Interaction and motion of two neighboring Leidenfrost droplets on oil surface

Wang Hao; Xu Jin-Liang

doi:10.7498/aps.72.20221822

Abstract

Evaporation of droplets on a hot oil surface is a natural phenomenon. However, most of existing studies focus on the evaporation of a single droplet, and the evaporation of multiple droplets is insufficiently understood. Here, we explore the Leidenfrost evaporation of two identical FC-72 droplets on the surface of a hot oil bath. The oil temperature ranges from 73.6 to 126.6 ℃, and the evaporation of droplets each with an initial diameter of 1.5 mm is recorded by an infrared thermographer and a high-speed camera. The shallow oil depth keeps the oil temperature uniform relatively in the slot compared with that in the deep liquid pool due to the larger ratio of the surface area for copper-oil contact to the slot volume. We find that the neighboring droplets evaporate in three stages: non-coalescing, bouncing, and separating. The radius of neighboring Leidenfrost droplets follows the power law R(t)~(1−t/τ)ⁿ, where τ is the characteristic droplet lifetime and n is an exponent factor. Moreover, the diffusion-mediated interaction between the neighboring droplets slows down the evaporation process compared with the action of isolated Leidenfrost droplet and leads to an asymmetric temperature field on the droplet surface, thereby breaking the balance of the forces acting on the droplets. A simple dual-droplet evaporation model is developed which considers four forces acting horizontally on the droplet, namely, the Marangoni force resulting from the non-uniform droplet temperature, the gravity component, the lubrication-propulsion force, and the viscous drag force. Scale analysis shows that the Marangoni force and gravity component dominate dual-droplet evaporation dynamics. In the non-coalescence stage, the gravity component induces the droplets to attract each other, while the vapor film trapped between droplets prevents them from directly contacting. When the droplets turn smaller, the gravity component is insufficient to overcome the Marangoni force. Hence, the droplets separate in the final evaporation stage. Finally, we conclude that the competition between Marangoni force and gravitational force is the origin of the bounce evaporation by comparing the theoretical and experimental transition times at distinct stages. This study contributes to explaining the complex Leidenfrost droplet dynamics and evaporation mechanism.

Keywords:

Authors and contacts

Wang Hao¹,
Xu Jin-Liang^1,2

1.
Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, China
2.
Key Laboratory of Power Station Energy Transfer Conversion and System, Ministry of Education, North China Electric Power University, Beijing 102206, China

Corresponding author: Xu Jin-Liang, xjl@ncepu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52130608, 51821004).

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References

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Cited By

图 1 (a) 实验装置图; (b), (c)放大的带有薄液池的加热铜块(1-高速摄像机, 2-红外高速相机, 3-微量注射器, 4-位移调节平台, 5-电源变压器, 6-PID温度控制器, 7-带薄液池的铜块, 8-光源, 9-用于释放液滴的冷却针头)

Figure 1. Photograph of experimental setup (a) and enlarged copper block with thin liquid pool (b), (c) (1-high speed camera, 2-infrared radiation image camera, 3-micro-syringe pump, 4-displacement adjustment platform, 5-voltage transformer, 6-PID temperature controller, 7- copper block with thin liquid pool, 8-light source, 9-cooled dual-needles for droplet release).

DownLoad: Full-Size Img PowerPoint

图 2 (a) 油池在水平方向和深层方向的温度分布; (b) 硅油和FC-72的表面温度测量的校准; (c) 通过红外测量定位液滴界面的原理

Figure 2. (a) Temperature dispersion in the oil bath’s horizontal and deep directions; (b) calibration of surface temperature measurement for silicon oil and FC-72; (c) the principle to locate the drop interface by IR measurement.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 不同油面温度T_o下液滴寿命的两种分区; (b) 油面温度为88.2 ℃和128.0 ℃时液滴的直径与时间的关系

Figure 3. (a) Droplet diameters versus time at oil surface temperature of 88.2 ℃ and 128.0 ℃; (b) two regimes distribution of droplet life time at different oil surface temperatures.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 从a—i的9个特定时间的液滴动态图; (b), (c) 在T_o = 88.2 ℃时, 液滴整个寿命期的3种蒸发行为

Figure 4. (a) Droplet dynamics at nine specific time from a to i; (b), (c) three-regimes behavior of droplet dynamics during the whole droplet lifetime at T_o = 88.2 ℃.

DownLoad: Full-Size Img PowerPoint

图 5 双滴接触时刻, 液滴区域和背景区域的温度分布

Figure 5. Temperature distribution on the droplet-dominated and background-dominated regions at contact time.

DownLoad: Full-Size Img PowerPoint

图 6 红外相机俯拍得到液滴表面的温度轮廓线 (温度随着圆周角变化)

Figure 6. Droplet surface temperatures along top view circle (temperatures are plotted versus circumference angles).

