Analysis of nanobubble collapse process by molecular simulation method

Zhang Xue-Song; Fan Zhen-Zhong; Tong Qi-Lei; Fu Yuan-Feng

doi:10.7498/aps.73.20241105

Abstract

This study employs molecular dynamics simulations to investigate the process of nanobubble gradual indentation and eventual collapse. The research primarily focuses on the mechanisms by which impact velocity and bubble size influence the dynamic characteristics of nanobubble collapse. The results indicate that nanobubble collapse generally proceeds through three stages. Initially, there is a compression phase of water molecules surrounding the bubble, followed by a phase where the shock wave disrupts the stable structure of the liquid film, and finally, the complete collapse of the bubble. At higher impact velocities, smaller bubbles collapse more rapidly due to stronger shock effects. Post-collapse, a high-speed jet forms a protrusion on the right end of the velocity contour. The degree of protrusion increases with bubble size and impact velocity. Water molecules converge towards the bubble center, forming vortex structures above and below the bubble, effectively enhancing internal mass transfer. As bubble size and impact velocity increase, the density around the bubble gradually rises, reaching approximately 1.5 g/cm³ in localized areas upon complete collapse. When the bubble system decays to half its original size, a water hammer effect occurs. This effect becomes more pronounced with increasing bubble size and impact velocity. For a nanobubble structure with u_p = 3.0 km/s and D = 10 nm, the local pressure formed by the water hammer impact of the jet after collapse can reach 30 GPa.

Keywords:

Authors and contacts

Key Laboratory of Enhanced Oil and Gas Recovery, Ministry of Education, Northeast Petroleum University, Daqing 163318, China

Corresponding author: Fan Zhen-Zhong, fanzhenzhong@163.com

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References

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[15]	Wang X F, Tao G, Wen P, Ren B X, Pang C Q, Du C X 2020 J. Phys. Chem. B 124 9535 Google Scholar
[16]	Lu X, Yuan B, Zhang X, Yang K, Ma Y 2017 Appl. Phys. Lett. 110 023701 Google Scholar
[17]	Thompson A P, Aktulga H M, Berger R, Bolintineanu D S, Brown W M, Crozier P S, In ’T Veld P J, Kohlmeyer A, Moore S G, Nguyen T D, Shan R, Stevens M J, Tranchida J, Trott C, Plimpton S J 2022 Comput. Phys. Commun. 271 108171 Google Scholar
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图 1 纳米气泡冲击过程示意图

Figure 1. Schematic diagram of nanobubble impact process.

DownLoad: Full-Size Img PowerPoint

图 2 纯水体系在不同冲击速度条件下沿z轴一维密度分布　(a) 1.0—2.0 km/s; (b) 2.5—3.0 km/s

Figure 2. One-dimensional density distribution along the z-axis in the pure water system under different impact velocities:(a) 1.0–2.0 km/s; (b) 2.5–3.0 km/s.

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图 3 纯水体系在不同冲击速度条件下沿z轴一维密度分布曲线　(a) 1.0 km/s; (b) 1.5 km/s; (c) 2.0 km/s; (d) 2.5 km/s; (e) 3.0 km/s

Figure 3. One-dimensional density distribution curves along the z-axis in the pure water system under different impact velocities: (a) 1.0 km/s; (b) 1.5 km/s; (c) 2.0 km/s; (d) 2.5 km/s; (e) 3.0 km/s.

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图 4 u_p-u_s的Hugoniot冲击压缩图

Figure 4. Hugoniot shock compression diagram of u_p-u_s.

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图 5 纳米气泡体积归一化Ω(t)随冲击时间变化关系曲线　(a) 不同冲击速度; (b) 不同气泡尺寸

Figure 5. Normalized Ω(t) curves of nanobubble volume as a function of impact time: (a) Different impact velocitys; (b) different nanobubble sizes.

DownLoad: Full-Size Img PowerPoint

图 6 不同时刻下的纳米气泡结构变化情况(D = 10 nm, u_p = 3.0 km/s)

Figure 6. Changes in nanobubble structure at different times (D = 10 nm, u_p = 3.0 km/s).

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图 7 纳米气泡溃灭前后的z 方向速度分布情况　(a) 不同冲击速度; (b) 不同气泡尺寸

Figure 7. z-direction velocity distribution before and after the collapse of the nanobubble: (a) Different impact velocities; (b) different bubble sizes.

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图 8 1.4—3.0 ps纳米气泡外层液膜的运动轨迹曲线(单位: km/s)

Figure 8. Motion trajectory curve of outer liquid film of 1.4–3.0 ps nanobubble (unit: km/s).

