有界黏性流体中自由球形粒子的声辐射力

刘腾; 乔玉配; 宫门阳; 刘晓宙

doi:10.7498/aps.74.20241354

摘要

声辐射力的研究是提高粒子操控技术的精确性和有效性的重要基础. 基于声波动理论, 建立了有界黏性流体中自由球形粒子的声辐射力计算模型, 结合球函数的加性定理, 推导了平面波垂直入射情况下相应的声辐射力解析表达式. 理论计算中考虑了小球为自由状态, 将粒子的动力学方程作为计算声辐射力的修正项. 在考虑流体黏度、粒子材料、粒子位置以及边界等因素对声辐射力影响的基础上进行数值计算. 结果表明, 随着流体黏度的增大, 声辐射力曲线的共振峰被拓宽; 相比于液体材料的小球, 弹性材料小球的声辐射力的振荡现象更明显; 随着阻抗边界反射系数的增大, 声辐射力振幅增大; 小球位置的不同主要影响其声辐射力的振荡现象. 该研究为有界黏性流体中自由粒子的声操控提供了理论基础, 并有助于生物医学等领域更好地利用声辐射力操控粒子.

关键词:

Abstract

The manipulation of particles by acoustic radiation force (ARF) has the advantages of non-invasiveness, high biocompatibility, and wide applicability. The study of acoustic radiation force is an important foundation for improving the accuracy and effectiveness of particle manipulation technology. Based on the acoustic wave theory, a theoretical model for the ARF of a free spherical particle in a bounded viscous fluid is established. The ARF for the case of a normal incident plane wave is derived by applying the translation addition theorem to spherical function. The dynamic equation of a free sphere is required as a correction term for calculating the ARF. The effects of the fluid viscosity, particle material, particle distance from boundary, and the boundary on the ARF are analyzed by numerical simulation. The results show that the resonance peak of the ARF curve is broadened with the increase of the viscosity of the fluid. Compared with the values of the ARFs of a PE sphere in a viscous and an ideal fluid, the fluid viscosity has a small influence and the viscosity effect can be ignored when kR is much less than 1. However, for the cases where kR is greater than or equal to 1, the amplitude of the ARF experienced by a particle in a viscous fluid is much greater than that in an ideal fluid. The influence of fluid viscosity on the ARF is significant and cannot be ignored. Moreover, compared with a liquid material sphere, the oscillation of ARF in an elastic material sphere is more pronounced. This is because the momentum transfer between sound waves and elastic materials is greater than that between sound waves and liquid materials. In addition, the amplitude of the ARF increases with the increase of the reflection coefficient of the impedance boundary, but its resonance frequency is not affected. Finally, the position of the sphere mainly affects the oscillation phenomenon of its ARF. The peaks and dips of the ARF become more densely packed with the growth of distance-to-radius. It is worth noting that the reflection coefficient mainly affects the amplitude of the ARF, while the position of the sphere affects the period of the ARF function. The results indicate that more efficient manipulation of particles can be achieved through appropriate parameter selection. This study provides a theoretical basis for acoustically manipulating a free particle in a bounded viscous fluid and contributes to the better utilization of ARF for particle manipulation in biomedical and other fields.

Keywords:

作者及机构信息

1.
南京大学声学研究所, 近代声学教育部重点实验室, 南京　210093

2.
贵州师范大学物理与电子科学学院, 贵阳　550025

3.
南京信息工程大学电子与信息工程学院, 南京　210044

通信作者: 乔玉配, yupeiqiao@gznu.edu.cn ; 刘晓宙, xzliu@nju.edu.cn

基金项目: 国家重点研发计划(批准号: 2020YFA0211400)、国家自然科学基金(批准号: 12174192, 12204119)、声场声信息国家重点实验室开放课题研究基金(批准号: SKLA202410)和贵州省科技计划(批准号: ZK[2023]249)资助的课题.

Authors and contacts

1.
Key Laboratory of Modern Acoustics, Institute of Acoustics and School of Physics, Nanjing University, Nanjing 210093, China

2.
School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550025, China

3.
School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

Corresponding author: QIAO Yupei, yupeiqiao@gznu.edu.cn ; LIU Xiaozhou, xzliu@nju.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2020YFA0211400), the National Natural Science Foundation of China (Grant Nos. 12174192, 12204119), the State Key Laboratory of Acoustics, Chinese Academy of Sciences (Grant No. SKLA202410), and the Science and Technology Foundation of Guizhou Province, China (Grant No. ZK[2023]249).

