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The thermocapillary migration characteristics of a self-wetting drop on the non-uniformly heated, horizontal, solid substrate are investigagted by numerical simulation. Based on the lubrication theory, an evolution equation for the height of the two-dimensional drop is established. The substrate underlying the drop is subjected to a temperature gradient which induces surface tension gradient-driven drop deformation and migration. The self-rewetting fluid has non-monotonic dependence of the surface tension on temperature with a well-defined minimum, and the position of the minimum corresponding to the temperature on the substrate is called the critical point. The effect of the relationship between the critical point and the drop position on drop dynamics is analyzed. With the temperature sensitivity coefficient of three interfaces under the same condition, the substrate is illustrated with constant wettability. The direction of drop migration will alter as the initial drop location moves to the left relative to the critical point position, resulting from the variation of the interplay among thermocapillary, gravity, and capillarity forces within the drop. But the drop always migrates toward the high interfacial tension region due to the thermocapillary force. In the presence of substrate wettability variations, the drop migrates toward the low temperature region no matter where the drop is placed relative to the critical point. This is due to the fact that the deterioration of substrate wettability on the right side of the drop prevents the drop from migrating toward the hot region. Under the critical point being on the left or within the drop, as the initial drop location moves to the left relative to the critical point position, the enhancement of the thermocapillary force toward the left leads to increased moving speed of the left contact line and increased spreading area. When the critical point is positioned on the outer right side of the drop, the speed of the left contact line sharply decreases at t=6103, caused by the suddenly deteriorating substrate wettability. Hence, it is effective to manipulate the self-wetting drop movement by regulating the relationship between the critical point and the initial drop location. To inhibit the migration of the drop toward the cold region, the drop should be placed on the right side of the critical point.
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Keywords:
- self-rewetting /
- drop /
- contact line /
- thermocapillary
[1] Wu Z B 2017 Int. J. Heat Mass Transf. 105 704
[2] Chaudhury K, Chakraborty S 2015 Langmuir 31 4169
[3] Legros J C, Limbourg-Fontaine M C, Petre G 1984 Acta Astronaut. 11 143
[4] Abe Y, Iwasaki A, Tanaka K 2004 Ann. NY Acad. Sci. 1027 269
[5] Oron A, Rosenau P 1994 J. Fluid Mech. 273 361
[6] Batson W, Agnon Y, Oron A 2017 J. Fluid Mech. 819 562
[7] Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310
[8] Mamalis D, Koutsos V, Sefiane K 2016 Appl. Phys. Lett. 109 231601
[9] Mamalis D, Koutsos V, Sefiane K 2017 Int. J. Therm. Sci. 117 146
[10] Ouenzerfi S, Harmand S 2016 Langmuir 32 2378
[11] Di Francescantonio N, Savino R, Abe Y 2008 Int. J. Heat Mass Transf. 51 6199
[12] Hu Y, Zhang S, Li X, Wang S 2015 Int. J. Heat Mass Transf. 83 64
[13] Zhou L P, Li Y Y, Wei L T, Du X Z, Wang B X 2014 J. Chem. Ind. Eng. 65 79 (in Chinese) [周乐平, 李媛园, 魏龙亭, 杜小泽, 王补宣 2014 化工学报 65 79]