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图 9 u_p = 3.0 km/s, D = 10 nm纳米气泡二维流场(y-z平面)速度矢量分布　(a) 1.3 ps; (b) 2.2 ps; (c) 2.8 ps; (d) 3.4 ps (单位: km/s, 由于比例问题, 气泡呈椭圆形)

Figure 9. Velocity vector distribution of two-dimensional flow field (y-z plane) of nanobubble with u_p = 3.0 km/s and D = 10 nm: (a) 1.3 ps; (b) 2.2 ps; (c) 2.8 ps; (d) 3.4 ps (unit: km/s, due to proportional issues, the bubble is elliptical in shape).

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图 10 不同气泡尺寸及冲击速度大小的气泡流场速度分布　(a) 不同气泡尺寸; (b) 不同冲击速度

Figure 10. Velocity distribution of the bubble flow field at different bubble sizes and impact velocities: (a) Different bubble sizes; (b) different impact velocities.

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图 11 不同冲击速度下的体系势能PE (a)和动能KE (b)沿z轴一维分布曲线(3.3 ps)

Figure 11. One dimensional distribution curves of system potential energy PE (a) and kinetic energy KE (b) along the z-axis at different impact velocities (3.3 ps).

DownLoad: Full-Size Img PowerPoint

图 12 纳米气泡周围水分子质量密度沿z轴一维分布曲线

Figure 12. One dimensional distribution curve of water molecule mass density around nanobubble along the z-axis.

DownLoad: Full-Size Img PowerPoint

图 13 纳米气泡周围水分子质量密度的y-z平面二维云图　(a) 不同气泡尺寸; (b) 不同冲击速度

Figure 13. Two dimensional cloud map of y-z plane of water molecule mass density around nanobubble: (a) Different nanobubble sizes; (b) different impact velocities.

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图 14 纳米气泡射流前沿x-y平面(径向)二维云图(单位: km/s)

Figure 14. Two dimensional cloud map of the front x-y plane (radial) of the nanobubble jet (unit: km/s).

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图 15 纳米气泡射流产生局部压强的y-z平面二维云图　(a) 不同气泡尺寸; (b) 不同冲击速度

Figure 15. Two dimensional cloud map of y-z plane generated local pressure by nanobubble jet: (a) Different nanobubble size; (b) different impact velocity.

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表 1 SPC/E刚性分子模型势能参数

Table 1. Potential energy parameters of SPC/E rigid molecular model.

type	ε/(kcal·mol^–1)	σ/Å	q/e
O	3.166	0.15535	–0.8476
H	0	0	0.4238

DownLoad: CSV

表 2 不同条件下的粒子速度和冲击速度对应结果

Table 2. Corresponding results of particle velocity and impact velocity under different conditions.

u_p/(km·s^–1)	u_s1	u_s2	u_s3	u_exp	u_sim	ε/%
1.0	3.21	3.26	3.17	3.57	3.61	9.8
1.5	4.06	4.14	4.16	4.40	4.30	6.4
2.0	5.07	5.06	5.16	5.25	5.18	2.9
2.5	5.89	5.93	5.99	5.93	5.51	0.6

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表 3 不同粒子速度和尺寸下的纳米气泡破裂时间

Table 3. Breakdown time of nanobubble at different particle velocities and sizes.

粒子速度 u_p/(km·s^–1)	气泡尺寸 D/nm	气泡破裂时间 τ/ps
粒子速度 u_p/(km·s^–1)	气泡尺寸 D/nm	MD	Rayleigh	差值
1.0	8	3.3	3.8	0.5
	10	4.2	4.7	0.3
	12	4.6	5.7	1.0
1.5	8	2.2	2.5	0.3
	10	2.7	3.1	0.4
	12	3.4	3.7	0.3
2.0	8	1.8	2.1	0.3
	10	2.2	2.3	0.1
	12	2.6	2.8	0.2
2.5	8	1.4	1.5	0.1
	10	1.9	1.8	0.1
	12	2.1	2.2	0.1
3.0	8	1.2	1.1	0.1
	10	1.6	1.4	0.2
	12	1.9	1.7	0.2

DownLoad: CSV

表 4 MD模拟和Rankine–Hugoniot计算冲击压力结果

Table 4. MD simulation and Rankine-Hugoniot calculation of impact pressure results.