文章全文 : translate this paragraph

参考文献

[1]	Ozcelik A, Rufo J, Guo F, Gu Y Y, Li P, Lata J, Huang T J 2018 Nat. Methods 15 1021 Google Scholar
[2]	Meng L, Cai F Y, Li F, Zhou W, Niu L L, Zheng H R 2019 J. Phys. D Appl. Phys. 52 273001 Google Scholar
[3]	King L V 1934 Proc. R. Soc. London 147 861 Google Scholar
[4]	Hasegawa T, Yosioka K 1969 J. Acoust. Soc. Am. 46 5 Google Scholar
[5]	Marston P L 2006 J. Acoust. Soc. Am. 120 3518 Google Scholar
[6]	Gong Z X, Marston P L, Li W 2019 Phys. Rev. E 99 063004 Google Scholar
[7]	臧雨宸, 苏畅, 吴鹏飞, 林伟军 2022 物理学报 71 104302 Google Scholar Zang Y C, Su C, Wu P F, Lin W J 2022 Acta Phys. Sin. 71 104302 Google Scholar
[8]	Li S Y, Shi J Y, Zhang X F, Zhang G B 2019 J. Acoust. Soc. Am. 145 5 Google Scholar
[9]	Azarpeyvand M, Azarpeyvand M 2013 J. Sound Vib. 332 9 Google Scholar
[10]	Zang Y C, Lin W 2019 Results Phys. 16 102847 Google Scholar
[11]	Mitri F G 2009 Ultrasonics 49 794 Google Scholar
[12]	Marston P L 2009 J. Acoust. Soc. Am. 125 6 Google Scholar
[13]	Gong M Y, Shi M J, Li Y Y, Xu X, Fei Z H, Qiao Y P, Liu J H, He A J, Liu X Z 2023 Phys. Fluids 35 057108 Google Scholar
[14]	Gong M Y, Xu X, Qiao Y P, Liu J H, He A J, Liu X Z 2024 Chin. Phys. B 33 014302 Google Scholar
[15]	Gaunaurd G C, Huang H 1991 J. Acoust. Soc. Am. 96 2526 Google Scholar
[16]	Miri A K, Mitri F G 2011 Ultrasound Med. Biol. 37 2 Google Scholar
[17]	Westervelt P J 1951 J. Acoust. Soc. Am. 23 3 Google Scholar
[18]	Doinikov A A 1994 J. Fluid Mech. 267 1 Google Scholar
[19]	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
[20]	Kundu P K, Cohen I M 2002 Fluid Mechanics (San Diego: Academic Press) p78, p96
[21]	Huang H, Gaunaurd G C 1997 Int. J. Solids Struct. 34 591 Google Scholar
[22]	Hasheminejad S M 2001 Acta Acust. United Ac. 87 4
[23]	Embleton T F W 1954 J. Acoust. Soc. Am. 26 1 Google Scholar
[24]	Yosioka K, Kawasima Y 1955 Acta. Acust. United Ac. 5 3
[25]	Wang H B, Gao S, Qiao Y P, Liu J H, Liu X Z 2019 Phys. Fluids 31 047103 Google Scholar
[26]	Hartman B, Jarzynski J 1972 J. Appl. Phys. 43 11 Google Scholar

施引文献

图 1 平面波入射有界黏性流体中自由球形粒子的几何关系示意图

Fig. 1. Schematic diagram of a free spherical particle in a bounded viscous fluid with a plane wave incidence.

下载: 全尺寸图片幻灯片

图 2 自由PE小球在不同${\delta {/ } R}$的流体中声辐射力随kR的变化

Fig. 2. ARFs for a free PE sphere versus kR at different ${\delta {/ } R}$.

下载: 全尺寸图片幻灯片

图 3 低黏流体(水)中不同材料自由球形粒子的声辐射力随kR的变化

Fig. 3. ARFs for a free sphere with different materials versus kR in the low viscosity liquid (water).

下载: 全尺寸图片幻灯片

图 4 低黏流体(水)中自由PE小球在不同阻抗边界附近的声辐射力随kR的变化

Fig. 4. ARFs for a free PE sphere versus kR in the low viscosity liquid (water) with different ${R_{\text{s}}}$.

下载: 全尺寸图片幻灯片

图 5 低黏流体(水)中自由PE小球放置于距边界不同位置处的声辐射力随kR的变化

Fig. 5. ARFs for a free PE sphere in the low viscosity liquid (water) versus kR at different d.

下载: 全尺寸图片幻灯片

表 1 自由球形粒子构成材料的物理参量^[25,26]

Table 1. Physical parameters of free spherical particles^[25,26].

