Effect and relational analysis of physical parameters on coalescence-induced self-propelled jumping of droplets

Wang Yu-Hang; Yuan Meng; Ming Ping-Jian

doi:10.7498/aps.70.20201714

Abstract

Coalescence-induced self-propelled jumping of droplets on superhydrophobic surfaces has been widely concerned because of a great number of potential applications such as in the enhancement of condensation heat transfer, self-cleaning and anti-icing. The droplet jumping phenomenon exists in a gas-liquid two-phase system, and the physical parameters of fluid cannot be ignored. However, there are few reports on the influence of physical parameters on droplet jumping dynamics at present. In this paper, the three-dimensional volume-of-fluid method is used to simulate the coalescence-induced self-propelled jumping behaviors of droplets, then the energy terms are studied, and finally the grey relational analysis method is used to calculate the relation degree of the change of physical parameters (the viscosity and the density) to the real jumping velocity and the real solid-liquid contact time at the droplet departure time, respectively. Based on the changing trend of jumping velocity, the process of coalescence-induced self-propelled jumping can be divided into four stages, namely, the expansion of liquid bridge, the impact between the liquid bridge and the surface, the droplet departure from the surface, and the deceleration and oscillation in the air. Under the condition of dimensionless time, the dynamic characteristics of coalescence and jumping of droplets are affected only by Oh number, which is independent of the viscosity and the density. In addition, the change of Oh number only affects the above third stage of droplet departure from the surface. Under the condition of real time, the varied viscosity has no connection with the real time of droplet coalescence, and it only changes the real time of the third stage before droplet jumping. Meanwhile, the dimensionless jumping velocity decreases with Oh number increasing, while the real jumping velocity increases when the viscosity and the density both descend. According to the calculated results of grey relational degree, the relation between the change of viscosity and the real jumping velocity is greater, while the relation between the change of density and the real contact time is greater. This work not only is favorable for a better understanding of droplet jumping, but also provides more ideas and theoretical bases for follow-up relevant studies.

Keywords:

Authors and contacts

1.
College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China
2.
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China

Corresponding author: Ming Ping-Jian, mingpj@mail.sysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51479038), the Fundamental Research Funds for the Central Universities, China (Grant No. HEUCFP201711), and the China Scholarship Council (Grant No. 202006680020)

