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Influence of equilibrium contact angle on spreading dynamics of a heated droplet on a horizontal plate

Ye Xue-Min Li Yong-Kang Li Chun-Xi

Influence of equilibrium contact angle on spreading dynamics of a heated droplet on a horizontal plate

Ye Xue-Min, Li Yong-Kang, Li Chun-Xi
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  • In most of researches about the droplet spreading on a substrate, one adopts aprecursor layer to relieve the stress singularity near the contact line without considering wall properties, which, however, is inapplicable for studying the relationship of the wettability with wall temperature. In this paper, the spreading of a heated droplet on the solid substrate, under the action of the three-phase contact line, is simulated. The influences of the wall temperature on wettability and droplet spreading are examined from the viewpoint of equilibrium contact angle. The simulated results show that when the wall temperature is uniform, the evolution of droplet spreading is dominated only by the gravity, illustrating symmetrical spreading characteristics. When the temperature gradient is applied to the wall, the combination of thermocapillary force and gravity drives the droplet into spreading, therefore the main part of the droplet migrates toward the low temperature region due to the Marangoni effect. The left contact line continually moves toward the left side while the right contact line first moves toward the right side, then turns to the left side after the receding time. The spreading range of the droplet is changed notably because of different travelling speeds of the contact line on both sides. With the increase of the temperature gradient, the Marangoni effect is promoted, resulting in a faster migration toward the low temperature region. A thin film is formed between the contact line in the hotter region and the bulk of the droplet, where the gravity and thermocapillary force dominate the spreading successively. The present simulation shows that the surface wettability is not only dependent on its chemical composition and geometrical morphology, but also closely related to wall temperature. When the sensitivities of the liquid-solid, liquid-gas and solid-gas interfacial tensions to temperature are all identical, the equilibrium contact angle between the droplet and the wall keeps constant, leading to a uniform wettability on the wall. When the liquid-solid interfacial tension or the liquid-gas interfacial tension is more sensitive to temperature than the other two interfaces, the equilibrium contact angle increases and the wettability tends to be worse, presenting a more hydrophobic substrate, which decelerates the spreading of the droplet with the contact line moving to the colder region. As the solid-gas interfacial tension is more sensitive to temperature than the other two interfaces, the equilibrium contact angle tends to lessen, and the contact line feels a more hydrophilic substrate (the droplet wets perfectly when the equilibrium contact angle decreases to zero), hence the spreading is enhanced. The present results indicate that the equilibrium contact angle plays a key role in the evolution of a heated droplet on a horizontal plate. The simulation conclusions can provide a theoretical basis for relevant experimental findings, which promotes the understanding of the relationship between wall temperature and its wettability.
      Corresponding author: Ye Xue-Min, yexuemin@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11202079) and the Natural Science Foundation of Hebei Province, China (Grant No. A2015502058).
    [1]

    Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131

    [2]

    Lee K S, Ivanova N, Starov V M, Hilal N, Dutschk V 2008 Adv. Colloid Interface Sci. 144 54

    [3]

    Zhu J Y, Duan Y Y, Wang X D, Min Q 2014 CIESC Journal 03 765 (in Chinese) [朱君悦, 段远源, 王晓东, 闵琪 2014 化工学报 03 765]

    [4]

    Liu S S, Zhang C H, Zhang H B, Zhou J, He J G, Yin H Y 2013 Chin. Phys. B 22 0106801

    [5]

    Daniel S, Chaudhury M K, Chen J C 2001 Science 291 633

    [6]

    Sato M, Araki K, Matsuura M, Hasegawa K, Endo A 2001 Proceedings of the 2nd Pan Pacific Basin Workshop on Microgravity Sciences Pasadena, CA, May 1-4, 2001 pIF-1123

    [7]

    Pratap V, Moumen N, Subramanian R S 2008 Langmuir 24 5185

    [8]

    Wang X D, Peng X F, Wang B X 2004 Journal of Basic Science and Engineering 11 396 (in Chinese) [王晓东, 彭晓峰, 王补宣 2004 应用基础与工程科学学报 11 396]

    [9]

