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基于润滑理论和滑移边界条件, 构建了考虑接触角迟滞时液滴在均匀加热固体壁面上蒸发的数学模型, 探讨了接触角迟滞对蒸发液滴动力学的影响, 并分析了不同气-液界面张力温度敏感性的液滴蒸发特征. 研究结果表明: 接触角迟滞对液滴蒸发过程有较大影响, 随接触角迟滞增大, 液滴的接触线钉扎时间延长, 铺展阶段和去钉扎阶段时长缩短, 液滴蒸发显著加快; 迟滞角的增大使前进接触角增加, 后退接触角减小, 且后退接触角减小的幅度大于前进接触角增加的幅度. 提高气-液界面张力对温度的敏感性系数可通过减小后退接触角, 改善液滴在壁面上的润湿性, 从而加强液滴传热, 致使加快液滴蒸干. 因此, 改变接触角迟滞和气-液界面张力对温度的敏感性均可实现对液滴运动的调控, 从而控制其蒸发进程.
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关键词:
- 液滴蒸发 /
- 动力学特性 /
- 接触角迟滞 /
- 气-液界面张力温度敏感性
The evaporation process of drops on a solid surface is widely applied to daily life and industrial fields. Both contact angle hysteresis and the sensitivity of gas-liquid interfacial tension to temperature are important factors affecting the drop evaporation reflected in the contact line and contact angle. To investigate the internal mechanism, according to the lubrication theory and slip boundary conditions, we establish a mathematical model of the drop evaporation on a uniformly heated solid wall with considering the effect of contact angle hysteresis. This model is numerically solved by using a coordinate transformation method and Freefem++14.3, a highly efficient solver. The accuracy of the numerical calculation method is verified by comparing the numerical results with experimental results, and the grid independence is validated. The effect of contact angle hysteresis on the dynamics of evaporating drops is discussed, and the evaporation characteristics of drops with different tension sensitivities of the air-liquid interface to temperature are further investigated. The results show that the contact angle hysteresis has an apparent influence on the drop evaporation process which includes drop spreading stage, contact line pinning stage, and depinning stage. In the drop spreading stage, the increase in the hysteresis angle shortens the spreading time, and reduces the spreading velocity and radius, while in the contact line pinning stage, the pinning time is prolonged and the reduction of drop mass is significantly increased with hysteresis angle increasing. In the contact line depinning stage, the contact angle hysteresis reduces the contact angle, and a flatter shape emerges, thereby enhancing the ability to transfer heat and accelerating evaporation as well as shortening the depinning time. In addition, the large hysteresis angle leads to a large advancing contact angle and a small receding contact angle. The reduction in receding contact angle is more notable than the increment of advancing contact angle. The temperature sensitivity coefficient of the gas-liquid interfacial tension can be increased by reducing the receding contact angle, thereby improving the wettability of the drops on the wall enhancing the heat transfer and accelerating the evaporation. Regulating the contact angle hysteresis and the sensitivity of the interfacial tension to temperature can realize the manipulation of the drop movement, thus controlling the evaporation process.-
Keywords:
- drop evaporation /
- dynamics /
- contact angle hysteresis /
- sensitivity of air-liquid interfacial tension to temperature
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图 1 液滴在加热表面铺展示意图
Fig. 1. Schematic of a drop disposed on a horizontally heated substrate.
图 2 计算模型的验证 (a) 接触角的演化过程; (b) 接触线的演化过程; (c) 网格无关性验证
Fig. 2. Verification of the computational model: (a) Evolution of contact angle; (b) evolution of contact line; (c) validation of grid independence.
图 3 不同Δθ时液滴演化过程中的特征参数变化 (a) 接触角; (b) 接触半径; (c) 接触线移动速度; (d) 蒸发剩余质量
Fig. 3. Characteristic parameters of drop evolution with time at different Δθ: (a) Dynamic contact angle; (b) contact line; (c) contact line velocity; (d) remaining mass.
图 5 动态接触角与接触线移动速度关系图
Fig. 5. Relation between the dynamic contact angle and velocity of contact line.
图 4 液滴演化过程轮廓图 (a) t = 10000; (b) t = 50000; (c) t = 70000; (d) t = 74000
Fig. 4. Drop profile during the drop evolution process: (a) t = 10000; (b) t = 50000; (c) t = 70000; (d) t = 74000.
图 6 液滴演化过程中的特征参数变化 (a) 接触角; (b) 接触半径; (c) 接触线移动速度; (d) 蒸发剩余质量
Fig. 6. Characteristic parameters of drop evolution with time: (a) Dynamic contact angle; (b) contact line; (c) contact line velocity; (d) remaining mass.
表 1 不同Δθ对液滴演化时间的影响
Table 1. Effect of varied Δθ on the drop evolution time.
Δθ 钉扎时刻 去钉扎时刻 蒸干时刻 铺展阶段 钉扎阶段 去钉扎阶段 0.27 18910 39750 78000 0—18910 18910—39750 39750—78000 0.35 16530 43250 76200 0—16530 16530—43250 43250—76200 0.40 14620 45100 74600 0—14620 14620—45100 45100—74600 
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表 2 不同迟滞角下θa 和θr 变化
Table 2. Variation in θa and θr of drop with different Δθs
Δθ θa θr Δθa Δθr 0.27 0.966 0.696 0.106 –0.164 0.35 0.997 0.647 0.031 –0.049 0.40 1.016 0.616 0.019 –0.031
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表 3 不同Ωlg时液滴演化过程中参数变化
Table 3. Varieties of parameters during drop evolution with different Ωlg.
