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The capillary-driven liquid flow in tubes connected to containers under a microgravity condition is systematically studied in a drop tower experimentally. The microgravity time lasts up to 3.6 s and the working liquids are mixtures of ethanol and deionized water with different ratios. Theoretically, based on the previous theory for tubes directly immersed in fluid, a modified formula is developed to describe the change tendency of the height of meniscus with microgravity time for such a container/tube system exposed to a microgravity environment. From the theoretical formula, the numerical results of meniscus height at different microgravity time can be obtained, utilizing the geometrical parameters of container/tube systems and the relevant physical quantities of Eth/H2O mixtures with different ratios. By comparing the numerical results with experimental results for different contact angles between working liquid and container in different container/tube systems, we show that the theoretical model is able to quantitatively predict the capillary-driven flow in tubes connected to containers, and the numerical results have good consistence with the experimental results. In addition, the experimental results also show that though the ratio of ethanol to deionized water can change the contact angle remarkably, it has little influence on the capillary flow if the geometrical parameters of the container/tube systems are the same. This is because not only the contact angle, but also the surface tension and viscosity coefficient of the working liquid change with the ratio of ethanol to deionized water. It is found that when the contact angle increases from 42° to 66°, the surface tension increases from 0.0328 N/m to 0.0443 N/m correspondingly, but the viscosity coefficient decreases from 2.11 cSt to1.49 cSt. As a result, the changes of surface tension and viscosity coefficient offset the influence of the change of contact angle, which can be explained by our theoretical model. Compared with the extensively studied system in which tubes are directly immersed into liquid, the container/tube system studied in this paper is more similar to many actual systems such as fluid transfer systems in the microgravity condition and in micro-fluidic devices. Therefore, this study is useful for predicting and analyzing the capillary flows of these actual systems.
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Keywords:
- capillary flow /
- capillary tube /
- microgravity /
- contact angle
[1] Oron A, Davis S H, Bankoff S G 1997 Rev. Mod. Phys. 69 931
[2] Sui Y, Ding H, Spelt P D M 2014 Annu. Rev. Fluid Mech. 46 97
[3] Benner E M, Petsev D N 2013 Phys. Rev. E 87 033008
[4] Gunde A, Babadagli T, Roy S S 2013 J. Petrol. Sci. Eng. 103 106
[5] Kim D S, Lee K C, Kwon T H, Lee S S 2002 J. Micromech. Microeng. 12 236
[6] Chen Y, Collicott S H 2004 AIAA J. 42 305
[7] Chen Y, Collicott S H 2005 AIAA J. 43 2395
[8] Chen Y, Collicott S H 2006 AIAA J. 44 859
[9] Dreyer M E, Delgado A, Rath H J 1994 J. Colloid Interf. Sci. 163 158
[10] Stange M, Dreyer M E, Rath H J 2003 Phys. Fluids 15 2587
[11] Wang C X, Xu S H, Sun Z W, Hu W R 2009 AIAA J. 47 2642
[12] Wang L W 2012 M. S. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese) [王林伟 2012 硕士学位论文 (北京: 中国科学院大学)]
[13] Conrath M, Canfield P J, Bronowicki P M, Dreyer M E, Weislogel M M, Grah A 2013 Phys. Rev. E 88 063009
[14] Zhang X Q, Yuan L G, Wu W D, Tian L Q, Yao K Z 2005 Sci. China: Ser. E 35 523 (in Chinese) [张孝谦, 袁龙根, 吴文东, 田兰桥, 姚康庄 2005 中国科学 E 辑 35 523]
[15] Wang C X, Xu S H, Sun Z W, Hu W R 2010 Int. J. Heat Mass Trans. 53 1801
[16] Xu S H, Zhou H W, Wang C X, Wang L W, Sun Z W 2013 Acta Phys. Sin. 62 134702 (in Chinese) [徐升华, 周宏伟, 王彩霞, 王林伟, 孙祉伟 2013 62 134702]
[17] Weislogel M M, Ross H D 1990 NASA-TM-103641 (NASA report)
[18] Schmidt F W, Zeldin B 1969 AIChE J. 15 612
[19] Sparrow E M, Lin S H, Lundgren T S 1964 Phys. Fluids 7 338
[20] He C H, Feng X 2001 Principles of Chemical Engineering (Beijing: Science Press) p50 (in Chinese) [何潮洪, 冯霄 2001 化工原理 (北京: 科学出版社) 第50页]
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[1] Oron A, Davis S H, Bankoff S G 1997 Rev. Mod. Phys. 69 931
[2] Sui Y, Ding H, Spelt P D M 2014 Annu. Rev. Fluid Mech. 46 97
[3] Benner E M, Petsev D N 2013 Phys. Rev. E 87 033008
[4] Gunde A, Babadagli T, Roy S S 2013 J. Petrol. Sci. Eng. 103 106
[5] Kim D S, Lee K C, Kwon T H, Lee S S 2002 J. Micromech. Microeng. 12 236
[6] Chen Y, Collicott S H 2004 AIAA J. 42 305
[7] Chen Y, Collicott S H 2005 AIAA J. 43 2395
[8] Chen Y, Collicott S H 2006 AIAA J. 44 859
[9] Dreyer M E, Delgado A, Rath H J 1994 J. Colloid Interf. Sci. 163 158
[10] Stange M, Dreyer M E, Rath H J 2003 Phys. Fluids 15 2587
[11] Wang C X, Xu S H, Sun Z W, Hu W R 2009 AIAA J. 47 2642
[12] Wang L W 2012 M. S. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese) [王林伟 2012 硕士学位论文 (北京: 中国科学院大学)]
[13] Conrath M, Canfield P J, Bronowicki P M, Dreyer M E, Weislogel M M, Grah A 2013 Phys. Rev. E 88 063009
[14] Zhang X Q, Yuan L G, Wu W D, Tian L Q, Yao K Z 2005 Sci. China: Ser. E 35 523 (in Chinese) [张孝谦, 袁龙根, 吴文东, 田兰桥, 姚康庄 2005 中国科学 E 辑 35 523]
[15] Wang C X, Xu S H, Sun Z W, Hu W R 2010 Int. J. Heat Mass Trans. 53 1801
[16] Xu S H, Zhou H W, Wang C X, Wang L W, Sun Z W 2013 Acta Phys. Sin. 62 134702 (in Chinese) [徐升华, 周宏伟, 王彩霞, 王林伟, 孙祉伟 2013 62 134702]
[17] Weislogel M M, Ross H D 1990 NASA-TM-103641 (NASA report)
[18] Schmidt F W, Zeldin B 1969 AIChE J. 15 612
[19] Sparrow E M, Lin S H, Lundgren T S 1964 Phys. Fluids 7 338
[20] He C H, Feng X 2001 Principles of Chemical Engineering (Beijing: Science Press) p50 (in Chinese) [何潮洪, 冯霄 2001 化工原理 (北京: 科学出版社) 第50页]
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