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In order to explore the dynamic characteristics of bubbles in the cavitation bubble cluster in detail, the dynamic equation of a bubble with arbitrary location inside the bubble cluster is established in this paper, based on the interactions between bubbles inside the bubble cluster driven by ultrasound. The effects of evaporation and condensation of the water vapor are also taken into account in the derivation process. Based on the proposed equation, the influences of the bubble position, number of bubbles, and initial radius of bubbles on the dynamic characteristics of cavitation bubbles are studied, and the corresponding change laws of the bubble radius, energy, temperature, pressure, as well as the number of water vapor molecules in a bubble are investigated under ultrasound. The calculation results are shown below. 1) Comparing with an isolated bubble, the oscillation of a bubble inside the bubble cluster is suppressed by its surrounding bubbles, which leads to the fact that the vibration amplitude of a bubble inside the bubble cluster is smaller, and that the internal energy, maximum temperature, maximum pressure and the number of water molecules in the bubble all become smaller. As the distance between the bubble and the center of the bubble cluster increases, the vibration amplitude of the bubble become larger. 2) The initial radii of the bubbles in the bubble cluster can significantly affect the normalized vibration amplitude, collapse time, internal energy, temperature, and pressure of bubbles, as well as the number of water vapor molecules in bubbles of the bubble cluster. 3) As the number of bubbles in the bubble cluster increases, the vibration amplitudes of the bubbles decrease. 4) The higher the ultrasonic frequency, the smaller the oscillation amplitude of the bubble; the smaller the maximum pressure and energy of the bubble, the larger the minimum value of the internal pressure and temperature of the bubble and the less the number of water molecules in the bubble. When the ultrasonic frequency increases, the cavitation effects of bubbles in the bubble cluster are suppressed. 5) As the ultrasonic sound pressure increases, the oscillation amplitudes of the bubbles in the bubble cluster increase, the maximum values of the bubbles' radii increase, the collapse times of the cavitation bubbles increase, and the number of oscillations of bubbles decreases after the cavitation bubbles have collapsed. Additionally, the maximum value of internal energy, temperature, pressure, and the number of water molecules in the bubble also increase as the ultrasonic sound pressure increases, while the minimum value of the pressure and temperature of the bubble decrease. Besides, when the ultrasonic sound pressure increases, the cavitation effects of the bubbles in the bubble cluster turn stronger. This paper focuses on the dynamic characteristics of ultrasonic cavitation bubble cluster from the theoretical aspect and the results can be further applied to experimental analysis. -
Keywords:
- ultrasonic cavitation /
- spherical bubble group /
- evaporation and condensation /
- dynamic characteristics
[1] 莫润阳, 林书玉, 王成会 2009 应用声学 8 389
Google Scholar
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[2] 张婵, 郑爽英 2009 水资源与水工程学报 20 136
Zhang C, Zheng S Y 2009 Journal of Water Resources and Water Engineering 20 136
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Google Scholar
[4] Eddingsaas N C, Suslick K S 2006 Nature 444 163
Google Scholar
[5] Suslick K S, Didenko Y, Fang M M, Hyeon T, Kolbeck K J 2000 Philos. Trans. R. Soc. London, Ser. B 357 335
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[6] Flannigan D J, Hopkins S D, Camara C G, Putterman S J, Suslick K S 2006 Phys. Rev. Lett. 96 204301
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[7] Xu H, Suslick K S 2010 Phys. Rev. Lett. 104 244301
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Feng R, Li H M 2000 Appl. Acoust. 19 35
Google Scholar
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Cheng X R, Zhang S Y, Fang N 2018 Appl Chemical Industry 47 1753
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Google Scholar
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Gou J, Chen W Z 2012 Sci. China, Ser. G 42 217
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Wang C H, Mo R Y, Hu J, Zhang M D 2017 Sci. China, Ser. G 47 59
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Google Scholar
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图 1 单泡、泡群中心的泡和泡群表面的泡的动力学特性 (a) 气泡归一化半径随时间的变化曲线; (b) 气泡内内能随时间的变化曲线; (c) 气泡内温度随时间的变化曲线; (d) 气泡内压力随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线
Figure 1. Dynamical behaviors of a single bubble, a bubble at the center of a bubble group and a bubble on the surface of a bubble group: (a) Change curve of the normalized radius with the time for the bubble; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.
图 2 泡群中不同初始半径的泡的动力学特性 (a) 气泡归一化半径随时间的变化; (b) 气泡内内能随时间的变化曲线; (c) 气泡内温度随时间的变化曲线; (d) 气泡内压力随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线
Figure 2. Dynamic characteristics of the bubbles with different initial radii in bubble group: (a) Change curve of the normalized radius with the time; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.
图 3 泡群中不同位置的泡的动力学特性
Figure 3. Dynamic characteristics of bubbles at different positions in a bubble group.
