Abstract
In the microgravity environment, liquid is usually adsorbed in corners or slots. Liquid accumulated in these regions is difficult to be removed and used. A mathematical model describing static profiles of the liquid accumulated in the corner of truncated-cone-shaped containers under microgravity is obtained through theoretical derivation in this paper. The profiles have two cases according to liquid’s wettability and the angle of containers’ corners. Once coordinates of an endpoint of the profile are known, the profile and volume of the liquid can be obtained using the Shooting method according to the mathematical model. Besides, if abscissa values of the endpoints are unknown, the profile of the liquid can also be obtained using the dichotomy method and shooting method when liquid volume is given. It is easier to use these methods than others proposed before and they can also be used to predict liquid’s profiles in other conditions. Numerical simulation is performed with the volume of fluid method and the results are in good agreement with theoretical ones. Based on the mathematical model, the profile and volume of the liquid accumulated in the corner can be predicted accurately.
摘要
在微重力环境中, 液体通常吸附在夹角或缝隙中. 积聚在这些区域的液体难以排出和使用. 本文通过理论推导得到了微重力环境下圆台形容器内角处液体的气液界面轮廓. 根据液体的润湿性和内角大小, 界面轮廓可分为两种情况. 一旦知道轮廓某个端点的坐标, 就可以根据数学模型使用打靶法获得液面轮廓和体积. 此外, 如果轮廓端点的横坐标值无法测量得到, 在给定液体体积的情况下,也可以使用二分法和打靶法获得液面轮廓. 本文提出的方法比之前提出的基于Gibbs自由能的方法更容易. 该方法也可用来预测其他结构间的液面轮廓. 本文采用有限体积法开展数值模拟, 仿真结果与理论值吻合良好. 基于该数学模型, 可准确预测圆台形容器内角处积聚液体的液面轮廓和体积.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Lucas, Rate of capillary ascension of liquids, Kolloid-Zeitschrift 23, 15 (1918).
E. W. Washburn, The dynamics of capillary flow, Phys. Rev. 17, 273 (1921).
S. Levine, P. Reed, E. J. Watson, and G. Neale, A theory of the rate of rise of a liquid in a capillary, J. Colloid Interface Sci. 3, 403 (1976).
M. Stange, M. E. Dreyer, and H. J. Rath, Capillary driven flow in circular cylindrical tubes, Phys. Fluids 15, 2587 (2003).
S. Chen, Z. Ye, L. Duan, and Q. Kang, Capillary driven flow in oval tubes under microgravity, Phys. Fluids 33, 032111 (2021).
J. Lei, Z. Xu, F. Xin, and T. J. Lu, Dynamics of capillary flow in an undulated tube, Phys. Fluids 33, 052109 (2021).
B. Figliuzzi, and C. R. Buie, Rise in optimized capillary channels, J. Fluid Mech. 731, 142 (2013).
S. Chen, Y. Chen, L. Duan, and Q. Kang, Capillary rise of liquid in concentric annuli under microgravity, Microgravity Sci. Technol. 34, 30 (2022).
R. Chassagne, F. Dörfler, M. Guyenot, and J. Harting, Modeling of capillary-driven flows in axisymmetric geometries, Comput. Fluids 178, 132 (2019).
D. A. Bolleddula, Y. Chen, B. Semerjian, N. Tavan, and M. M. Weislogel, Compound capillary flows in complex containers: Drop tower test results, Microgravity Sci. Technol. 22, 475 (2010).
X. Wang, Y. Pang, Y. Ma, Y. Ren, and Z. Liu, Flow regimes of the immiscible liquids within a rectangular microchannel, Acta Mech. Sin. 37, 1544 (2021).
C. E. Wu, J. Qin, and P. Gao, Experiment on gas-liquid displacement in a capillary, Acta Mech. Sin. 38, 321386 (2022).
M. Dreyer, A. Delgado, and H. J. Path, Capillary rise of liquid between parallel plates under microgravity, J. Colloid Interface Sci. 163, 158 (1994).
S. Chen, L. Duan, Y. Li, F. Ding, J. Liu, and W. Li, Capillary phenomena between plates from statics to dynamics under microgravity, Microgravity Sci. Technol. 34, 70 (2022).
T. S. Ramakrishnan, P. Wu, H. Zhang, and D. T. Wasan, Dynamics in closed and open capillaries, J. Fluid Mech. 872, 5 (2019).
M. M. Weislogel, and S. Lichter, Capillary flow in an interior corner, J. Fluid Mech. 373, 349 (1998).
M. M. Weislogel, and C. L. Nardin, Capillary driven flow along interior corners formed by planar walls of varying wettability, Microgravity Sci. Technol 17, 45 (2005).
