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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.
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关键词:
- 零阶Bessel驻波 /
- 声辐射力 /
- 声辐射力矩 /
- Born近似
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:
- zero-order standing Bessel beam /
- acoustic radiation force /
- acoustic radiation torque /
- Born approximation
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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, 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 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)${\rm {Im}} ({{f_2}})$ 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
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Google Scholar
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Google Scholar
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Google Scholar
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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
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Google Scholar
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Google Scholar
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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
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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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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[32] Nikolaeva A V, Kryzhanovsky M A, Tsysar S A, Kreider, W, Sapozhnikov O A 2015 AIP Conference Proceedings 1685 040009
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[37] Glynne-Jones P, Mishra P P, Boltryk R J, Hill M 2013 J. Acoust. Soc. Am. 133 1885
Google Scholar
[38] Wei W, Thiessen D B, Marston P L 2004 J. Acoust. Soc. Am. 116 201
Google Scholar
[39] Hasheminejad S M, Sanaei R 2007 J. Comput. Acoust. 15 377
Google Scholar
[40] Marston P L, Wei W, Thiessen D B 2006 AIP Conf. Proc. 838 495
Google Scholar
[41] Mitri F G 2016 Ultrasonics 66 27
Google Scholar
[42] Mitri F G 2015 J. Appl. Phys. 118 214903
Google Scholar
[43] Mitri F G 2015 Wave Motion 57 231
Google Scholar
[44] Mitri F G 2015 EPL 112 34002
Google Scholar
[45] Mitri F G 2017 Ultrasonics 74 62
Google Scholar
[46] Silva G T, Drinkwater B W 2018 J. Acoust. Soc. Am. 144 EL453
Google Scholar
[47] Jerome T S, Ilinskii Yu A, Zabolotskaya E A, Hamilton M F 2020 J. Acoust. Soc. Am. 148 2403
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[51] Mitri F G 2008 Ann. Phys. 323 1604
Google Scholar
[52] Mitri F G 2009 Ultrasonics 49 794
Google Scholar
[53] Mitri F G 2009 IEEE UFFC 56 1059
Google Scholar
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Google Scholar
[55] Mitri F G 2009 Eur. Phys. J. E 28 469
Google Scholar
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Google Scholar
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Google Scholar
[58] Zhang L K, Marston P L 2011 J. Acoust. Soc. Am. 129 2381
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Google Scholar
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Google Scholar
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Google Scholar
[62] Jerome T S, Hamilton M F 2020 Proc. Meet. Acoust. 39 045007
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Google Scholar
[64] Ilinskii Yu A, Zabolotskaya E A, Hamilton M F 2012 AIP Conf. Proc. 1474 255
[65] Sapozhnikov O A, Bailey M R 2013 J. Acoust. Soc. Am. 133 661
Google Scholar
[66] Ilinskii Yu A, Zabolotskaya E A, Treweek B C, Hamilton M F 2018 J. Acoust. Soc. Am. 144 568
Google Scholar
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Google Scholar
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Google Scholar
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