图 4 不同频率下泡群中泡的动力学特性 (a) 气泡归一化半径随时间的变化; (b) 气泡内内能随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线
Figure 4. Dynamic characteristics of the bubbles in bubble groups at different frequencies: (a) Change curve of the normalized radius with the time for the bubble; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.
图 5 不同声压下泡群中泡的动力学特性 (a) 气泡归一化半径随时间的变化; (b) 气泡内内能随时间的变化曲线; (c) 气泡内温度随时间的变化曲线; (d) 气泡内压力随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线
Figure 5. Dynamic characteristics of bubbles in bubble groups under different sound pressures: (a) Change curve of the normalized radius with the time for the bubble; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.
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[1] 莫润阳, 林书玉, 王成会 2009 应用声学 8 389
Google Scholar
Mo R, Lin S Y, Wang C H 2009 Appl. Acoust. 8 389
Google Scholar
[2] 张婵, 郑爽英 2009 水资源与水工程学报 20 136
Zhang C, Zheng S Y 2009 Journal of Water Resources and Water Engineering 20 136
[3] Suslick K S 1989 Sci. Am. 260 80
Google Scholar
[4] Eddingsaas N C, Suslick K S 2006 Nature 444 163
Google Scholar
[5] Suslick K S, Didenko Y, Fang M M, Hyeon T, Kolbeck K J 2000 Philos. Trans. R. Soc. London, Ser. B 357 335
Google Scholar
[6] Flannigan D J, Hopkins S D, Camara C G, Putterman S J, Suslick K S 2006 Phys. Rev. Lett. 96 204301
Google Scholar
[7] Xu H, Suslick K S 2010 Phys. Rev. Lett. 104 244301
Google Scholar
[8] 刘坤, 张建国, 屈策计, 李忠厚 2012 中国石油和化工标准与质量 32 93
Google Scholar
Liu K, Zhang J G, Qu C J, Li Z H 2012 China Petroleum and Chemical Standard and Quality 32 93
Google Scholar
[9] Luo X M, Gong H Y, He Z L, Zhang P, He L M 2021 Ultrason. Sonochem. 70 105337
Google Scholar
[10] 冯若, 李化茂 2000 应用声学 19 35
Google Scholar
Feng R, Li H M 2000 Appl. Acoust. 19 35
Google Scholar
[11] 程效锐, 张舒研, 房宁 2018 应用化工 47 1753
Google Scholar
Cheng X R, Zhang S Y, Fang N 2018 Appl Chemical Industry 47 1753
Google Scholar
[12] 熊宜栋 2002 应用声学 21 33
Google Scholar
Xiong Y D 2002 Appl. Acoust. 21 33
Google Scholar
[13] Hilgenfeldt S, Lohse D, Brenner M P 1996 Phys. Fluids 8 2808
Google Scholar
[14] Kyuichi Y 1997 Phys. Rev. E 56 6750
Google Scholar
[15] Toegel R, Lohse D 2003 J. Chem. Phys. 118 1863
Google Scholar
[16] 高贤娴, 陈伟中, 黄威, 徐俊峰, 徐兴华, 刘亚楠, 梁越 2009 科学通报 54 408
Google Scholar
Gao X X, Chen W Z, Huang W, Xu J F, Xu X H, Liu Y N, Liang Y 2009 Chin. Sci. Bull. 54 408
Google Scholar
[17] 苟杰, 陈伟中 2012 中国科学: 物理学 力学 天文学 42 217
Gou J, Chen W Z 2012 Sci. China, Ser. G 42 217
[18] 沈阳, 朱彤, 由美雁, 糜彬, 韩进, 谢元华, 李现瑾, Kyuichi Yasui 2015 高校化学工程学报 29 809
Google Scholar
Shen Y, Zhu D, You M Y, Mei B, Han J, Xie Y H, Li X J, Kyuichi Y 2015 Journal of Chemical Engineering of Chinese Universities 29 809
Google Scholar
[19] Lin Z Y, Zhu X J, Yao L 2019 Ultrason. Sonochem. 59 104744
Google Scholar
[20] An Y 2011 Phys. Rev. E 83 066313
Google Scholar
[21] 沈壮志, 吴胜举 2012 61 124301
Google Scholar
Shen Z Z, Wu S J 2012 Acta Phys. Sin. 61 124301
Google Scholar
[22] 王成会, 莫润阳, 胡静, 张明铎 2017 中国科学: 物理学 力学 天文学 47 59
Wang C H, Mo R Y, Hu J, Zhang M D 2017 Sci. China, Ser. G 47 59
[23] 张鹏利, 林书玉, 朱华泽, 张涛 2019 68 134301
Google Scholar
Zhang P L, Lin S Y, Zhu H Z, Zhang T 2019 Acta Phys. Sin. 68 134301
Google Scholar
[24] Shen Z Z 2020 Chin. Phys. B 29 417
Google Scholar
[25] 清河美, 那仁满都拉 2020 69 184301
Google Scholar
Qing H M, Naranmandula 2020 Acta Phys. Sin. 69 184301
Google Scholar
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