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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 Wea, is derived. When Wea≤1, the droplet interface stays in equilibrium, and when Wea >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%.
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Keywords:
- ultrasonic standing wave /
- droplet /
- instability /
- dynamics
[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
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Google Scholar
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Google Scholar
Yan Z L, Xie W J, Shen C L, Wei B B 2011 Acta Phys. Sin. 60 064302
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
[21] Flammer C 1957 Spheroidal Wave Functions (Stanford, CA: Stanford University Press
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图 1 实验装置
Figure 1. Experimental setup.
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
Figure 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.
图 3 不同强度驻波声场中的声致液滴失稳现象 (a) paa = 7.5 kPa; (b) paa = 8.2 kPa
Figure 3. The phenomenon of acoustic induced droplet instability in standing wave sound fields of different intensities: (a) paa = 7.5 kPa; (b) paa = 8.2 kPa.
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
Figure 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.
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
Figure 5. Droplet acceleration instability phenomenon: (a) Expansion velocity of the droplet's equatorial plane; (b) expansion acceleration of the droplet's equatorial plane.
图 6 液滴位于波节处时表面声压及声辐射压分布曲线
Figure 6. Surface sound pressure and sound radiation pressure distribution curve of liquid droplets at wave nodes.
图 7 驻波声场轴线上的声压及声辐射负压分布
Figure 7. Distribution of sound pressure and negative pressure of sound radiation on the axis of standing wave sound field.
图 8 液滴赤道毛细管压力
Figure 8. Equatorial capillary pressure of liquid droplets.
图 9 液滴初始时刻表面声辐射压力分布随长径比的变化
Figure 9. The variation of surface acoustic radiation pressure distribution with aspect ratio at the initial moment of liquid droplets.
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
Figure 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.
图 11 液滴表面声辐射压力随驻波场最高声压幅值的变化
Figure 11. The variation of surface acoustic radiation pressure of liquid droplets with the highest amplitude of standing wave field sound pressure.
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
Figure 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.
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
Figure 13. Theoretical and numerical comparison of acoustic radiation pressure at the equator of droplets corresponding to different aspect ratios.
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
Figure 14. The trend of sound pressure threshold for acoustic droplet instability with respect to droplet properties:(a) Different surface tension coefficients; (b) different viscosities.
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
Figure 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 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 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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