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Versatile analysis of closed-end capillary invasion of viscous fluids

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Abstract

When a fluid invades a closed-end capillary, the fluid flows owing to surface tension overcoming the viscous resistance, gravity, and the gas pressure from the entrapped gas, and the fluid spontaneously reaches a certain height. An experiment was conducted to observe the rise of the viscous fluid in a closed-end capillary, and the results are compared with a one-dimensional theoretical model and a numerical simulation solved using a level set method. When a static contact angle was used in the theoretical model, the result was different from the experimental result, because the radius of curvature increased as the fluid rose. Therefore, the dynamic contact angle during the increase was measured, and the geometrical equation was developed. This empirical equation was applied to the modified theoretical model, and the result agreed well with the experiment and simulation. Additionally, the effect of the shear stress at the inner wall was investigated, and it was directly affected by the velocity profile of the fluid, especially at the early stage when t < 0.01 s. Therefore, the effects of dynamic contact angle change and the entrance length is important to analyze accurately the dynamics of viscous fluid invasion in a closed-end capillary.

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Acknowledgements

This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2014M3C1B1033982, 2017R1A2B2006964), and by the National Research Council of Science & Technology (NST) grant by the Korean government (MSIT) [No. CMP-16-04-KITECH].

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Author notes

  1. Hosub Lim and Minki Lee contributed equally to this work.

Authors and Affiliations

  1. School of Mechanical Engineering, Sungkyunkwan University, Suwon, Gyeonggi-do, 16419, Republic of Korea

    Hosub Lim, Minki Lee & Jinkee Lee

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  1. Hosub Lim
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  2. Minki Lee
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Correspondence to Jinkee Lee.

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Lim, H., Lee, M. & Lee, J. Versatile analysis of closed-end capillary invasion of viscous fluids. JMST Adv. 1, 73–79 (2019). https://doi.org/10.1007/s42791-019-0001-5

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