DownLoad: Full-Size Img PowerPoint

图 7 油面双滴非聚合蒸发的力学分析　(a) 施加在倾斜液滴上的各种力; (b) 润滑推动力; (c) Leidenfrost蒸气层与空气交界处的Marangoni力; (d) 气膜出口位置的液滴表面张力圆周分布; (e) 沿x方向分布的液滴表面温度; (f) 作用在倾斜油面上的液滴重力; (g) 油面倾斜角α 与液滴邦德数Bo之间的关系

Figure 7. Force analysis explaining the non-coalescence phenomenon of dual-droplets over oil surface: (a) Various forces exerted on inclined droplets; (b) lubrication-propulsion force; (c) Marangoni force along circumference direction at the junction between Leidenfrost vapor layer and air; (d) distribution of droplet surface tension along the x-direction at the vapor outlet; (e) distribution of droplet surface temperature along the x-direction; (f) droplet gravity on the inclined oil surface; (g) the relationship between the oil surface’s inclination angle α and the droplet’s bond number.

DownLoad: Full-Size Img PowerPoint

图 8 液滴温度和各种力的变化　(a) 测量的液滴温度与时间的关系, 以及用简单的拟合得到的两条曲线; (b) 各种力大小的比较; (c) 竞争的重力F_{g, x}和Marangoni力F_{σ, x}主导了液滴动力学的三态行为

Figure 8. Variation of droplet temperatures and various forces: (a) The measured droplet temperature versus time and two curve obtained with simple fitting; (b) comparison of various forces magnitudes; (c) competing gravity force F_{g, x} and Marangoni force F_{σ, x} dominate the three-regimes behavior of droplet dynamics.

DownLoad: Full-Size Img PowerPoint

表 1 在1 atm (1 atm = 1.013×10⁵ Pa) 的压力下, FC-72和硅油的物性参数

Table 1. Physical properties of FC-72 and silicon oil at 1 atm (1 atm = 1.013×10⁵ Pa).

	参数	值
FC-72 (液体)	饱和温度 (1 atm) T_sat/℃	56.6
	密度 ρ_d/( kg·m^–3)	1680
	比热容 c_pl/(J·m^–1·K^–1)	1100
	潜热 L/(kJ·kg^–1)	88
	导热率 λ_d(W·m^–1·K^–1)	0.057
	动力黏度 μ_d/(kg·m^–1·s^–1)	0.64×10^–3
FC-72 (蒸气)	密度 ρ_v/(kg·m^–3)	9.7
	比热容 c_pv/(J·m^–1·K^–1)	900
	热导率 λ_v/(W·m^–1·K^–1)	0.0235
	动力黏度 μ_v/(kg·m^–1·s^–1)	1.31×10^–6
硅油	密度 ρ_o/(kg·m^–3)	960
	比热容 c_po/(J·m^–1·K^–1)	1460
	动力黏度 μ_o/(kg·m^–1·s^–1)	0.048
	表面张力(25 ℃) σ_o/(N·m^–1)	0.0208

