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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.
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Keywords:
- zero-order standing Bessel beam /
- acoustic radiation force /
- acoustic radiation torque /
- Born approximation
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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
[6] Baudoin M, Thomas J L 2020 Annu. Rev. Fluid Mech. 52 205
Google Scholar
[7] Lierke E G 1996 Acustica 82 220
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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
[11] Yosioka K, Kawasima Y 1955 Acta Acust. United Ac. 5 167
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Google Scholar
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Google Scholar
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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
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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
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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
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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
[52] Mitri F G 2009 Ultrasonics 49 794
Google Scholar
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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
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[64] Ilinskii Yu A, Zabolotskaya E A, Hamilton M F 2012 AIP Conf. Proc. 1474 255
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Google Scholar
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Google Scholar
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Google Scholar
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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
Figure 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
Figure 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)
Figure 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)
Figure 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)
Figure 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)
Figure 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)
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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)
Figure 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)
Figure 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) $ Figure 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
Figure 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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[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
[29] Mitri F G 2021 Chin. Phys. B 30 024302
Google Scholar
[30] Mitri F G 2006 New J. Phys. 8 138
Google Scholar
[31] Aglyamov S R, Karpiouk A B, Ilinskii Y A, Zabolotskaya E A, Emelianov S Y 2007 J. Acoust. Soc. Am. 122 1927
Google Scholar
[32] Nikolaeva A V, Kryzhanovsky M A, Tsysar S A, Kreider, W, Sapozhnikov O A 2015 AIP Conference Proceedings 1685 040009
[33] Garbin A, Leibacher I, Hahn P, Le Ferrand H, Studart A R, Dual J 2015 J. Acoust. Soc. Am. 138 2759
Google Scholar
[34] Johnson K A, Vormohr H R, Doinikov A A, Bouakaz A, Shields C W, Lopez G P, Dayton P A 2016 Phys Rev. E 93 053109
Google Scholar
[35] Qiao Y P, Gong M Y, Wang H B, Lan J, Liu T, Liu J H, Mao Y W, He A J, Liu X Z 2021 Phys. Fluids 33 047107
Google Scholar
[36] Wijaya F B, Lim K M 2015 Acta Acust. 101 531
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
[48] Jerome T S, Ilinskii Yu A, Zabolotskaya E A, Hamilton M F 2021 J. Acoust. Soc. Am. 149 2081
Google Scholar
[49] Marston P L 2006 J. Acoust. Soc. Am. 120 3518
Google Scholar
[50] Marston P L 2009 J. Acoust. Soc. Am. 125 3539
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
[54] Mitri F G 2009 J. Phys. A, Math. Theor. 42 245202
Google Scholar
[55] Mitri F G 2009 Eur. Phys. J. E 28 469
Google Scholar
[56] Zhang L K, Marston P L 2011 J. Acoust. Soc. Am. 129 1679
Google Scholar
[57] Zhang L K, Marston P L 2011 Phys. Rev. E 84 065601
Google Scholar
[58] Zhang L K, Marston P L 2011 J. Acoust. Soc. Am. 129 2381
[59] Zhang L K 2018 Phys. Rev. Appl. 10 034039
Google Scholar
[60] Gong Z X, Marston P L 2019 Phys. Rev. Appl. 11 064022
Google Scholar
[61] Jerome T S, Ilinskii Yu A, Zabolotskaya E A, Hamilton M F 2019 J. Acoust. Soc. Am. 145 36
Google Scholar
[62] Jerome T S, Hamilton M F 2020 Proc. Meet. Acoust. 39 045007
[63] Jerome T S, Hamilton M F 2021 J. Acoust. Soc. Am. 150 3417
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
[67] Durnin J 1987 J. Opt. Soc. Am. A 4 651
Google Scholar
[68] Rayleigh L 1884 Philos. Trans. R. Soc. London 175 1
[69] Landau L D, Lifshitz E M 1993 Fluid Mechanics (2nd Ed.) (Vol. 6) Course of Theoretical Physics (Oxford: Pergamon)
[70] Settnes M, Bruus H 2012 Phys. Rev. E 85 016327
Google Scholar
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