声致液滴失稳动力学研究

刘贺; 杨亚晶; 唐玉凝; 魏衍举

doi:10.7498/aps.73.20240965

摘要

声场中液滴稳定性理论的完善对超声雾化技术和超声悬浮技术的发展具有重要价值. 本文通过实验、理论、数值模拟相结合的方式, 研究了驻波声场(19.8 kHz)中的液滴失稳现象及其动力学机制. 结果表明, 随着声场强度的增大, 液滴失稳模式由圆盘失稳转变为边缘锐化失稳, 更重要的是, 液滴在失稳过程中其赤道面扩张加速度存在自发增大的现象. 经分析, 本文揭示了液滴变形过程中其赤道处声辐射负压与长径比之间的正反馈机制, 前者与后者的二次方成正比, 阐明了液滴自加速失稳的形成原因. 之后, 建立了包含表面张力和考虑正反馈机制的声辐射压力的液滴界面平衡方程, 最终得到了声致液滴失稳的无量纲判据, 即当声韦伯数We_a ≤ 1时, 液滴界面保持平衡; We_a > 1时, 赤道声吸力大于表面张力, 液滴发生失稳, 该理论判据与实验结果吻合良好.

关键词:

超声驻波 /
液滴 /
失稳 /
动力学

Abstract

The advancement of the theory of droplet stability in the acoustic field is of significant value in improving ultrasonic atomization and ultrasonic levitation technology. In this work, in order to reveal the detailed mechanism of acoustic droplet instability and give the instability criterion for easy application, the dynamics of droplet instability in standing wave acoustic field (19.8 kHz) is studied by combining practical experiment, theoretical derivation and numerical calculation. The acoustic instability of the droplet occurring near the wave nodes is mainly manifested in two typical modes: disk instability and edge-sharpening instability. The appearance of these two instability modes depends on the relative magnitude of the standing wave field strength. Specifically, with the gradual enhancement of the intensity of the standing wave field, the instability mode of the droplet will gradually change from disc instability to edge-sharpened instability.The droplets show obvious self-accelerating expansion in the equatorial plane in the instability process. The positive feedback between the droplet aspect ratio and the negative pressure of acoustic radiation at the equator of the droplet is the reason for the above self-accelerating behavior. The theoretical results obtained through deduction indicate that the amplitude of the negative acoustic radiation pressure at the droplet equator is proportional to the square of the droplet aspect ratio. The surface tension of the droplet is the main factor hindering its deformation, while the acoustic radiation suction at the equator is the main factor driving the deformation of the droplet. Based on this, the force equilibrium equation of the droplet interface is established, and the dimensionless criterion of acoustic droplet instability, i.e. the acoustic Weber number We_a, is derived. When We_a≤1, the droplet interface stays in equilibrium, and when We_a >1, the equatorial acoustic suction is larger than the surface tension, and the droplet instability occurs, and the average error between the experimental results and the theoretical results is only 9%.

Keywords:

作者及机构信息

1.
西安交通大学能源与动力工程学院, 西安　710049

2.
西安交通大学航天学院, 机械结构强度与振动国家重点实验室, 西安　710049

通信作者: 魏衍举, weiyanju@xjtu.edu.cn

基金项目: 国家自然科学基金 (批准号: 52176128)资助的课题.

Authors and contacts

1.
School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

2.
State Key Laboratory of Mechanical Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: Wei Yan-Ju, weiyanju@xjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52176128).

