid Mech. 46 615
[3] Jensen K H, Berg-Sorensen K, Bruus H, Holbrook N M, Liesche J, Schulz A, Zwieniecki M A, Bohr T 2016 Rev. Mod. Phys. 88 035007
Google Scholar
[4] Minnaert M S D 1933 Philos. Maga. 16 235
Google Scholar
[5] Prosperetti A 1987 Phys. Fluids 30 3626
Google Scholar
[6] Blake J R, Gibson D C 1987 Ann. Rev. Fluid Mech. 19 99
Google Scholar
[7] Strasberg M 1953 J. Acoust. Soc. Am. 25 536
Google Scholar
[8] Geld C W M V D, Kuerten J G M 2009 J. Fluid Mech. 640 265
Google Scholar
[9] Ouz H N, Prosperetti A 1998 J. Acoust. Soc. Am. 103 3301
Google Scholar
[10] Martynov S, Eleanor S, Nader S 2009 J. Acoust. Soc. Am. 126 2963
Google Scholar
[11] Wang Q X 2017 Phys. Fluids 29 072101
Google Scholar
[12] Doinikov A A, Benjamin D, Philippe M 2018 Phy. Rev. E 97 013108
Google Scholar
[13] Vincent O, Marmottant P, Gonzalez-Avila S R, Ando K, Ohl C D 2014 Soft Matter 10 1455
Google Scholar
[14] Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628
Google Scholar
[15] Doinikov A A 2001 Phy. Rev. E 64 026301
Google Scholar
[16] Ilinskii Y A, Hamilton M F, Zabolotskaya E A 2007 J. Acoust. Soc. Am. 121 786
Google Scholar
[17] 王成会, 林书玉 2011 声学学报 3 325
Wang C H, Lin S Y 2011 Acta Acust. 3 325
[18] Hay T A, Hamilton M F, Ilinskii Y A, Zabolotskaya E A 2009 J. Acoust. Soc. Am. 125 1331
Google Scholar
[19] Li S, Han R, Zhang A M 2016 J. Fluids Struct. 65 333
Google Scholar
[20] Doinikov A A, Diane B S, Roberto G A, Ohl C D, Philippe M 2019 Physical Review E 99 053106
Google Scholar
[21] Wu Y R, Wang C H 2017 Chin. Phys. B 26 114303
Google Scholar
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