零阶Bessel驻波场中任意粒子声辐射力和力矩的Born近似

臧雨宸; 苏畅; 吴鹏飞; 林伟军

doi:10.7498/aps.71.20212251

摘要

声辐射力和声辐射力矩的计算是实现粒子精准操控的重要基础. 基于经典声散射理论的偏波级数展开法较难直接用于复杂模型的研究, 而纯数值的方法则不利于进行系统的参数化分析. 基于Born近似的基本原理, 推导了低频情况下零阶Bessel驻波场中心任意粒子的声辐射力和力矩表达式. 在此基础上, 以球形粒子、椭球形粒子和柱形粒子为例进行详细地计算, 并考虑声参数的非均匀性对声辐射力和力矩的影响. 仿真结果表明, 在低频范围内Born近似具有很高的精度, 随着频率的增加和粒子与流体的阻抗匹配变差, Born近似的精度逐渐下降. 对于倾斜放置于零阶Bessel驻波场中的椭球形粒子和柱形粒子, 非对称性会导致其受到声辐射力矩的作用. 在粒子尺寸远小于波长的情况下, 声辐射力特性与粒子的具体形状几乎无关, 但声辐射力矩不然. 最后, 引入周围流体的黏滞效应并对声辐射力的表达式进行了修正. 该研究预期可以为生物医学、材料科学等领域利用驻波场声镊子实现微小粒子的精准操控提供一定的理论指导.

关键词:

Abstract

The calculation of acoustic radiation force and acoustic radiation torque is an important basis for the precise manipulation of particles. It is difficult to directly apply the partial-wave series expansion method based on the classical acoustic scattering theory to the study of complicated models, while pure numerical methods are not conducive to the parametric analyses of the system. Based on the basic principle of Born approximation, the expressions of acoustic radiation force and torque acting on an arbitrary particle located in the center of a zero-order Bessel standing wave field are derived at low frequencies. On this basis, the numerical simulations are systematically performed by taking spherical, spheroidal and cylindrical particles as examples. The effects of inhomogeneity on the acoustic radiation force and torque are also investigated. The simulation results show that the Born approximation method has a high accuracy in the low frequency range. As the frequency increases and the impedance matching between the particle and the fluid becomes worse, the accuracy of Born approximation will gradually decrease. An acoustic radiation torque caused by asymmetry will be exerted on spheroidal and cylindrical particles obliquely positioned in a zero-order Bessel standing wave field. When the particle size is much smaller than the wavelength, the acoustic radiation force is nearly independent of the particle shape, but this is not the case for acoustic radiation torque. Finally, viscous effect of the surrounding fluid is introduced and the expression of acoustic radiation force is corrected accordingly. The study is expected to provide a theoretical guide for the precise manipulation of small particles using standing wave acoustic tweezers in biomedicine and material sciences.

Keywords:

作者及机构信息

1.
中国科学院声学研究所, 北京　100190

2.
中国科学院大学, 北京　100049

3.
北京市海洋深部钻探测量工程技术研究中心, 北京　100190

通信作者: 苏畅, suchang@mail.ioa.ac.cn

基金项目: 国家自然科学基金 (批准号: 81527901)、国家重点研发计划 (批准号: 2018YFC0114900)、中国科学院声学研究所自主部署“目标导向”类项目(批准号: MBDX202113)和中国科学院青年创新促进会项目(批准号: 2019024)资助的课题

Authors and contacts

1.
Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

2.
University of Chinese Academy of Sciences, Beijing 100049, China

3.
Beijing Deep See Drilling Measurement Engineering Technology Research Center, Beijing 100190, China

Corresponding author: Su Chang, suchang@mail.ioa.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 81527901), the National Key R&D Program of China (Grant No. 2018YFC0114900), the Goal-oriented Project Deployed by Institute of Acoustics, Chinese Academy of Sciences, China (Grant No. MBDX202113) and the Youth Innovation Promotion Association, Chinese Academy of Sciences, China (Grant No. 2019024).