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References

[1]	Boreyko J B, Chen C H 2009 Phys. Rev. Lett. 103 184501 Google Scholar
[2]	Chen X, Wu J, Ma R, Hua M, Koratkar N, Yao S, Wang Z 2011 Adv. Funct. Mater. 21 4617 Google Scholar
[3]	Miljkovic N, Enright R, Nam Y, Lopez K, Dou N, Sack J, Wang E N 2013 Nano Lett. 13 179 Google Scholar
[4]	He M, Ding Y, Chen J, Song Y 2016 ACS Nano 10 9456 Google Scholar
[5]	Han T, Kwak H J, Kim J H, Kwon J T, Kim M H 2019 Langmuir 35 9093 Google Scholar
[6]	Hou Y, Yu M, Chen X, Wang Z, Yao S 2015 ACS Nano 9 71 Google Scholar
[7]	Zhu J, Luo Y, Tian J, Li J, Gao X 2015 ACS Appl. Mater. Interfaces 7 10660 Google Scholar
[8]	Zhao Y, Luo Y, Zhu J, Li J, Gao X 2015 ACS Appl. Mater. Interfaces 7 11719 Google Scholar
[9]	Watson G S, Gellender M, Watson J A 2014 Biofouling 30 427 Google Scholar
[10]	Wisdom K M, Watson J A, Qu X, Liu F, Watson G S, Chen C H 2013 Proc. Natl. Acad. Sci. U. S. A. 110 7992 Google Scholar
[11]	Chavez R L, Liu F, Feng J J, Chen C H 2016 Appl. Phys. Lett. 109 011601 Google Scholar
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[19]	Wang K, Li R, Liang Q, Jiang R, Zheng Y, Lan Z, Ma X 2017 Appl. Phys. Lett. 111 061603 Google Scholar
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[23]	Khatir Z, Kubiak K Z, Jimack P K, Mathia T G 2016 Appl. Therm. Eng. 106 1337 Google Scholar
[24]	Chu F, Yuan Z, Zhang X, Wu X 2018 Int. J. Heat Mass Transfer 121 315 Google Scholar
[25]	Attarzadeh R, Dolatabadi A 2017 Phys. Fluids 29 012104 Google Scholar
[26]	Liang Z, Keblinski P 2015 Appl. Phys. Lett. 107 143105 Google Scholar
[27]	Gao S, Liao Q, Liu W, Liu Z 2018 J. Phys. Chem. Lett. 9 13 Google Scholar
[28]	Wang Y, Ming P 2021 J. Appl. Phys. 129 014702 Google Scholar
[29]	刘天庆, 孙玮, 李香琴, 孙相彧, 艾宏儒 2014 63 086801 Google Scholar Liu T Q, Sun W, Li X Q, Sun X Y, Ai H R 2014 Acta Phys. Sin. 63 086801 Google Scholar
[30]	Mouterde T, Nguyen T V, Takahashi H, Clanet C, Shimoyama I, Quéré D 2017 Phys. Rev. Fluids 2 112001 Google Scholar
[31]	王晨阳, 段倩倩, 周凯, 姚静, 苏敏, 傅意超, 纪俊羊, 洪鑫, 刘雪芹, 汪志勇 2020 69 100701 Google Scholar Wang C Y, Duan Q Q, Zhou K, Yao J, Su M, Fu Y C, Ji J Y, Hong X, Liu X Q, Wang Z Y 2020 Acta Phys. Sin. 69 100701 Google Scholar

Cited By

图 1 计算域的边界条件与网格

Figure 1. Boundary conditions and grids of computational domain.

DownLoad: Full-Size Img PowerPoint

图 2 不同网格尺寸条件下的最大真实弹跳速度

Figure 2. Maximum real jumping velocity with different mesh sizes of core region.

DownLoad: Full-Size Img PowerPoint

图 3 不同黏度比条件下液滴的聚并和自弹跳过程　(a), (f), (k) t^* = 0.168; (b), (g), (l) t^* = 0.604; (c), (h), (m) t^* = 1.309; (d), (i), (n) t^* = 2.686; (e), (j), (o) t^* = 3.257

Figure 3. Coalescence and jumping process of droplets with different viscosity ratios: (a), (f), (k) t^* = 0.168; (b), (g), (l) t^* = 0.604; (c), (h), (m) t^* = 1.309; (d), (i), (n) t^* = 2.686; (e), (j), (o) t^* = 3.257.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 不同黏度比时液滴质心处的无量纲弹跳速度; (b) 黏度变化对液滴跳离表面前所经历的各个阶段的无量纲持续时间的影响

Figure 4. (a) Dimensionless jumping velocity of droplet with different viscosity ratios; (b) effects of the change of viscosity on the dimensionless duration of each stage prior to droplet jumping.

DownLoad: Full-Size Img PowerPoint

图 5 不同黏度比条件下流场的速度矢量图　(a), (d), (g) t^* = 1.309; (b), (e), (h) t^* = 2.686; (c), (f), (i) t^* = 3.257

Figure 5. Vectors of flow field with different viscosity ratios: (a), (d), (g) t^* = 1.309; (b), (e), (h) t^* = 2.686; (c), (f), (i) t^* = 3.257.

DownLoad: Full-Size Img PowerPoint

图 6 (a) 不同黏度比时聚并自弹跳过程中表面能的变化; (b) 不同黏度比的液滴在跳起时具有的黏性耗散能; (c) 不同黏度比的液滴在跳起时刻具有的动能

Figure 6. (a) Surface energy variation with different viscosity ratios during the coalescence and jumping process; (b) viscous dissipation energy of jumping droplets with different viscosity ratios at departure time; (c) kinetic energy of jumping droplets with different viscosity ratios at departure time.