DownLoad: CSV

[1]	Biance A L, Clanet C, Quééréé D 2003 Phys. Fluids 15 1632 Google Scholar
[2]	Tran T, Staat H J, Prosperetti A, Sun C, Lohse D 2012 Phys. Rev. Lett. 108 036101 Google Scholar
[3]	Davanlou A, Kumar R 2015 Sci. Rep. 5 9531 Google Scholar
[4]	Luo C, Mrinal M, Wang X 2017 Sci. Rep. 7 12018 Google Scholar
[5]	Abdelaziz R, Disci-Zayed D, Hedayati M K, Pohls J H, Zillohu A U, Erkartal B, Chakravadhanula V S, Duppel V, Kienle L, Elbahri M 2013 Nat. Commun. 4 2400 Google Scholar
[6]	Schwenzer B 2014 MRS Bull. 39 7 Google Scholar
[7]	Kleinstreuer C, Zhang Z 2010 Annu. Rev. Fluid Mech. 42 301 Google Scholar
[8]	Bouillant A, Mouterde T, Bourrianne P, Lagarde A, Clanet C, Quéré D 2018 Nat. Phys. 14 1188 Google Scholar
[9]	Graeber G, Regulagadda K, Hodel P, Kuttel C, Landolf D, Schutzius T M, Poulikakos D 2021 Nat. Commun. 12 1727 Google Scholar
[10]	Brunet P, Snoeijer J H 2011 Eur. Phys. J. Spec. Top. 192 207 Google Scholar
[11]	Linke H, Aleman B J, Melling L D, Taormina M J, Francis M J, Dow-Hygelund C C, Narayanan V, Taylor R P, Stout A 2006 Phys. Rev. Lett. 96 154502 Google Scholar
[12]	Bouillant A, Lafoux B, Clanet C, Quere D 2021 Soft Matter 17 8805 Google Scholar
[13]	van Limbeek M A J, Sobac B, Rednikov A, Colinet P, Snoeijer J H 2019 J. Fluid Mech. 863 1157 Google Scholar
[14]	Gauthier A, Diddens C, Proville R, Lohse D, van der Meer D 2019 Proc. Natl. Acad. Sci. USA 116 1174 Google Scholar
[15]	Matsumoto R, Hasegawa K 2021 Sci. Rep. 11 3954 Google Scholar
[16]	Gauthier A, Lajoinie G, Snoeijer J H, van der Meer D 2020 Soft Matter 16 4043 Google Scholar
[17]	Maquet L, Sobac B, Darbois-Texier B, Duchesne A, Brandenbourger M, Rednikov A, Colinet P, Dorbolo S 2016 Phys. Rev. Fluids 1 053902
[18]	Pacheco-Vazquez F, Ledesma-Alonso R, Palacio-Rangel J L, Moreau F 2021 Phys. Rev. Lett. 127 204501 Google Scholar
[19]	Carrier O, Shahidzadeh-Bonn N, Zargar R, Aytouna M, Habibi M, Eggers J, Bonn D 2016 J. Fluid Mech. 798 774 Google Scholar
[20]	Schäfle C, Bechinger C, Rinn B, David C, Leiderer P 1999 Phys. Rev. Lett. 83 5302 Google Scholar
[21]	Kobayashi M, Makino M, Okuzono T, Doi M 2010 J. Phys. Soc. Jpn. 79 044802
[22]	Couder Y, Protiere S, Fort E, Boudaoud A 2005 Nature 437 208 Google Scholar
[23]	Harris D M, Bush J W M 2014 J. Fluid Mech. 739 444 Google Scholar
[24]	Bozzano G, Dente M 2013 Icheap-11:11 th International Conference on Chemical and Process Engineering, Pts 1-4 32 1489 Google Scholar
[25]	Valani R N, Slim A C, Simula T 2019 Phys. Rev. Lett. 123 024503 Google Scholar
[26]	Yan X, Xu J, Meng Z, Xie J, Liu G 2020 Langmuir 36 1680 Google Scholar
[27]	Xu J L, Yan X, Liu G H, Xie J 2019 Nano Energy 57 791 Google Scholar
[28]	Zawala J, Dorbolo S, Terwagne D, Vandewalle N, Malysa K 2011 Soft Matter 7 6719 Google Scholar
[29]	Khilifi D, Foudhil W, Fahem K, Harmand S, Ben Jabrallah S 2019 Therm. Sci. 23 1105 Google Scholar
[30]	Wang H, Xu J, Ma X, Xie J 2022 Phys. Fluids 34 093320
[31]	Inamuro T, Tajima S, Ogino F 2004 Int. J. Heat Mass Transfer 47 4649 Google Scholar
[32]	Leong F Y, Le D V 2020 Phys. Fluids 32 062102
[33]	Annamalai K, Ryan W 1992 Prog. Energy Combust. Sci. 18 221 Google Scholar
[34]	Zheng S F, Eimann F, Philipp C, Fieback T, Gross U 2019 Int. J. Heat Mass Transfer 141 34 Google Scholar
[35]	Annamalai K, Ryan W, Chandra S 1993 J. Heat Transfer 115 707 Google Scholar
[36]	Sokuler M, Auernhammer G K, Liu C J, Bonaccurso E, Butt H J 2010 Epl. Europhys. Lett. 89 36004 Google Scholar
[37]	Pradhan T K, Panigrahi P K 2016 Colloid Surface A 500 154 Google Scholar
[38]	Larson R G 2014 AlChE J. 60 1538 Google Scholar
[39]	Fairhurst D J 2022 J. Fluid Mech. 934 F1
[40]	Wray A W, Wray P S, Duffy B R, Wilson S K 2021 Phys. Rev. Fluids 6 073604
[41]	Wray A W, Duffy B R, Wilson S K 2020 J. Fluid Mech. 884 A45
[42]	Bergman T L, Bergman T L, Incropera F P, Dewitt D P, Lavine A S 2011 Fundamentals of Heat and Mass Transfer (John Wiley & Sons)
[43]	Yu X, Xu J 2020 Appl. Phys. Lett. 116 253903
[44]	Ding Y J, Liu J 2016 Appl. Phys. Lett. 109 121904
[45]	Yan X, Xu J, Meng Z, Xie J, Wang H 2020 Small 16 e2001548 Google Scholar
[46]	Janssens S D, Koizumi S, Fried E 2017 Phys. Fluids 29 032103

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