[14] Sitar A, Golobic I 2015 Int. J. Heat Mass Transf. 81 198
[15] Wu S C 2015 Int. J. Therm. Sci. 98 374
[16] Gao P, Yin Z H, Hu W R 2008 Adv. Mech. 38 329 (in Chinese) [高鹏, 尹兆华, 胡文瑞 2008 力学进展 38 329]
[17] Gomba J M, Homsy G M 2010 J. Fluid Mech. 647 125
[18] Pratap V, Moumen N, Subramanian R S 2008 Langmuir 24 5185
[19] Nguyen H B, Chen J C 2010 Phys. Fluids 22 062102
[20] Dai Q, Khonsari M M, Shen C, Huang W, Wang X 2016 Langmuir 32 7485
[21] Sui Y 2014 Phys. Fluids 26 092102
[22] Ye X M, Li Y K, Li C X 2016 Acta Phys. Sin. 65 104704 (in Chinese) [叶学民, 李永康, 李春曦 2016 物理学报 65 104704]
[23] Karapetsas G, Chamakos N T, Papathanasiou A G 2017 Langmuir 33 10838
[24] Zhao Y P 2012 Phys. Mech. Surf. Interface (Beijing: Science Press) p185, 186 (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社)第185, 186 页]
[25] Mukhopadhyay S, Murisic N, Behringer R P, Kondic L 2011 Phys. Rev. E 83 046302
[26] Craster R V, Matar O K 2000 J. Fluid Mech. 425 235
[27] Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892
[28] Karapetsas G, Sahu K C, Matar O K 2016 Langmuir 32 6871
[29] Ehrhard P, Davis S H 1991 J. Fluid Mech. 229 365
[30] Bakli C, Sree Hari P D, Chakraborty S 2017 Nanoscale 9 12509
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[1] Wu Z B 2017 Int. J. Heat Mass Transf. 105 704
[2] Chaudhury K, Chakraborty S 2015 Langmuir 31 4169
[3] Legros J C, Limbourg-Fontaine M C, Petre G 1984 Acta Astronaut. 11 143
[4] Abe Y, Iwasaki A, Tanaka K 2004 Ann. NY Acad. Sci. 1027 269
[5] Oron A, Rosenau P 1994 J. Fluid Mech. 273 361
[6] Batson W, Agnon Y, Oron A 2017 J. Fluid Mech. 819 562
[7] Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310
[8] Mamalis D, Koutsos V, Sefiane K 2016 Appl. Phys. Lett. 109 231601
[9] Mamalis D, Koutsos V, Sefiane K 2017 Int. J. Therm. Sci. 117 146
[10] Ouenzerfi S, Harmand S 2016 Langmuir 32 2378
[11] Di Francescantonio N, Savino R, Abe Y 2008 Int. J. Heat Mass Transf. 51 6199
[12] Hu Y, Zhang S, Li X, Wang S 2015 Int. J. Heat Mass Transf. 83 64
[13] Zhou L P, Li Y Y, Wei L T, Du X Z, Wang B X 2014 J. Chem. Ind. Eng. 65 79 (in Chinese) [周乐平, 李媛园, 魏龙亭, 杜小泽, 王补宣 2014 化工学报 65 79]
[14] Sitar A, Golobic I 2015 Int. J. Heat Mass Transf. 81 198
[15] Wu S C 2015 Int. J. Therm. Sci. 98 374
[16] Gao P, Yin Z H, Hu W R 2008 Adv. Mech. 38 329 (in Chinese) [高鹏, 尹兆华, 胡文瑞 2008 力学进展 38 329]
[17] Gomba J M, Homsy G M 2010 J. Fluid Mech. 647 125
[18] Pratap V, Moumen N, Subramanian R S 2008 Langmuir 24 5185
[19] Nguyen H B, Chen J C 2010 Phys. Fluids 22 062102
[20] Dai Q, Khonsari M M, Shen C, Huang W, Wang X 2016 Langmuir 32 7485
[21] Sui Y 2014 Phys. Fluids 26 092102
[22] Ye X M, Li Y K, Li C X 2016 Acta Phys. Sin. 65 104704 (in Chinese) [叶学民, 李永康, 李春曦 2016 物理学报 65 104704]
[23] Karapetsas G, Chamakos N T, Papathanasiou A G 2017 Langmuir 33 10838
[24] Zhao Y P 2012 Phys. Mech. Surf. Interface (Beijing: Science Press) p185, 186 (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社)第185, 186 页]
[25] Mukhopadhyay S, Murisic N, Behringer R P, Kondic L 2011 Phys. Rev. E 83 046302
[26] Craster R V, Matar O K 2000 J. Fluid Mech. 425 235
[27] Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892
[28] Karapetsas G, Sahu K C, Matar O K 2016 Langmuir 32 6871
[29] Ehrhard P, Davis S H 1991 J. Fluid Mech. 229 365
[30] Bakli C, Sree Hari P D, Chakraborty S 2017 Nanoscale 9 12509
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