Motion law of cavitation bubbles in ultrasonic field and mechanism of their interaction with dendrites

Zhang Xin-Yi; Wu Wen-Hua; Wang Jian-Yuan; Zhang Ying; Zhai Wei; Wei Bing-Bo

doi:10.7498/aps.73.20240721

Abstract

Ultrasound treatment (UST) has been demonstrated to be an effective approach to refining the microstructures of metallic alloys during solidification. The cavitation-induced fragmentation is considered as the major mechanism for grain refinement in the recent study, but the interaction between dynamic bubble motion and dendrite behaviour has been rarely investigated previously. In this work, the dynamic behaviour of cavitation bubbles and their interactions with succinonitrile (SCN)-2% (mole fraction) water organic transparent alloy are systematically investigated by high-speed digital image technique and numerical simulation. It is found that increasing the driving pressure transforms the bubble oscillation mode from volume oscillation to splitting oscillation, which significantly enhances the transient pressure and flow strength in the liquid. When a dendrite exists below the bubble, the fracture mode of the secondary branch undergoes a transition from high peripheral fatigue fracture to low peripheral fatigue fracture and to overload fracture with the increase of the driving acoustic pressure, and the fracture period is shortened in the form of a power function trend. The closer the bubble is to the dendrite, the longeritudinal radius of the bubble is gradually larger than the transverse radius during compression, and with the bubble shrink time increasing, the minimum bubble volume decreases. In addition, the decrease in distance between bubbles and dendrites leads to a significant reduction in the maximum pressure generated by bubble collapse, while the maximum flow rate shows a trend of first increasing and then decreasing. When the root radius of the secondary branch decreases or its length increases, the number of fatigue fracture cycles of the secondary branch decreases significantly. The calculated bubble expansion and contraction and secondary dendrite rupture processes are basically consistent with the experimental results, which indicates that the model constructed in this work can accurately predict the bubble motion and its interaction with dendrite in ultrasonic field.

Keywords:

Authors and contacts

School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding author: Zhai Wei, zhaiwei322@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52088101, 52130405) and the Basic Research Project of Shaanxi Natural Science Foundation, China (Grant No. 2023-JC-JQ-28).

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References

[1]	He L, Wu M, Li L, Hao H 2006 Appl. Phys. Lett. 89 131504 Google Scholar
[2]	Huang H, Qin L, Tang H B, Shu D, Yan W T, Sun B D, Mi J W 2021 Ultrason. Sonochem. 80 105832 Google Scholar
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图 1 超声场中气泡振荡和溃灭模型的几何示意　(a) 单个气泡运动模型; (b) 气泡与枝晶间相互作用模型; 1, 变幅杆; 2, 气泡; 3, SCN-H₂O溶液; 4, SCN枝晶

Figure 1. Geometrical schematic of the bubble oscillation and collapse model within the ultrasonic field: (a) Model of single bubble motion; (b) model of bubble-dendrite interaction; 1, horn; 2, bubble; 3, SCN-H₂O solution; 4, SCN dendrite.

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图 2 不同声压振幅条件下的气泡形貌和声场及流场分布　(a) P_a = 0.4P_B; (b) P_a = P_B

Figure 2. Bubble morphology and distributions of acoustic field and flow field with different ultrasonic amplitudes: (a) P_a = 0.4P_B; (b) P_a = P_B.

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图 3 气泡动力学与超声振幅的相关性　(a) 气泡体积随时间的变化; (b) 最大声压及最大声流与声压振幅 P_a 的关系

Figure 3. Correlation between bubble dynamics and ultrasonic amplitude: (a) Bubble volume versus time; (b) maximum sound pressure and maximum sound flow versus sound pressure amplitude P_a.

DownLoad: Full-Size Img PowerPoint

图 4 声压幅值 0.4P_B 时气泡振荡过程中二次分枝上应力分布　(a)二次分枝下表面应力分布; (b) 不同高度二次分枝根部应力

Figure 4. Stress distribution on the secondary branch during bubble oscillation at a sound pressure amplitude of 0.4P_B: (a) Stress distribution on the lower surface of the secondary branch; (b) stress on the secondary branch root at different heights.

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图 5 不同声压条件下二次分枝偏转角度随时间变化　(a) P_a = 0.4P_B; (b) P_a = P_B

Figure 5. Changes of the deflection angle of the secondary branch with time under different sound pressures: (a) P_a = 0.4P_B; (b) P_a = P_B.

