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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

臧雨宸 苏畅 吴鹏飞 林伟军

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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

臧雨宸, 苏畅, 吴鹏飞, 林伟军

Born approximation of acoustic radiation force and torque for an arbitrary particle in a zero-order standing Bessel beam

Zang Yu-Chen, Su Chang, Wu Peng-Fei, Lin Wei-Jun
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  • 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.
    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.
      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
      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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  • 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.

    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, kzh = π /4, ρm/ρ0 = 1) (a) cm/c0 = 1.01; (b) cm/c0 = 1.05; (c) cm/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, kzh = π/4, ρm/ρ0 = 1): (a) cm/c0 = 1.01; (b) cm/c0 = 1.05; (c) cm/c0 = 1.1.

    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, kzh = π/4, ρm/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, kzh = π/4, ρm/ρ0 = 1).

    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(fA = fC = 0, β = π/6, kzh = π/4)

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

    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(fA = fC = 0, kR = 0.5, kzh = π/4)

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

    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, θs = π/6, ρm/ρ0 = 1, cm/c0 = 1.05) (a)归一化声辐射力(kzh = π/4); (b)归一化声辐射力矩(kzh = 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, θs = π/6, ρm/ρ0 = 1, cm/c0 = 1.05): (a) Dimensionless acoustic radiation force (kzh = π/4); (b) dimensionless acoustic radiation torque (kzh = 0).

    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θs的变化(kb = 0.5, β = π/6, ρm/ρ0 = 1, cm/c0 = 1.05) (a)归一化声辐射力(kzh = π/4); (b)归一化声辐射力矩(kzh = 0)

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

    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, θs = π/6, kzh = π/4): (a) fA = 0.137, fB = 0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –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, θs = π/6, kzh = π/4): (a) fA = 0.137, fB = 0.254, fC=0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –0.056

    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, θs = π/6, kzh = 0) (a) fA = 0.137, fB = 0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –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, θs = π/6, kzh = 0): (a) fA = 0.137, fB = 0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –0.056.

    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θs的变化(kb = 0.5, β = π/6, kzh = π/4) (a) fA = 0.137, fB = 0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –0.056

    Fig. 10.  The dimensionless acoustic radiation force plots for an inhomogeneous spheroid versus θs in a zero-order standing Bessel beam (kb = 0.5, β = π/6, kzh = π/4): (a) fA = 0.137, fB = 0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –0.056.

    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θs的变化(kb = 0.5, β = π/6, kzh = 0) (a) fA = 0.137, fB = 0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –0.056

    Fig. 11.  The dimensionless acoustic radiation torque plots for an inhomogeneous spheroid versus θs in a zero-order standing Bessel beam (kb = 0.5, β = π/6, kzh = 0): (a) fA = 0.137, fB=0.254, fC = 0.026, fD = 0.051; (b) fA = –0.160, fB = –0.349, fC = –0.027, fD = –0.056.

    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, θs = π/6, ρm/ρ0 = 1, cm/c0 = 1.05) (a)归一化声辐射力(kzh = π/4); (b)归一化声辐射力矩(kzh = 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, θs = π/6, ρm/ρ0 = 1, cm/c0 = 1.05): (a) Dimensionless acoustic radiation force (kzh = π/4); (b) dimensionless acoustic radiation torque (kzh = 0).

    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θs的变化(β = π/6, kL = 0.5, ρm/ρ0 = 1, cm/c0 = 1.05) (a)归一化声辐射力(kzh = π/4); (b)归一化声辐射力矩(kzh = 0)

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

    图 14  均匀球形粒子的偶极散射系数f2$ \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) ${\rm {Im}} ({{f_2}})$

    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, kzh = π/4, ρm/ρ0 = 1.2, cm/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, kzh = π/4, ρm/ρ0 = 1.1, cm/c0 = 1.1): (a) Dimensionless acoustic radiation force; (b) difference of dimensionless acoustic radiation force in a viscous fluid and in an ideal fluid

  • [1]

    Wu J R 1991 J. Acoust. Soc. Am. 89 2140Google Scholar

    [2]

    Lee J W, Ha K L, Shung K K 2005 J. Acoust. Soc. Am. 117 3273Google Scholar

    [3]

    Lee J W, Shung K K 2006 J. Acoust. Soc. Am. 120 1084Google Scholar

    [4]

    黄先玉, 蔡飞燕, 李文成, 郑海荣, 何兆剑, 邓科, 赵鹤平 2017 物理学报 66 044301Google 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 044301Google Scholar

    [5]

    Ozcelik A, Rufo J, Guo F, Guo Y Y, Li P, Lata J, Huang T J 2018 Nat. Methods. 15 1021Google Scholar

    [6]

    Baudoin M, Thomas J L 2020 Annu. Rev. Fluid Mech. 52 205Google Scholar

    [7]

    Lierke E G 1996 Acustica 82 220

    [8]

    Yarin A L, Pfaffenlehner M, Tropea C 1998 J. Fluid Mech. 356 65Google Scholar

    [9]

    King L V 1934 Proc. Roya. Soc. London, Ser. A 147 212Google 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 1139Google Scholar

    [13]

    Hasegawa T, Watanabe Y 1978 J. Acoust. Soc. Am. 63 1733Google Scholar

    [14]

    Hasegawa T 1979 J. Acoust. Soc. Am. 65 32Google Scholar

    [15]

    Hasegawa T 1979 J. Acoust. Soc. Am. 65 41Google Scholar

    [16]

    Hasegawa T, Saka K, Inoue N, Matsuzawa K 1988 J. Acoust. Soc. Am. 83 1770Google Scholar

    [17]

    Silva G T, Lobo T P, Mitri F G 2012 EPL 97 54003Google Scholar

    [18]

    Gong Z X, M. Baudoin 2020 J. Acoust. Soc. Am. 148 3131Google Scholar

    [19]

    Hasegawa T, Hino Y, Annou A, Noda H, Kato M, Inoue N 1993 J. Acoust. Soc. Am. 93 154Google Scholar

    [20]

    Mitri F G 2005 Ultrasonics 43 681Google Scholar

    [21]

    Mitri F G 2006 Ultrasonics 44 244Google Scholar

    [22]

    Wang Y Y, Yao J, Wu X W, Wu D J, Liu X J 2017 J. Appl. Phys. 122 094902Google Scholar

    [23]

    Peng X J, He W, Xin F X, Genin G M, Lu T J 2020 Ultrasonics 108 106205Google Scholar

    [24]

    Peng X J, He W, Xin F X, Genin G M, Lu T J 2020 J. Mech. Phys. Solids 145 104134Google 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 144903Google 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 034302Google Scholar

    [27]

    Zang Y C, Lin W J 2020 Results Phys. 16 102847Google Scholar

    [28]

    Mitri F G 2020 Chin. Phys. B 29 114302Google Scholar

    [29]

    Mitri F G 2021 Chin. Phys. B 30 024302Google Scholar

    [30]

    Mitri F G 2006 New J. Phys. 8 138Google Scholar

    [31]

    Aglyamov S R, Karpiouk A B, Ilinskii Y A, Zabolotskaya E A, Emelianov S Y 2007 J. Acoust. Soc. Am. 122 1927Google Scholar

    [32]

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出版历程
  • 收稿日期:  2021-12-06
  • 修回日期:  2022-02-09
  • 上网日期:  2022-02-16
  • 刊出日期:  2022-05-20

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