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参考文献

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施引文献

图 1 倾斜放置于零阶Bessel驻波场中心的任意轴对称粒子

Fig. 1. An arbitrary object with axisymmetric geometry obliquely positioned in a zero-order standing Bessel beam.

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图 2 零阶Bessel驻波场中心均匀球形粒子受到的归一化声辐射力随kR的变化(β = π/6, k_zh = π /4, ρ_m/ρ₀ = 1)　(a) c_m/c₀ = 1.01; (b) c_m/c₀ = 1.05; (c) c_m/c₀ = 1.1

Fig. 2. The dimensionless acoustic radiation force plots for a homogeneous sphere versus kR in a zero-order standing Bessel beam (β = π/6, k_zh = π/4, ρ_m/ρ₀ = 1): (a) c_m/c₀ = 1.01; (b) c_m/c₀ = 1.05; (c) c_m/c₀ = 1.1.

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图 3 零阶Bessel驻波场中心均匀球形粒子受到的归一化声辐射力随β的变化(kR = 0.5, k_zh = π/4, ρ_m/ρ₀ = 1)

Fig. 3. The dimensionless acoustic radiation force plots for a homogeneous sphere versus β in a zero-order standing Bessel beam (kR = 0.5, k_zh = π/4, ρ_m/ρ₀ = 1).

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图 4 零阶Bessel驻波场中心非均匀球形粒子受到的归一化声辐射力随kR的变化(f_A = f_C = 0, β = π/6, k_zh = π/4)

Fig. 4. The dimensionless acoustic radiation force plots for an inhomogeneous sphere versus kR in a zero-order standing Bessel beam (f_A = f_C = 0, β = π/6, k_zh = π/4).

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图 5 零阶Bessel驻波场中心非均匀球形粒子受到的归一化声辐射力随β的变化(f_A = f_C = 0, kR = 0.5, k_zh = π/4)

Fig. 5. The dimensionless acoustic radiation force plots for an inhomogeneous sphere versus β in a zero-order standing Bessel beam (f_A = f_C = 0, kR = 0.5, k_zh = π/4).

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图 6 零阶Bessel驻波场中心均匀椭球形粒子受到的归一化声辐射力和力矩随kb的变化(β = π/6, θ_s = π/6, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05)　(a)归一化声辐射力(k_zh = π/4); (b)归一化声辐射力矩(k_zh = 0)

Fig. 6. The dimensionless acoustic radiation force and torque plots for a homogeneous spheroid versus kb in a zero-order standing Bessel beam (β = π/6, θ_s = π/6, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05): (a) Dimensionless acoustic radiation force (k_zh = π/4); (b) dimensionless acoustic radiation torque (k_zh = 0).

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图 7 零阶Bessel驻波场中心均匀椭球形粒子受到的归一化声辐射力和力矩随θ_s的变化(kb = 0.5, β = π/6, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05)　(a)归一化声辐射力(k_zh = π/4); (b)归一化声辐射力矩(k_zh = 0)

Fig. 7. The dimensionless acoustic radiation force and torque plots for a homogeneous spheroid versus θ_s in a zero-order standing Bessel beam (kb = 0.5, β = π/6, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05): (a) Dimensionless acoustic radiation force (k_zh = π/4); (b) dimensionless acoustic radiation torque (k_zh = 0).

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图 8 零阶Bessel驻波场中心非均匀椭球形粒子受到的归一化声辐射力随kb的变化(β = π/6, θ_s = π/6, k_zh = π/4):　(a) f_A = 0.137, f_B = 0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056

Fig. 8. The dimensionless acoustic radiation force plots for an inhomogeneous spheroid versus kb in a zero-order standing Bessel beam (β = π/6, θ_s = π/6, k_zh = π/4): (a) f_A = 0.137, f_B = 0.254, f_C=0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056

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图 9 零阶Bessel驻波场中心非均匀椭球形粒子受到的归一化声辐射力矩随kb的变化(β = π/6, θ_s = π/6, k_zh = 0)　(a) f_A = 0.137, f_B = 0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056

Fig. 9. The dimensionless acoustic radiation torque plots for an inhomogeneous spheroid versus kb in a zero-order standing Bessel beam (β = π/6, θ_s = π/6, k_zh = 0): (a) f_A = 0.137, f_B = 0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056.

