Thermocapillary migration of heterogeneous droplets with unidirectional temperature gradient

doi:10.12034/j.issn.1009-606X.217349

Abstract

Abstract: The phenomenon of thermocapillary migration of the heterogeneous droplets of paraffin oil and deionized water in different proportions placed on the metal substrate surface driven by the nonuniform temperature field was investigated, a theoretical model was set up. The morphological changes of the droplets driven by temperature gradient from the high temperature region to the low temperature region were recorded by high-speed camera. The results showed that the contact angle of heterogeneous droplets decreased with the rising of temperature and the wettability was enhanced. The migration velocity of heterogeneous droplets decreased with the increasing of viscosity and increased with the increasing of temperature gradient, and the difference of velocities under different viscosities increased with the increasing of temperature gradient. The variation trend of migration velocities with time decreased rapidly, and then slowly decreased to 0. The relationship between the migration velocity and the Marangoni number (Ma) was derived and verified, which indicated that the migration velocity increased markedly with the increasing of Ma. The greater the Ma was, the higher the matching degree between the experimental and simulation results were.

Key words: thermocapillary migration, contact angle, temperature gradient, moisture content, viscosity, Marangoni effect, heat and mass transfer

摘要： 石蜡油与去离子水按多种比例混合形成异质液滴，放置在金属基板表面，在外加不均匀温度场作用下进行热毛细迁移，采用高速摄像机记录温度梯度驱动液滴从高温区迁移至低温区过程中液滴的形态，建立了理论模型. 结果表明，异质液滴的接触角随温度升高而减小，润湿性增强；异质液滴的迁移速度随粘度增加而减小，随温度梯度增加而增加，不同粘度下的速度差随温度梯度增大而增大，迁移速度随时间增加迅速降低，后缓慢减小到趋于0. 推导了迁移速度与Marangoni数Ma的关系式并进行了实验验证，迁移速度随Ma增加而显著增加，Ma越大，实验结果与模拟结果的匹配程度越高.

关键词: 热毛细迁移, 接触角, 温度梯度, 含水率, 粘度, Marangoni效应, 传热传质

Yuan ZHONG Haicun DU Ying ZHANG Huiying PENG. Thermocapillary migration of heterogeneous droplets with unidirectional temperature gradient[J]. Chin. J. Process Eng., 2018, 18(4): 697-703.

钟源杜海存张莹彭慧颖. 单向温度梯度下异质液滴的热毛细迁移[J]. 过程工程学报, 2018, 18(4): 697-703.