DownLoad: Full-Size Img PowerPoint

图 6 不同声压条件下二次分枝断裂机制　(a) 0.4P_B 和 P_B 振幅下气泡内外压差; (b) 0.4P_B 驱动声压下A点应力随时间的变化; (c) P_B 驱动声压下 A 点应力随时间的变化; (d) 分枝断裂所需弯折周期随声压幅值 P_a 的变化

Figure 6. Mechanism of secondary branch breakage under different sound pressures: (a) Pressure difference between inside and outside the bubble at 0.4P_B and P_B; (b) variation of stress at point A with time at the ultrasonic amplitude of 0.4P_B; (c) variation of stress at point A with time at the ultrasonic amplitude of P_B; (d) variation of fragmentation cycle number with sound pressure amplitude P_a.

DownLoad: Full-Size Img PowerPoint

图 7 声压振幅 P_B 条件下气泡体积及最大压强与枝晶距离的相关性　(a)—(c) 气泡顶部开始凹陷时刻的压强分布图; (d) 气泡体积随时间变化, 其中插图为气泡体积最小时的形貌; (e) 流体中最大压强随时间的变化规律

Figure 7. Correlation of bubble volume and maximum pressure with the distance of dendrites under acoustic pressure amplitude P_B: (a)–(c) Pressure distributions at the moment when the top of the bubble starts to dimple; (d) variation of bubble volume with time, where the sugfigure shows the morphology of the bubble with the smallest volume; (e) evolution of the maximum pressure in the fluid with time.

DownLoad: Full-Size Img PowerPoint

图 8 P_a = P_B 条件下间距h对气泡溃灭和二次分支断裂的作用规律　(a) 气泡溃灭在流体中产生的最大压强和流速; (b) 二次分枝上最大应力及其断裂所需时间的变化规律

Figure 8. Effect of distance h on the bubble collapse and secondary branch fragmentatio P_a = P_B: (a) Maximum pressure and flow rate in the fluid produced by bubble collapse; (b) variation of the maximum stress on the secondary branch and fragmentation cycle number.

DownLoad: Full-Size Img PowerPoint

图 9 声压幅值 0.4P_B 作用下二次分枝根部A点应力和断裂周期与其根部半径 r 和长度 L 的关系　(a) L = 100 μm 时A点应力随时间变化; (b) r = 3 μm时A点一个周期内的平均应力与 L 的相关性; (c) 断裂周期与 r 和 L 的关系

Figure 9. Relationship of the stress at point A and fragmentation cycle number to root radius r and length L of the secondary branch at P_a = 0.4P_B: (a) Stress versus time for L = 100 μm; (b) correlation of the average stress over a cycle with L for r = 3 μm; (c) fragmentation cycle number versus r and L.

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图 10 数值模拟与 K-M 方程计算的气泡体积随时间的变化　(a) R₀ = 10 μm; (b) R₀ = 50 μm

Figure 10. Comparison of the numerical results and K-M equation for volume oscillation: (a) R₀ = 10 μm; (b) R₀ = 50 μm.

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图 11 超声作用下气泡与枝晶动态相互作用的实验观测和数值模拟对比　(a) 实验观测; (b) 数值模拟

Figure 11. Comparison of dynamic interaction between bubbles and dendrites by experimental observations and numerical simulation under ultrasound: (a) Experimental observations; (b) numerical simulation.

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图 12 二次分枝根部应力和气泡形貌与时间的相关性　(a) 根部应力变化的模拟结果; (b) 气泡半径变化的实验验证

Figure 12. Correlation of secondary branch root stress and bubble morphology with time: (a) Simulation results of root stress variation; (b) experimental validation of bubble radius variation.

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表 1 声场和流场计算所用物理量数值

Table 1. Values of physical parameters used in sound and flow field calculations.

物理量	单位	数值
气泡初始半径 R₀	μm	50
液体密度 ρ_l ^[24]	kg/m³	970
饱和蒸汽压 P_v ^[25]	Pa	2330
表面张力 σ_g ^[24]	10^–2 N/m	3.85
液体声速 c_l ^[26]	m/s	1500
液体黏度 μ_l ^[24]	10^–3 Pa·s	2.66
液体静压力 P₀	10⁵ Pa	1.013
超声频率 f	kHz	20
气体比热系数 γ ^[26]	/	1.4
气体热扩散系数 κ ^[26]	10⁵ m²/s	2.19
SCN的杨氏模量 E ^[19]	10¹¹ Pa	2.11
SCN泊松比 ν ^[19]	/	0.33

