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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.
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Keywords:
- Leidenfrost droplets /
- droplet dynamics /
- evaporation /
- heat transfer
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[14] Gauthier A, Diddens C, Proville R, Lohse D, van der Meer D 2019 Proc. Natl. Acad. Sci. USA 116 1174
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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).
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.
图 3 (a) 不同油面温度To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.
图 4 (a) 从a—i的9个特定时间的液滴动态图; (b), (c) 在To = 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 To = 88.2 ℃.
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.
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).
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.
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Fg, x和Marangoni力Fσ, 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 Fg, x and Marangoni force Fσ, x dominate the three-regimes behavior of droplet dynamics.
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) Tsat/℃ 56.6 密度 ρd/( kg·m–3) 1680 比热容 cpl/(J·m–1·K–1) 1100 潜热 L/(kJ·kg–1) 88 导热率 λd(W·m–1·K–1) 0.057 动力黏度 μd/(kg·m–1·s–1) 0.64×10–3 FC-72
(蒸气)密度 ρv/(kg·m–3) 9.7 比热容 cpv/(J·m–1·K–1) 900 热导率 λv/(W·m–1·K–1) 0.0235 动力黏度 μv/(kg·m–1·s–1) 1.31×10–6 硅油 密度 ρo/(kg·m–3) 960 比热容 cpo/(J·m–1·K–1) 1460 动力黏度 μo/(kg·m–1·s–1) 0.048 表面张力(25 ℃) σo/(N·m–1) 0.0208 
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[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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