Ωlg 钉扎时刻 去钉扎时刻 蒸干时刻 θe θa θr 0.003 18910 39750 78000 0.860 0.966 0.686 0.005 20280 40140 76700 0.837 0.942 0.672 0.01 22200 40260 71000 0.775 0.880 0.610
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[1] Kavehpour P, Ovryn B, McKinley G H 2002 Colloids Surf., A 206 409
Google Scholar
[2] Lee K S, Ivanova N, Starov V M, Hilal N, Dutschk V 2008 Adv. Colloid Interface Sci. 144 54
Google Scholar
[3] Wijshoff H 2010 Phys. Rep. 491 77
Google Scholar
[4] Putnam S A, Briones A M, Byrd L W, Ervin J S, Hanchak M S, White A, Jones J G 2012 Int. J. Heat Mass Transfer 55 5793
Google Scholar
[5] Ye X M, Zhang X S, Li M L, Li C X 2018 Phys. Fluids 30 112103
Google Scholar
[6] Lopes M C, Bonaccurso E 2012 Soft Matter 8 7875
Google Scholar
[7] Kiper I, Fulcrand R, Pirat C, Simon G, Stutz B, Ramos S M M 2015 Colloids Surf., A 482 617
Google Scholar
[8] Eral H B, Mannetje D, Oh J M 2013 Colloid. Polym. Sci. 291 247
Google Scholar
[9] Neumann A W, Good R J 1972 J. Colloid Interface Sci. 38 341
Google Scholar
[10] Johnson R E, Dettre R H 1964 Contact Angle, Wettability, and Adhesion (Washington: American Chemical Society) pp112−135
[11] Dettre R H, Johnson R E 1964 Contact Angle, Wettability, and Adhesion (Washington: American Chemical Society) pp136−144
[12] Yu H Z, Soolaman D M, Rowe A W, Banks J T 2004 ChemPhysChem 5 1035
Google Scholar
[13] Li Y F, Sheng Y J, Tsao H K 2013 Langmuir 29 7802
Google Scholar
[14] Trybala A, Okoye A, Semenov S, Agogo H, Rubio R G, Ortega F, Starov V M 2013 J. Colloid Interface Sci. 403 49
Google Scholar
[15] Kulinich S A, Farzaneh M 2009 Appl. Surf. Sci. 255 4056
Google Scholar
[16] Lin T S, Zeng Y H, Tsay R Y, Lin S Y 2016 J. Taiwan Inst. Chem. Eng. 62 54
Google Scholar
[17] Kuznetsov G V, Feoktistov D V, Orlova E G, Batishcheva K A 2016 Colloid J. 78 335
Google Scholar
[18] Ajaev V S 2005 J. Fluid Mech. 528 279
Google Scholar
[19] Masoud H, Felske J D 2009 Phys. Rev. E 79 016301
Google Scholar
[20] Semenov S, Starov V M, Rubio R G, Agogo H, Velarde M G 2012 Math. Modell. Nat. Phenom. 7 82
Google Scholar
[21] Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892
Google Scholar
[22] Ye X M, Zhang X S, Li M L, Li C X, Dong S 2019 Int. J. Heat Mass Transfer 128 1263
Google Scholar
[23] 叶学民, 李永康, 李春曦 2016 65 104704
Google Scholar
Ye X M, Li Y K, Li C X 2016 Acta Phys. Sin. 65 104704
Google Scholar
[24] Karapetsas G, Craster R V, Matar O K 2011 J. Fluid Mech. 670 5
Google Scholar
[25] 焦云龙, 刘小君, 逄明华, 刘焜 2015 65 016801
Google Scholar
Jiao Y L, Liu X J, Pang M H, Liu K 2015 Acta Phys. Sin. 65 016801
Google Scholar
[26] Nagy M, Škvarla J 2013 Acta Montan. Slovaca 18 125
[27] 王晓东, 彭晓峰, 陆建峰, 王补宣 2003 应用基础与工程科学学报 11 174
Google Scholar
Wang X D, Peng X F, Wang B X 2003 Chin. J. Chem. Eng. 11 174
Google Scholar
[28] Smith M K 1995 J. Fluid Mech. 294 209
Google Scholar
[29] Craster R V, Matar O 2000 J. Fluid Mech. 425 235
Google Scholar
[30] Ma C, Liu J, Xie S, Liu Y 2020 Chem. Eng. Sci. 214 115418
Google Scholar
[31] Vasu B, Dubey A, Bég O A, Gorla R S R 2020 Comput. Biol. Med. 126 104025
Google Scholar
[32] Jiménez Bolaños S, Vernescu B 2017 Phys. Fluids 29 057103
Google Scholar
[33] 朱仙仙, 闵春华, 郭宇虹, 王坤, 解立垚 2021 热科学与技术 20 28
Zhu X X, Min C H, Guo Y H, Wang K, Xie L Y 2021 J. Therm. Sci. Tech. 20 28
[34] Hu H, Larson R G 2005 Langmuir 21 3963
Google Scholar
[35] Gatapova E Y, Semenov A A, Zaitsev D V, Kabov O A 2014 Colloids Surf., A 441 776
Google Scholar
[36] Chu F, Wu X, Zhu Y, Yuan Z 2017 Int. J. Heat Mass Transfer 111 836
Google Scholar
[37] Bormashenko E, Musin A, Zinigrad M 2011 Colloids Surf., A 385 235
Google Scholar
[38] Brutin D, Sobac B (Brutin D Ed.) 2015 Droplet Wetting and Evaporation (Oxford: Academic Press) pp25−30
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