    Beacham D R, Matar O K, Craster R V 2009 Langmuir 25 14174

    [10]

    Goddard J V, Naire S 2015 J. Fluid Mech. 772 535

    [11]

    Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 174702 (in Chinese) [李春曦, 裴建军, 叶学民 2013 物理学报 62 174702]

    [12]

    Li C X, Chen P Q, Ye X M 2015 Acta Phys. Sin. 64 014702 (in Chinese) [李春曦, 陈朋强, 叶学民 2015 物理学报 64 014702]

    [13]

    Ye X M, Jiang K, Li C X 2013 CIESC Journal 64 3581 (in Chinese) [叶学民, 姜凯, 李春曦 2013 化工学报 64 3581]

    [14]

    Zhao Y P, Yuan Q Z 2013 Advances in Mechanics 43 I0006 (in Chinese) [赵亚溥, 袁泉子 2013力学进展 43 I0006]

    [15]

    Yao Y, Zhou Z W,Hu G H 2013 Acta Phys. Sin. 62 134701 (in Chinese) [姚祎, 周哲玮, 胡国辉 2013 物理学报 62 134701]

    [16]

    Yang C W, He F, Hao P F 2010 Scientia Sinica Chimica 53 912 (in Chinese) [杨常卫, 何枫, 郝鹏飞 2010 中国科学: 化学 53 912]

    [17]

    Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892

    [18]

    Amir A, Reghan J H 2015 Condens. Matter 1507 06549

    [19]

    Hu H B, Chen L B, Bao L Y, Huang S H 2014 Chin. Phys. B 23 074702

    [20]

    Karapetsas G, Craster R V, Matar O K 2011 J. Fluid Mech. 670 5

    [21]

    Mukhopadhyay S, Murisic N, Behringer R P, Kondic L 2011 Phys. Rev. E 83 046302

    [22]

    Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310

    [23]

    Ehrhard P 1993 J. Fluid Mech. 257 463

    [24]

    Gomba J M, Homsy G M 2010 J. Fluid Mech. 647 125

  • [1]

    Craster R V, Matar O K 2009 Rev. Mod. Phys. 81 1131

    [2]

    Lee K S, Ivanova N, Starov V M, Hilal N, Dutschk V 2008 Adv. Colloid Interface Sci. 144 54

    [3]

    Zhu J Y, Duan Y Y, Wang X D, Min Q 2014 CIESC Journal 03 765 (in Chinese) [朱君悦, 段远源, 王晓东, 闵琪 2014 化工学报 03 765]

    [4]

    Liu S S, Zhang C H, Zhang H B, Zhou J, He J G, Yin H Y 2013 Chin. Phys. B 22 0106801

    [5]

    Daniel S, Chaudhury M K, Chen J C 2001 Science 291 633

    [6]

    Sato M, Araki K, Matsuura M, Hasegawa K, Endo A 2001 Proceedings of the 2nd Pan Pacific Basin Workshop on Microgravity Sciences Pasadena, CA, May 1-4, 2001 pIF-1123

    [7]

    Pratap V, Moumen N, Subramanian R S 2008 Langmuir 24 5185

    [8]

    Wang X D, Peng X F, Wang B X 2004 Journal of Basic Science and Engineering 11 396 (in Chinese) [王晓东, 彭晓峰, 王补宣 2004 应用基础与工程科学学报 11 396]

    [9]

    Beacham D R, Matar O K, Craster R V 2009 Langmuir 25 14174

    [10]

    Goddard J V, Naire S 2015 J. Fluid Mech. 772 535

    [11]

    Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 174702 (in Chinese) [李春曦, 裴建军, 叶学民 2013 物理学报 62 174702]

    [12]

    Li C X, Chen P Q, Ye X M 2015 Acta Phys. Sin. 64 014702 (in Chinese) [李春曦, 陈朋强, 叶学民 2015 物理学报 64 014702]

    [13]

    Ye X M, Jiang K, Li C X 2013 CIESC Journal 64 3581 (in Chinese) [叶学民, 姜凯, 李春曦 2013 化工学报 64 3581]

    [14]