DownLoad: Full-Size Img PowerPoint

图 7 不同密度比条件下液滴的聚并和自弹跳过程　(a), (f), (k) t^* = 0.168; (b), (g), (l) t^* = 0.604; (c), (h), (m) t^* = 1.309; (d), (i), (n) t^* = 2.686; (e), (j), (o) t^* = 3.257

Figure 7. Coalescence and jumping process of droplets with different density ratios: (a), (f), (k) t^* = 0.168; (b), (g), (l) t^* = 0.604; (c), (h), (m) t^* = 1.309; (d), (i), (n) t^* = 2.686; (e), (j), (o) t^* = 3.257.

DownLoad: Full-Size Img PowerPoint

图 8 (a) 密度变化对液滴跳离表面前所经历的各个阶段的无量纲持续时间的影响; (b) 密度变化对液滴跳离表面前所经历的各个阶段的真实持续时间的影响; (c)不同密度比时液滴质心处的无量纲弹跳速度

Figure 8. (a) Effect of the change of density on the dimensionless duration of each stage prior to droplet jumping; (b) effect of the change of density on the real time of each stage prior to droplet jumping; (c) dimensionless jumping velocity of droplet with different density ratios.

DownLoad: Full-Size Img PowerPoint

图 9 (a) 不同密度比时聚并自弹跳过程中表面能的变化; (b) 不同密度比的液滴在跳起时具有的黏性耗散能; (c) 不同密度比的液滴在跳起时具有的动能

Figure 9. (a) Surface energy variation with different density ratios during the coalescence and jumping process; (b) viscous dissipation energy of jumping droplets with different density ratios at departure time; (c) kinetic energy of jumping droplets with different density ratios at departure time.

DownLoad: Full-Size Img PowerPoint

图 10 不同密度比条件下流场的速度矢量图　(a), (d), (g) t^* = 1.309; (b), (e), (h) t^* = 2.686; (c), (f), (i) t^* = 3.257

Figure 10. Vectors of flow field with different density ratios: (a), (d), (g) t^* = 1.309; (b), (e), (h) t^* = 2.686; (c), (f), (i) t^* = 3.257.

DownLoad: Full-Size Img PowerPoint

表 1 流体物性参数

Table 1. Physical parameters of fluids.

温度T/℃ 表面张力系数σ/(N·m^–1) 液体密度ρ_l/(kg·m^–3) 液体黏度μ_l/(Pa·s) 气体密度ρ_g/(kg·m^–3) 气体黏度μ_g/(Pa·s)

20 0.072 998 1.071 × 10^–3 1.19 1.8 × 10^–5

DownLoad: CSV

表 2 物性参数变化分别与真实弹跳速度和真实接触时间的关联度

Table 2. Relational degree of the change of physical parameters to the real jumping velocity and the real contact time, respectively, at droplet departure time.