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图 10 零阶Bessel驻波场中心非均匀椭球形粒子受到的归一化声辐射力随θ_s的变化(kb = 0.5, β = π/6, k_zh = π/4)　(a) f_A = 0.137, f_B = 0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056

Fig. 10. The dimensionless acoustic radiation force plots for an inhomogeneous spheroid versus θ_s in a zero-order standing Bessel beam (kb = 0.5, β = π/6, k_zh = π/4): (a) f_A = 0.137, f_B = 0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056.

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图 11 零阶Bessel驻波场中心非均匀椭球形粒子受到的归一化声辐射力矩随θ_s的变化(kb = 0.5, β = π/6, k_zh = 0)　(a) f_A = 0.137, f_B = 0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056

Fig. 11. The dimensionless acoustic radiation torque plots for an inhomogeneous spheroid versus θ_s in a zero-order standing Bessel beam (kb = 0.5, β = π/6, k_zh = 0): (a) f_A = 0.137, f_B=0.254, f_C = 0.026, f_D = 0.051; (b) f_A = –0.160, f_B = –0.349, f_C = –0.027, f_D = –0.056.

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图 12 零阶Bessel驻波场中心均匀柱形粒子受到的归一化声辐射力和力矩随kL的变化(β=π/6, θ_s = π/6, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05)　(a)归一化声辐射力(k_zh = π/4); (b)归一化声辐射力矩(k_zh = 0)

Fig. 12. The dimensionless acoustic radiation force and torque plots for a homogeneous cylinder versus kL in a zero-order standing Bessel beam (β = π/6, θ_s = π/6, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05): (a) Dimensionless acoustic radiation force (k_zh = π/4); (b) dimensionless acoustic radiation torque (k_zh = 0).

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图 13 零阶Bessel驻波场中心均匀柱形粒子受到的归一化声辐射力和力矩随θ_s的变化(β = π/6, kL = 0.5, ρ_m/ρ₀ = 1, c_m/c₀ = 1.05)　(a)归一化声辐射力(k_zh = π/4); (b)归一化声辐射力矩(k_zh = 0)

Fig. 13. The dimensionless acoustic radiation force and torque plots for a homogeneous cylinder versus θ_s in a zero-order standing Bessel beam (β = π/6, kL = 0.5, ρ_m/ρ₀=1, c_m/c₀=1.05): (a) Dimensionless acoustic radiation force (k_zh = π/4); (b) dimensionless acoustic radiation torque (k_zh = 0).

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图 14 均匀球形粒子的偶极散射系数f₂随$ \bar \delta $的变化　(a) ${\rm {Re}} ( {{f_2}})/{\rm {Re}} ( {{f_{20}}} )$; (b) $ {\rm {Im}} \left( {{f_2}} \right) $

Fig. 14. The dipole scattering coefficient f₂ plots for a homogeneous sphere versus $ \bar \delta $ (a) ${\rm {Re}} ( {{f_2}})/{\rm {Re}} ( {{f_{20}}} )$; (b) ${\rm {Im}} ({{f_2}})$

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图 15 零阶Bessel驻波场中心均匀球形粒子受到的归一化声辐射力随kR的变化(β = π/6, k_zh = π/4, ρ_m/ρ₀ = 1.2, c_m/c₀ = 1.1)　(a) 归一化声辐射力; (b) 黏性流体与理想流体中归一化声辐射力的差值