文章全文 : translate this paragraph

参考文献

[1]	Shi T, Apfel R E 1995 Phys. Fluids 7 1545 Google Scholar
[2]	Anilkumar A V, Lee C P, Wang T G 1993 Phys. Fluids A Fluid Dynam. 5 2763 Google Scholar
[3]	Shi W T, Apfel R E 1996 J. Acoust. Soc. Am. 99 1977 Google Scholar
[4]	Tian Y, Holt R G, Apfel R E 1993 T J. Acoust. Soc. Am. 93 3096 Google Scholar
[5]	Xie W J, Wei B 2004 Phys. Rev. E 70 046611 Google Scholar
[6]	Lee C P, Anilkumar A V, Wang T G 1991 Phys. Fluids A Fluid Dynam. 3 2497 Google Scholar
[7]	Marston P L 1980 J. Acoust. Soc. Am. 67 15 Google Scholar
[8]	Marston P L 1981 J. Acoust. Soc. Am. 69 1499 Google Scholar
[9]	Trinh E H, Hsu C J 1986 J. Acoust. Soc. Am. 79 1335 Google Scholar
[10]	Di W L, Zhang Z H, Li L, Lin K, Li J, Li X, Binks B P, Chen X, Zang D Y 2018 Phys. Rev. Fluids 3 103606 Google Scholar
[11]	Zang D Y, Li L, Di W L, Zhang Z H, Ding C L, Chen Z, Shen W, Binks B P, Geng X G 2018 Nat. Commun. 9 3546 Google Scholar
[12]	鄢振麟, 解文军, 沈昌乐, 魏炳波 2011 物理学报 60 064302 Google Scholar Yan Z L, Xie W J, Shen C L, Wei B B 2011 Acta Phys. Sin. 60 064302 Google Scholar
[13]	邵学鹏, 解文军 2012 物理学报 61 134302 Google Scholar Shao X P, Xie W J 2012 Acta Phys. Sin. 61 134302 Google Scholar
[14]	Zhang Y J, Liu H, Wei Y J, Baig A, Yang Y J 2023 Aip Adv. 13 065316 Google Scholar
[15]	Wu Y C, Wu X C, Yang J, Wang Z H, Gao X, Zhou B W, Chen L H, Qiu K Z, Gréhan G, Cen K F 2014 Appl. Opt. 53 556 Google Scholar
[16]	Danilov S D 1992 J. Acoust. Soc. Am. 92 2747 Google Scholar
[17]	Lierke E G 2002 Acta Acust. United Ac. 88 206
[18]	Andrade M, Marzo A 2019 Phys. Fluids 31 117101 Google Scholar
[19]	Chen H Y, Li A N, Zhang Y J, Zhang X Q, Zang D Y 2022 Phys. Fluids 34 092108 Google Scholar
[20]	Saha A, Basu S, Kumar R 2012 Phys. Lett. A 376 3185 Google Scholar
[21]	Flammer C 1957 Spheroidal Wave Functions (Stanford, CA: Stanford University Press

施引文献

图 1 实验装置

Fig. 1. Experimental setup.

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图 2 仿真相关设置　(a)二维轴对称几何模型及边界设置; (b)网格划分示意图; (c)实验装置纹影图与数值计算结果对比

Fig. 2. Simulation-related settings: (a) Two-dimensional axisymmetric geometric model and boundary settings; (b) schematic diagram of mesh division; (c) comparison of experimental setup ripple shadow map and numerical calculation results.

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图 3 不同强度驻波声场中的声致液滴失稳现象　(a) p_aa = 7.5 kPa; (b) p_aa = 8.2 kPa

Fig. 3. The phenomenon of acoustic induced droplet instability in standing wave sound fields of different intensities: (a) p_aa = 7.5 kPa; (b) p_aa = 8.2 kPa.

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图 4 声致液滴失稳过程中液滴形态参数的变化, D₀ = 0.7 mm　(a)液滴极半径b; (b)液滴赤道半径a

Fig. 4. Changes in droplet morphology parameters during acoustic droplet instability process, D₀ = 0.7 mm: (a) Polar radius of the droplet b; (b) equatorial radius of the droplet a.

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图 5 液滴加速失稳现象　(a)液滴赤道面扩张速度; (b)液滴赤道面扩张加速度

Fig. 5. Droplet acceleration instability phenomenon: (a) Expansion velocity of the droplet's equatorial plane; (b) expansion acceleration of the droplet's equatorial plane.

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图 6 液滴位于波节处时表面声压及声辐射压分布曲线

Fig. 6. Surface sound pressure and sound radiation pressure distribution curve of liquid droplets at wave nodes.

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图 7 驻波声场轴线上的声压及声辐射负压分布

Fig. 7. Distribution of sound pressure and negative pressure of sound radiation on the axis of standing wave sound field.

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图 8 液滴赤道毛细管压力

Fig. 8. Equatorial capillary pressure of liquid droplets.

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图 9 液滴初始时刻表面声辐射压力分布随长径比的变化

Fig. 9. The variation of surface acoustic radiation pressure distribution with aspect ratio at the initial moment of liquid droplets.

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图 10 驻波声场中初始时刻最高声压幅值随液滴长径比的变化

Fig. 10. The variation of the maximum sound pressure amplitude at the initial moment in a standing wave sound field with respect to the droplet aspect ratio.