材料	密度 /(kg·m^–3)	纵波声速 /(m·s^–1)	横波声速 /(m·s^–1)
油酸	938	1450	—
聚乙烯(PE)	957	2430	950
聚甲基丙烯酸甲酯(PMMA)	1190	2690	1340

下载: 导出CSV

表 2 流体的声学参量^[18]

Table 2. Acoustic parameters of fluids^[18].

流体	密度/(kg·m^–3)	声速/(m·s^–1)	动力黏度μ′/(Pa·s)
水	1000	1500	0.001
甘油	1260	1900	1.48

下载: 导出CSV

表 3 黏性流体和理想流体中自由PE小球所受声辐射力对比

Table 3. Comparisons of the ARFs on a free PE sphere in a viscous and an ideal fluid.

流体类型		kR
流体类型		1.0×10^–4	1.0×10^–2	1.0×10^–1	1.0	5.0
黏性流体	δ/R=0.002	4.8×10^–12 N	5.2×10^–12 N	1.1×10^–10 N	–2.1×10^–7 N	5.6×10^–8 N
	δ/R=0.004	4.8×10^–12 N	5.2×10^–12 N	1.4×10^–9 N	–2.2×10^–7 N	–3.7×10^–6 N
	δ/R=0.02	4.8×10^–12 N	5.2×10^–12 N	5.3×10^–8 N	–2.7×10^–7 N	–6.7×10^–6 N
理想流体	λ′=μ′=0	4.8×10^–12 N	5.2×10^–12 N	1.2×10^–11 N	1.7×10^–13 N	6.2×10^–14 N

下载: 导出CSV

[1]	Ozcelik A, Rufo J, Guo F, Gu Y Y, Li P, Lata J, Huang T J 2018 Nat. Methods 15 1021 Google Scholar
[2]	Meng L, Cai F Y, Li F, Zhou W, Niu L L, Zheng H R 2019 J. Phys. D Appl. Phys. 52 273001 Google Scholar
[3]	King L V 1934 Proc. R. Soc. London 147 861 Google Scholar
[4]	Hasegawa T, Yosioka K 1969 J. Acoust. Soc. Am. 46 5 Google Scholar
[5]	Marston P L 2006 J. Acoust. Soc. Am. 120 3518 Google Scholar
[6]	Gong Z X, Marston P L, Li W 2019 Phys. Rev. E 99 063004 Google Scholar
[7]	臧雨宸, 苏畅, 吴鹏飞, 林伟军 2022 物理学报 71 104302 Google Scholar Zang Y C, Su C, Wu P F, Lin W J 2022 Acta Phys. Sin. 71 104302 Google Scholar
[8]	Li S Y, Shi J Y, Zhang X F, Zhang G B 2019 J. Acoust. Soc. Am. 145 5 Google Scholar
[9]	Azarpeyvand M, Azarpeyvand M 2013 J. Sound Vib. 332 9 Google Scholar
[10]	Zang Y C, Lin W 2019 Results Phys. 16 102847 Google Scholar
[11]	Mitri F G 2009 Ultrasonics 49 794 Google Scholar
[12]	Marston P L 2009 J. Acoust. Soc. Am. 125 6 Google Scholar
[13]	Gong M Y, Shi M J, Li Y Y, Xu X, Fei Z H, Qiao Y P, Liu J H, He A J, Liu X Z 2023 Phys. Fluids 35 057108 Google Scholar
[14]	Gong M Y, Xu X, Qiao Y P, Liu J H, He A J, Liu X Z 2024 Chin. Phys. B 33 014302 Google Scholar
[15]	Gaunaurd G C, Huang H 1991 J. Acoust. Soc. Am. 96 2526 Google Scholar
[16]	Miri A K, Mitri F G 2011 Ultrasound Med. Biol. 37 2 Google Scholar
[17]	Westervelt P J 1951 J. Acoust. Soc. Am. 23 3 Google Scholar
[18]	Doinikov A A 1994 J. Fluid Mech. 267 1 Google Scholar
[19]	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
[20]	Kundu P K, Cohen I M 2002 Fluid Mechanics (San Diego: Academic Press) p78, p96
[21]	Huang H, Gaunaurd G C 1997 Int. J. Solids Struct. 34 591 Google Scholar
[22]	Hasheminejad S M 2001 Acta Acust. United Ac. 87 4
[23]	Embleton T F W 1954 J. Acoust. Soc. Am. 26 1 Google Scholar
[24]	Yosioka K, Kawasima Y 1955 Acta. Acust. United Ac. 5 3
[25]	Wang H B, Gao S, Qiao Y P, Liu J H, Liu X Z 2019 Phys. Fluids 31 047103 Google Scholar
[26]	Hartman B, Jarzynski J 1972 J. Appl. Phys. 43 11 Google Scholar

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