Fig. 15. The dimensionless acoustic radiation force plots for a homogeneous sphere versus kR in a zero-order standing Bessel beam (β = π/6, k_zh = π/4, ρ_m/ρ₀ = 1.1, c_m/c₀ = 1.1): (a) Dimensionless acoustic radiation force; (b) difference of dimensionless acoustic radiation force in a viscous fluid and in an ideal fluid

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map

[1]	Wu J R 1991 J. Acoust. Soc. Am. 89 2140 Google Scholar
[2]	Lee J W, Ha K L, Shung K K 2005 J. Acoust. Soc. Am. 117 3273 Google Scholar
[3]	Lee J W, Shung K K 2006 J. Acoust. Soc. Am. 120 1084 Google Scholar
[4]	黄先玉, 蔡飞燕, 李文成, 郑海荣, 何兆剑, 邓科, 赵鹤平 2017 66 044301 Google Scholar Huang X Y, Cai F Y, Li W C, Zheng H R, He Z J, Deng K, Zhao H P 2017 Acta Phys. Sin. 66 044301 Google Scholar
[5]	Ozcelik A, Rufo J, Guo F, Guo Y Y, Li P, Lata J, Huang T J 2018 Nat. Methods. 15 1021 Google Scholar
[6]	Baudoin M, Thomas J L 2020 Annu. Rev. Fluid Mech. 52 205 Google Scholar
[7]	Lierke E G 1996 Acustica 82 220
[8]	Yarin A L, Pfaffenlehner M, Tropea C 1998 J. Fluid Mech. 356 65 Google Scholar
[9]	King L V 1934 Proc. Roya. Soc. London, Ser. A 147 212 Google Scholar
[10]	Awatani J 1953 J. Acous. Soc. Jpn. 9 140
[11]	Yosioka K, Kawasima Y 1955 Acta Acust. United Ac. 5 167
[12]	Hasegawa T, Yosioka K 1969 J. Acoust. Soc. Am. 46 1139 Google Scholar
[13]	Hasegawa T, Watanabe Y 1978 J. Acoust. Soc. Am. 63 1733 Google Scholar
[14]	Hasegawa T 1979 J. Acoust. Soc. Am. 65 32 Google Scholar
[15]	Hasegawa T 1979 J. Acoust. Soc. Am. 65 41 Google Scholar
[16]	Hasegawa T, Saka K, Inoue N, Matsuzawa K 1988 J. Acoust. Soc. Am. 83 1770 Google Scholar
[17]	Silva G T, Lobo T P, Mitri F G 2012 EPL 97 54003 Google Scholar
[18]	Gong Z X, M. Baudoin 2020 J. Acoust. Soc. Am. 148 3131 Google Scholar
[19]	Hasegawa T, Hino Y, Annou A, Noda H, Kato M, Inoue N 1993 J. Acoust. Soc. Am. 93 154 Google Scholar
[20]	Mitri F G 2005 Ultrasonics 43 681 Google Scholar
[21]	Mitri F G 2006 Ultrasonics 44 244 Google Scholar
[22]	Wang Y Y, Yao J, Wu X W, Wu D J, Liu X J 2017 J. Appl. Phys. 122 094902 Google Scholar
[23]	Peng X J, He W, Xin F X, Genin G M, Lu T J 2020 Ultrasonics 108 106205 Google Scholar
[24]	Peng X J, He W, Xin F X, Genin G M, Lu T J 2020 J. Mech. Phys. Solids 145 104134 Google Scholar
[25]	Wu R R, Cheng K X, Liu X Z, Liu J H, Mao Y W, Gong X F, Li Y F 2014 J. Appl. Phys. 116 144903 Google Scholar
[26]	Wang H B, Liu X Z, Gao S, Cui J, Liu J H, He A J, Zhang G T 2018 Chin. Phys. B 27 034302 Google Scholar
[27]	Zang Y C, Lin W J 2020 Results Phys. 16 102847 Google Scholar
[28]	Mitri F G 2020 Chin. Phys. B 29 114302 Google Scholar
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零阶Bessel驻波场中任意粒子声辐射力和力矩的Born近似