References

[1] 高鹏，尹兆华，胡文瑞. 液滴热毛细迁移问题的研究进展[J]. 力学进展，2008，(03):329-338.
GAO P，YIN Z H，HU W R. The progresses of drop thermocapillary migration research[J]. Advances in Mechanics，2008，(03):329-338.
[2] 武作兵. 大Marangoni数下液滴热毛细迁移实验的物理机制[C]. 全国实验流体力学学术会议，2013:4.
WU Z B. Physical mechanism of thermocapillary migration experiment of droplet at large Marangoni numbers[C]. National Conference on Experimental Fluid Mechanics，2013:4.
[3] 武作兵. 液滴热毛细迁移研究进展[C]. 中国计算力学大会，2012:5.
WU Z B. Advances in thermocapillary droplet migration[C]. Chinese Conference on Computational Mechanics，2012:5.
[4] 黄聪，胡良，康琦. 双液滴热毛细迁移的实验研究[J]. 力学学报，2005，37(2):232-237.
HUANG C，HU L，KANG Q. Experimental Investigation of thermocapillary migration of two drops[J]. Acta Mechanica Sinica，2005，37(2):232-237.
[5] 张朔婷，胡良，段俐，等. 多液滴热毛细迁移的研究[J]. 力学学报，2014，46(5):802-806.
ZHANG S T，HU L，DUAN L，et al. Droplet interactions in thermocapillary migration[J]. Chinese Journal of Theoretical and Applied Mechanics，2014，46(5):802-806.
[6] 郭子成，罗青枝，荣杰. 润湿现象和毛细现象的热力学描述[J]. 大学物理，2000，19(6):19-21.
GUO Z C，LUO Q Z，RONG J. Thermodynamic description of wetting phenomena and capillarity[J]. College Physics，2000，19(6):19-21.
[7] 高安然，李铁，刘翔，等. 基于温度梯度驱动的液滴传输行为研究[J]. 测试技术学报，2010，24(5):377-380.
GAO A R，LI T，LIU X，et al. Study on transportation behavior of droplet driven by thermal gradient[J]. Journal of Test and Measurement Technology，2010，24(5):377-380.
[8] PRADHAN T K，PANIGRAHI P K. Thermocapillary convection inside a stationary sessile water droplet on a horizontal surface with an imposed temperature gradient[J]. Experiments in Fluids，2015，56(9):178.
[9] DAI Q W，KHONSARI M M，SHEN C，et al. Thermocapillary migration of liquid droplets induced by a unidirectional thermal gradient[J]. Langmuir the Acs Journal of Surfaces & Colloids，2016，32(30):7485.
[10] DAI Q W，HUANG W，WANG X L. Surface roughness and orientation effects on the thermo-capillary migration of a droplet of paraffin oil[J]. Experimental Thermal & Fluid Science，2014，57(2 Suppl):200-206.
[11] DAI Q W，HUANG W，WANG X L. A surface texture design to obstruct the liquid migration Induced by omnidirectional thermal gradients. Langmuir 2015，31(37):10154-10160.
[12] JIAO Z J，HUANG X Y，NGUYEN N T，et al. Thermocapillary actuation of droplet in a planar microchannel[J]. Microfluidics & Nanofluidics，2008，5(2):205-214.
[13] ALHENDAL Y，TURAN A，KALENDAR A. Thermocapillary migration of an isolated droplet and interaction of two droplets in zero gravity[J]. Acta Astronautica，2016，126:265-274.
[14] YIN Z H，CHANG L，HU W R，et al. Thermocapillary migration and interaction of two nondeformable drops[J]. Applied Mathematics and Mechanics(English Edition)，2011，32(7):811-824.
[15] 高鹏，尹兆华，胡文瑞. 大Marangoni数下液滴热毛细迁移的数值研究[J]. 中国科学，2007，37(9):1232-1234.
GAO P，YIN Z H，HU W R. Numerical investigation of thermocapillary migration of droplet at large Marangoni numbers[J]. Science in China Series E，2007，37(9):1232-1234.
[16] 张昌艳. 油水混合物的转相及转相前后的粘度计算[J]. 科技创新导报，2010(1):50-50.
ZHANG C Y. Calculation of viscosity of oil-water mixtures before and after phase transformation[J]. Science and Technology Innovation Herald，2010(1):50-50.
[17] WU Z B. Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers[J]. International Journal of Heat & Mass Transfer，2017，105:704-711.
[18] HUANG W，WANG X L. No migration of ionic liquid under temperature gradient[J]. Colloids & Surfaces A Physicochemical & Engineering Aspects， 2016，497:167-170.
[19] METTU S，CHAUDHURY M K. Motion of drops on a surface induced by thermal gradient and vibration[J]. Langmuir the Acs Journal of Surfaces & Colloids，2008，24(19):10833-10837.
[20] TADMOR R. Line energy and the relation between advancing，receding，and young contact angles[J]. Langmuir the Acs Journal of Surfaces & Colloids， 2004，20(18):7659-7664.
[21] SEETON C J. Viscosity-temperature correlation for liquids[J]. Tribology Letters，2006，22(1):67-78.
[22] 武作兵. 大Marangoni数下液滴热毛细迁移实验的物理机制[C]. 全国实验流体力学学术会议，2013:2.
WU Z B. Physical mechanism of thermocapillary migration experiment of droplet at large Marangoni numbers[C]. National Conference on Experimental Fluid Mechanics，2013:2.
[23] RICHARDSON E G. The flow of emulsions. II[J]. Journal of Colloid Science，1953，8(3):367-373.
[24] 刘德生，宫敬，吴海浩，等. 三相流动条件下的油水混合物粘度[J]. 油气储运，2011，30(2):107-110.
LIU D S，GONG J，WU H H，et al. Viscosity of oil-water mixtures in three-phase flow[J]. Oil & Gas Storage and Transportation，2011，30(2):107-110.
[25] PRATAP V，MOUMEN N，SUBRAMANIAN R S. Thermocapillary motion of a liquid drop on a horizontal solid surface[J]. Langmuir the Acs Journal of Surfaces & Colloids，2008，24(9):5185-5193.
[26] BALASUBRAMANIAM R，SUBRAMANIAN R S. The migration of a drop in a uniform temperature gradient at large Marangoni numbers[J]. Physics of Fluids，2000，12(4):733-743.