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图 11 液滴表面声辐射压力随驻波场最高声压幅值的变化

Fig. 11. The variation of surface acoustic radiation pressure of liquid droplets with the highest amplitude of standing wave field sound pressure.

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图 12 液滴表面声辐射压力以及驻波场最高声压幅值随液滴赤道半径和长径比的变化

Fig. 12. The variation of surface acoustic radiation pressure of droplets and the highest amplitude of standing wave field acoustic pressure with the equatorial radius and aspect ratio of droplets.

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图 13 不同液滴长径比对应的液滴赤道处声辐射压力的理论与数值计算结果对比

Fig. 13. Theoretical and numerical comparison of acoustic radiation pressure at the equator of droplets corresponding to different aspect ratios.

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图 14 声致液滴失稳声压阈值随液滴物性的变化趋势　(a)不同表面张力系数; (b)不同黏度

Fig. 14. The trend of sound pressure threshold for acoustic droplet instability with respect to droplet properties:(a) Different surface tension coefficients; (b) different viscosities.

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图 15 声韦伯数在液滴失稳过程中的变化及其触发失稳的临界值　(a)失稳过程中的声韦伯数变化; (b)触发失稳的初始临界声韦伯数

Fig. 15. The variation of acoustic Weber number in the process of droplet instability and the critical value for triggering instability: (a) Variation of the acoustic Weber number during the instability process; (b) initial critical acoustic Weber number that triggers instability.

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[1]	Shi T, Apfel R E 1995 Phys. Fluids 7 1545 Google Scholar
[2]	Anilkumar A V, Lee C P, Wang T G 1993 Phys. Fluids A Fluid Dynam. 5 2763 Google Scholar
[3]	Shi W T, Apfel R E 1996 J. Acoust. Soc. Am. 99 1977 Google Scholar
[4]	Tian Y, Holt R G, Apfel R E 1993 T J. Acoust. Soc. Am. 93 3096 Google Scholar
[5]	Xie W J, Wei B 2004 Phys. Rev. E 70 046611 Google Scholar
[6]	Lee C P, Anilkumar A V, Wang T G 1991 Phys. Fluids A Fluid Dynam. 3 2497 Google Scholar
[7]	Marston P L 1980 J. Acoust. Soc. Am. 67 15 Google Scholar
[8]	Marston P L 1981 J. Acoust. Soc. Am. 69 1499 Google Scholar
[9]	Trinh E H, Hsu C J 1986 J. Acoust. Soc. Am. 79 1335 Google Scholar
[10]	Di W L, Zhang Z H, Li L, Lin K, Li J, Li X, Binks B P, Chen X, Zang D Y 2018 Phys. Rev. Fluids 3 103606 Google Scholar
[11]	Zang D Y, Li L, Di W L, Zhang Z H, Ding C L, Chen Z, Shen W, Binks B P, Geng X G 2018 Nat. Commun. 9 3546 Google Scholar
[12]	鄢振麟, 解文军, 沈昌乐, 魏炳波 2011 物理学报 60 064302 Google Scholar Yan Z L, Xie W J, Shen C L, Wei B B 2011 Acta Phys. Sin. 60 064302 Google Scholar
[13]	邵学鹏, 解文军 2012 物理学报 61 134302 Google Scholar Shao X P, Xie W J 2012 Acta Phys. Sin. 61 134302 Google Scholar
[14]	Zhang Y J, Liu H, Wei Y J, Baig A, Yang Y J 2023 Aip Adv. 13 065316 Google Scholar
[15]	Wu Y C, Wu X C, Yang J, Wang Z H, Gao X, Zhou B W, Chen L H, Qiu K Z, Gréhan G, Cen K F 2014 Appl. Opt. 53 556 Google Scholar
[16]	Danilov S D 1992 J. Acoust. Soc. Am. 92 2747 Google Scholar
[17]	Lierke E G 2002 Acta Acust. United Ac. 88 206
[18]	Andrade M, Marzo A 2019 Phys. Fluids 31 117101 Google Scholar
[19]	Chen H Y, Li A N, Zhang Y J, Zhang X Q, Zang D Y 2022 Phys. Fluids 34 092108 Google Scholar
[20]	Saha A, Basu S, Kumar R 2012 Phys. Lett. A 376 3185 Google Scholar
[21]	Flammer C 1957 Spheroidal Wave Functions (Stanford, CA: Stanford University Press

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声致液滴失稳动力学研究