Y. Chen, M. M. Weislogel, and C. L. Nardin, Capillary-driven flows along rounded interior corners, J. Fluid Mech. 566, 235 (2006).
Y. Li, M. Hu, L. Liu, Y. Y. Su, L. Duan, and Q. Kang, Study of capillary driven flow in an interior corner of rounded wall under microgravity, Microgravity Sci. Technol. 27, 193 (2015).
Z. Wu, Y. Huang, X. Chen, and X. Zhang, Capillary-driven flows along curved interior corners, Int. J. Multiphase Flow 109, 14 (2018).
Y. Tian, Y. Jiang, J. Zhou, and M. Doi, Dynamics of Taylor rising, Langmuir 35, 5183 (2019).
J. Zhou, and M. Doi, Universality of capillary rising in corners, J. Fluid Mech. 900, A29 (2020).
M. M. Weislogel, and J. T. McCraney, The symmetric draining of capillary liquids from containers with interior corners, J. Fluid Mech. 859, 902 (2018).
S. Chen, Z. Han, L. Duan, and Q. Kang, Experimental and numerical study on capillary flow along deflectors in plate surface tension tanks in microgravity environment, AIP Adv. 9, 025020 (2019).
S. Chen, L. Duan, and Q. Kang, Study on propellant management device in plate surface tension tanks, Acta Mech. Sin. 37, 1498 (2021).
P. Concus, and R. Finn, On capillary free surfaces in the absence of gravity, Acta Math. 132, 177 (1974).
B. J. Carroll, The accurate measurement of contact angle, phase contact areas, drop volume, and Laplace excess pressure in drop-onfiber systems, J. Colloid Interface Sci. 57, 488 (1976).
S. Michielsen, J. Zhang, J. Du, and H. J. Lee, Gibbs free energy of liquid drops on conical fibers, Langmuir 27, 11867 (2011).
J. Du, S. Michielsen, and H. J. Lee, Profiles of liquid drops at the tips of cylindrical fibers, Langmuir 26, 16000 (2010).
J. Du, S. Michielsen, and H. J. Lee, Profiles of liquid drops at the bottom of cylindrical fibers standing on flat substrates, Langmuir 28, 722 (2011).
G. Mason, and W. C. Clark, Liquid bridges between spheres, Chem. Eng. Sci. 20, 859 (1965).
W. C. Clark, J. M. Haynes, and G. Mason, Liquid bridges between a sphere and a plane, Chem. Eng. Sci. 23, 810 (1968).
M. A. Fortes, Axisymmetric liquid bridges between parallel plates, J. Colloid Interface Sci. 88, 338 (1982).
J. W. van Honschoten, N. R. Tas, and M. Elwenspoek, The profile of a capillary liquid bridge between solid surfaces, Am. J. Phys. 78, 277 (2010).
Y. Wang, S. Michielsen, and H. J. Lee, Symmetric and asymmetric capillary bridges between a rough surface and a parallel surface, Langmuir 29, 11028 (2013).
T. P. Farmer, and J. C. Bird, Asymmetric capillary bridges between contacting spheres, J. Colloid Interface Sci. 454, 192 (2015).
E. Reyssat, Capillary bridges between a plane and a cylindrical wall, J. Fluid Mech. 773, R1 (2015).
H. D. Mittelmann, Symmetric capillary surface in a cube, Math. Comput. Simul. 35, 139 (1993).
D. Langbein, Liquid surfaces in polyhedral containers, in: Capillary Surfaces (Springer, Berlin, Heidelberg, 2002), pp. 213–234.
J. B. Bostwick, and P. H. Steen, Stability of constrained capillary surfaces, Annu. Rev. Fluid Mech. 47, 539 (2015).
J. Zou, F. Lin, and C. Ji, Capillary breakup of armored liquid filaments, Phys. Fluids 29, 062103 (2017).
Acknowledgements
This work was supported by the China Manned Space Engineering Program (Fluid Physics Experimental Rack and the Priority Research Program of Space Station), and the National Natural Science Foundation of China (Grant No. 12032020).
Author information
Authors and Affiliations
Contributions
Shangtong Chen designed the research. Shangtong Chen and Chu Zhang wrote the first draft of the manuscript. Shangtong Chen and Chu Zhang set up the numerical set-up and processed the numerical data. Wen Li, Yong Li and Fenglin Ding helped organize the manuscript. Wen Li, Yong Li and Qi Kang revised and edited the final version.
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, S., Zhang, C., Li, W. et al. Capillary phenomena in the corner of truncated-cone-shaped containers under microgravity. Acta Mech. Sin. 39, 322347 (2023). https://doi.org/10.1007/s10409-022-22347-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10409-022-22347-x