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