参考序列/比较序列黏度μ_l 密度ρ_l

关联度r_{0i, velocity} (弹跳速度) 0.758 0.684
关联度r_{0i, time} (接触时间) 0.741 0.771

DownLoad: CSV

map

[1]	Boreyko J B, Chen C H 2009 Phys. Rev. Lett. 103 184501 Google Scholar
[2]	Chen X, Wu J, Ma R, Hua M, Koratkar N, Yao S, Wang Z 2011 Adv. Funct. Mater. 21 4617 Google Scholar
[3]	Miljkovic N, Enright R, Nam Y, Lopez K, Dou N, Sack J, Wang E N 2013 Nano Lett. 13 179 Google Scholar
[4]	He M, Ding Y, Chen J, Song Y 2016 ACS Nano 10 9456 Google Scholar
[5]	Han T, Kwak H J, Kim J H, Kwon J T, Kim M H 2019 Langmuir 35 9093 Google Scholar
[6]	Hou Y, Yu M, Chen X, Wang Z, Yao S 2015 ACS Nano 9 71 Google Scholar
[7]	Zhu J, Luo Y, Tian J, Li J, Gao X 2015 ACS Appl. Mater. Interfaces 7 10660 Google Scholar
[8]	Zhao Y, Luo Y, Zhu J, Li J, Gao X 2015 ACS Appl. Mater. Interfaces 7 11719 Google Scholar
[9]	Watson G S, Gellender M, Watson J A 2014 Biofouling 30 427 Google Scholar
[10]	Wisdom K M, Watson J A, Qu X, Liu F, Watson G S, Chen C H 2013 Proc. Natl. Acad. Sci. U. S. A. 110 7992 Google Scholar
[11]	Chavez R L, Liu F, Feng J J, Chen C H 2016 Appl. Phys. Lett. 109 011601 Google Scholar
[12]	Boreyko J B, Collier C P 2013 ACS Nano 7 1618 Google Scholar
[13]	Wiedenheft K F, Guo H A, Qu X, Boreyko J B, Liu F, Zhang K, Eid F, Choudhury A, Li Z, Chen C H 2017 Appl. Phys. Lett. 110 141601 Google Scholar
[14]	Liu F, Ghigliotti G, Feng J J, Chen C H 2014 J. Fluid Mech. 752 39 Google Scholar
[15]	Liu F, Ghigliotti G, Feng J J, Chen C H 2014 J. Fluid Mech. 752 22 Google Scholar
[16]	Farokhirad S, Morris J F, Lee T 2015 Phys. Fluids 27 102102 Google Scholar
[17]	Farokhirad S, Lee T 2017 Int. J. Multiphase Flow 95 220 Google Scholar
[18]	Shi Y, Tang G H, Xia H H 2015 Int. J. Heat Mass Transfer 88 445 Google Scholar
[19]	Wang K, Li R, Liang Q, Jiang R, Zheng Y, Lan Z, Ma X 2017 Appl. Phys. Lett. 111 061603 Google Scholar
[20]	Wang Y, Ming P 2018 AIP Adv. 8 065320 Google Scholar
[21]	Wang Y, Ming P 2019 Phys. Fluids 31 122108 Google Scholar
[22]	Wasserfall J, Figueiredo P, Kneer R, Rohlfs W, Pischke P 2017 Phys. Rev. Fluids 2 123601 Google Scholar
[23]	Khatir Z, Kubiak K Z, Jimack P K, Mathia T G 2016 Appl. Therm. Eng. 106 1337 Google Scholar
[24]	Chu F, Yuan Z, Zhang X, Wu X 2018 Int. J. Heat Mass Transfer 121 315 Google Scholar
[25]	Attarzadeh R, Dolatabadi A 2017 Phys. Fluids 29 012104 Google Scholar
[26]	Liang Z, Keblinski P 2015 Appl. Phys. Lett. 107 143105 Google Scholar
[27]	Gao S, Liao Q, Liu W, Liu Z 2018 J. Phys. Chem. Lett. 9 13 Google Scholar
[28]	Wang Y, Ming P 2021 J. Appl. Phys. 129 014702 Google Scholar
[29]	刘天庆, 孙玮, 李香琴, 孙相彧, 艾宏儒 2014 63 086801 Google Scholar Liu T Q, Sun W, Li X Q, Sun X Y, Ai H R 2014 Acta Phys. Sin. 63 086801 Google Scholar
[30]	Mouterde T, Nguyen T V, Takahashi H, Clanet C, Shimoyama I, Quéré D 2017 Phys. Rev. Fluids 2 112001 Google Scholar
[31]	王晨阳, 段倩倩, 周凯, 姚静, 苏敏, 傅意超, 纪俊羊, 洪鑫, 刘雪芹, 汪志勇 2020 69 100701 Google Scholar Wang C Y, Duan Q Q, Zhou K, Yao J, Su M, Fu Y C, Ji J Y, Hong X, Liu X Q, Wang Z Y 2020 Acta Phys. Sin. 69 100701 Google Scholar

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