粒子速度u_p/(km·s^–1)	冲击速度u_s/(km·s^–1)	冲击压力 P_s/GPa
粒子速度u_p/(km·s^–1)	冲击速度u_s/(km·s^–1)	MD	Rankine– Hugoniot	差值
1.0	3.22	3.09	3.20	0.11
1.5	4.12	6.16	6.18	0.02
2.0	5.09	10.19	10.18	0.01
2.5	5.93	14.96	14.82	0.14
3.0	6.80	20.63	20.40	0.23

DownLoad: CSV

[1]	马艳, 吴俊, 周维 2024 环境工程技术学报 14 1141 Google Scholar Ma Y, Wu J, Zhou W 2024 J. Environ. Eng. Technol. 14 1141 Google Scholar
[2]	杨丽, 廖传华, 朱跃钊, 陈海军, 金勤芳 2012 化工进展 31 1333 Yang L, Liao C H, Zhu Y Z, Chen H J, Jin Q F 2012 Chem. Ind. Eng. Prog. 31 1333
[3]	张立娟, 郑晋, 文博, 胡钧 2024 中国科学: 化学 54 85 Google Scholar Zhang L J, Zheng J, Wen B, Hu J 2024 Sci. Sin. Chem. 54 85 Google Scholar
[4]	张敏, 宋昭峥, 孙珊珊, 张志勇, 穆红岩, 赵立平, 李永峰, 张忠智 2016 环境工程学报 10 599 Google Scholar Zhang M, Song Z Z, Sun S S, Zhang Z Y, Mu H Y, Zhao L P, Li Y F, Zhang Z Z 2016 Chin. J. Environ. Eng. 10 599 Google Scholar
[5]	翟伟哲, 王永刚, 王旭, 董婧, 王恒嘉 2018 环境科学与管理 43 95 Google Scholar Zhai W Z, Wang Y G, Wang X, Dong J, Wang H J 2018 Environ. Sci. Manage. 43 95 Google Scholar
[6]	李恒震, 胡黎明, 辛鸿博 2015 岩土工程学报 37 115 Google Scholar Li H Z, Hu L M, Xin H B 2015 Chin. J. Geotech. Eng. 37 115 Google Scholar
[7]	Cook S S 1928 Proc. R. Soc. London, Ser. A 119 481 Google Scholar
[8]	Obara T B, Bourne N K, Field J E 1995 Wear 186 388
[9]	詹胜鹏 2022 博士学位论文 (北京: 机械科学研究总院) Zhan S P 2022 Ph. D Dissertation (Beijing: Academy of Machinery Science and Technology
[10]	王小峰, 陶钢, 徐宁, 王鹏, 李召, 闻鹏 2021 物理学报 70 134702 Google Scholar Wang X F, Tao G, Xu N, Wang P, Li Z, Wen P. 2021 Acta Phys. Sin. 70 134702 Google Scholar
[11]	Rawat S 2023 Phys. Fluids 35 097114 Google Scholar
[12]	Vedadi M H, Haas S 2011 Appl. Phys. Lett. 99 154105 Google Scholar
[13]	Zhou Y, Cao D, Zhang X 2022 Nanomaterials 12 2654 Google Scholar
[14]	Nan N, Si D, Hu G 2018 J. Chem. Phys. 149 074902 Google Scholar
[15]	Wang X F, Tao G, Wen P, Ren B X, Pang C Q, Du C X 2020 J. Phys. Chem. B 124 9535 Google Scholar
[16]	Lu X, Yuan B, Zhang X, Yang K, Ma Y 2017 Appl. Phys. Lett. 110 023701 Google Scholar
[17]	Thompson A P, Aktulga H M, Berger R, Bolintineanu D S, Brown W M, Crozier P S, In ’T Veld P J, Kohlmeyer A, Moore S G, Nguyen T D, Shan R, Stevens M J, Tranchida J, Trott C, Plimpton S J 2022 Comput. Phys. Commun. 271 108171 Google Scholar
[18]	Stukowski A 2010 Modell. Simul. Mater. Sci. Eng. 18 015012 Google Scholar
[19]	Berendsen H J C, Grigera J R, Straatsma T P 1987 J. Phys. Chem. 91 6269 Google Scholar
[20]	Zhou Y, Huang M, Tian F, Shi X, Zhang X 2024 J. Phys. Chem. 160 054109 Google Scholar
[21]	Rybakov A P, Rybakov I A 1995 Eur. J. Mech. B Fluids 14 323
[22]	Vedadi M, Choubey A, Nomura K, Kalia R K, Nakano A, Vashishta P, Van Duin A C T 2010 Phys. Rev. Lett. 105 014503 Google Scholar
[23]	Hołyst R, Litniewski M, Garstecki P 2010 Phys. Rev. E 82 066309 Google Scholar
[24]	Zhang A M, Cui P, Wang Y 2013 Exp. Fluids 54 1602 Google Scholar
[25]	Zhang H, Lu Z, Zhang P, Gu J, Luo C, Tong Y, Ren X 2021 Opt. Laser Technol. 138 106606 Google Scholar
[26]	Zhan S, Duan H, Pan L, Tu J, Jia D, Yang T, Li J 2021 Phys. Chem. Chem. Phys. 23 8446 Google Scholar

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