DownLoad: CSV

[1]	He L, Wu M, Li L, Hao H 2006 Appl. Phys. Lett. 89 131504 Google Scholar
[2]	Huang H, Qin L, Tang H B, Shu D, Yan W T, Sun B D, Mi J W 2021 Ultrason. Sonochem. 80 105832 Google Scholar
[3]	Wei X, Li X L, Zhang L Q, Lü Q G 2022 Int. J. Heat Mass Transfer 192 122914 Google Scholar
[4]	Wu W, Wang D, Zhai W, Wang J, Wei B 2023 J. Appl. Phys. 133 115102 Google Scholar
[5]	Sander J R G, Zeiger B W, Suslick K S 2014 Ultrason. Sonochem. 21 1908 Google Scholar
[6]	Cui B, Chen K, Yang Y, Lü Y, Zhang F, Liu S 2024 Mater. Chem. Phys. 318 129297 Google Scholar
[7]	Wang S, Kang J, Zhang X, Guo Z 2018 Ultrasonics 83 26 Google Scholar
[8]	Shu D, Sun B D, Mi J W, Grant P S 2012 Metall. Mater. Trans. A 43 3755 Google Scholar
[9]	Priyadarshi A, Khavari M, Subroto T, Conte M, Prentice P, Pericleous K, Eskin D, Durodola J, Tzanakis I J E 2021 Ultrason. Sonochem. 70 105260 Google Scholar
[10]	Wang B, Tan D Y, Lee T L, Khong J C, Wang F, Eskin D, Connolley T, Fezzaa K, Mi J W 2018 Acta Mater. 144 505 Google Scholar
[11]	马艳, 林书玉, 徐洁 2018 物理学报 67 034301 Google Scholar Ma Y, Lin S Y, Xu J 2018 Acta Phys. Sin. 67 034301 Google Scholar
[12]	Qu W X, Xie Y H, Shen Y, Han J, Zhu T 2017 Math. Model. Eng. Probl. 4 173 Google Scholar
[13]	Lind S J, Phillips T N 2012 Theor. Comput. Fluid Dyn. 26 245 Google Scholar
[14]	Samiei E, Shams M, Ebrahimi R 2011 Eur. J. Mech. B. Fluids 30 41 Google Scholar
[15]	吴学由, 梁金福 2021 物理学报 70 184301 Google Scholar Wu X Y, Liang J F 2021 Acta Phys. Sin. 70 184301 Google Scholar
[16]	Wang X J, Ning Z, Lü M, Yao J S, Sun C H 2022 J. Phys. Soc. Jpn 91 014401 Google Scholar
[17]	Cao S, Wang G, Coutier-Delgosha O, Wang K 2021 J. Fluid Mech. 907 A17 Google Scholar
[18]	Shan M L, Yang Y, Kan X F, Yin C, Han Q B 2024 Chin. Phys. B 33 064701 Google Scholar
[19]	张颖, 吴文华, 王建元, 翟薇 2022 物理学报 71 244303 Google Scholar Zhang Y, Wu W H, Wang J Y, Zhai W 2022 Acta Phys. Sin. 71 244303 Google Scholar
[20]	Hosseinkhah N, Chen H, Matula T J, Burns P N, Hynynen K 2013 J. Acoust. Soc. Am. 134 1875 Google Scholar
[21]	Delale C F, Pasinlioğlu Ş 2023 Phys. Fluids 35 023330 Google Scholar
[22]	Zakerzadeh R, Zunino P 2018 Meccanica 54 101 Google Scholar
[23]	秦对, 邹青钦, 李章勇, 王伟, 万明习, 冯怡 2021 物理学报 70 154701 Google Scholar Qian D, Zhou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701 Google Scholar
[24]	Wang S, Guo Z P, Zhang X P, Zhang A, Kang J W 2019 Ultrason. Sonochem. 51 160 Google Scholar
[25]	Murakami K, Yamakawa Y, Zhao J, Johnsen E, Ando K 2021 J. Fluid Mech. 924 A38 Google Scholar
[26]	Chen X S, Bayanheshig, Jiao Q B, Tan X, Wang W 2021 Int. J. Heat Mass Transfer 171 121074 Google Scholar
[27]	Wang S, Kang J, Guo Z P, Lee T L, Mi J W 2018 Acta Mater. 165 388 Google Scholar
[28]	Wu W H, Wang J Y, Zhai W, Wei B B 2023 Metall. Mater. Trans. B 54 1845 Google Scholar

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