    Zhao Y P, Yuan Q Z 2013 Advances in Mechanics 43 I0006 (in Chinese) [赵亚溥, 袁泉子 2013力学进展 43 I0006]

    [15]

    Yao Y, Zhou Z W,Hu G H 2013 Acta Phys. Sin. 62 134701 (in Chinese) [姚祎, 周哲玮, 胡国辉 2013 物理学报 62 134701]

    [16]

    Yang C W, He F, Hao P F 2010 Scientia Sinica Chimica 53 912 (in Chinese) [杨常卫, 何枫, 郝鹏飞 2010 中国科学: 化学 53 912]

    [17]

    Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892

    [18]

    Amir A, Reghan J H 2015 Condens. Matter 1507 06549

    [19]

    Hu H B, Chen L B, Bao L Y, Huang S H 2014 Chin. Phys. B 23 074702

    [20]

    Karapetsas G, Craster R V, Matar O K 2011 J. Fluid Mech. 670 5

    [21]

    Mukhopadhyay S, Murisic N, Behringer R P, Kondic L 2011 Phys. Rev. E 83 046302

    [22]

    Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310

    [23]

    Ehrhard P 1993 J. Fluid Mech. 257 463

    [24]

    Gomba J M, Homsy G M 2010 J. Fluid Mech. 647 125

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  • Received Date:  25 December 2015
  • Accepted Date:  05 February 2016
  • Published Online:  05 May 2016

Influence of equilibrium contact angle on spreading dynamics of a heated droplet on a horizontal plate

    Corresponding author: Ye Xue-Min, yexuemin@163.com
  • 1. Key Laboratory of Condition Monitoring and Control for Power Plant Equipment, North China Electric Power University, Baoding 071003, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11202079) and the Natural Science Foundation of Hebei Province, China (Grant No. A2015502058).

Abstract: In most of researches about the droplet spreading on a substrate, one adopts aprecursor layer to relieve the stress singularity near the contact line without considering wall properties, which, however, is inapplicable for studying the relationship of the wettability with wall temperature. In this paper, the spreading of a heated droplet on the solid substrate, under the action of the three-phase contact line, is simulated. The influences of the wall temperature on wettability and droplet spreading are examined from the viewpoint of equilibrium contact angle. The simulated results show that when the wall temperature is uniform, the evolution of droplet spreading is dominated only by the gravity, illustrating symmetrical spreading characteristics. When the temperature gradient is applied to the wall, the combination of thermocapillary force and gravity drives the droplet into spreading, therefore the main part of the droplet migrates toward the low temperature region due to the Marangoni effect. The left contact line continually moves toward the left side while the right contact line first moves toward the right side, then turns to the left side after the receding time. The spreading range of the droplet is changed notably because of different travelling speeds of the contact line on both sides. With the increase of the temperature gradient, the Marangoni effect is promoted, resulting in a faster migration toward the low temperature region. A thin film is formed between the contact line in the hotter region and the bulk of the droplet, where the gravity and thermocapillary force dominate the spreading successively. The present simulation shows that the surface wettability is not only dependent on its chemical composition and geometrical morphology, but also closely related to wall temperature. When the sensitivities of the liquid-solid, liquid-gas and solid-gas interfacial tensions to temperature are all identical, the equilibrium contact angle between the droplet and the wall keeps constant, leading to a uniform wettability on the wall. When the liquid-solid interfacial tension or the liquid-gas interfacial tension is more sensitive to temperature than the other two interfaces, the equilibrium contact angle increases and the wettability tends to be worse, presenting a more hydrophobic substrate, which decelerates the spreading of the droplet with the contact line moving to the colder region. As the solid-gas interfacial tension is more sensitive to temperature than the other two interfaces, the equilibrium contact angle tends to lessen, and the contact line feels a more hydrophilic substrate (the droplet wets perfectly when the equilibrium contact angle decreases to zero), hence the spreading is enhanced. The present results indicate that the equilibrium contact angle plays a key role in the evolution of a heated droplet on a horizontal plate. The simulation conclusions can provide a theoretical basis for relevant experimental findings, which promotes the understanding of the relationship between wall temperature and its wettability.

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