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TECHNICAL PAPERS

Evolution of Liquid Meniscus Shape in a Capillary Tube

[+] Author and Article Information
Shong-Leih Lee

Department of Power Mechanical Engineering,  National Tsing Hua University, Hsinchu 30013, Taiwansllee@pme.nthu.edu.tw

Hong-Draw Lee

Department of Power Mechanical Engineering,  National Tsing Hua University, Hsinchu 30013, Taiwan

J. Fluids Eng 129(8), 957-965 (Feb 02, 2007) (9 pages) doi:10.1115/1.2746898 History: Received August 27, 2005; Revised February 02, 2007

There are still many unanswered questions related to the problem of a capillary surface rising in a tube. One of the major questions is the evolution of the liquid meniscus shape. In this paper, a simple geometry method is proposed to solve the force balance equation on the liquid meniscus. Based on a proper model for the macroscopic dynamic contact angle, the evolution of the liquid meniscus, including the moving speed and the shape, is obtained. The wall condition of zero dynamic contact angle is allowed. The resulting slipping velocity at the contact line resolves the stress singularity successfully. Performance of the present method is examined through six well-documented capillary-rise examples. Good agreements between the predictions and the measurements are observable if a reliable model for the dynamic contact angle is available. Although only the capillary-rise problem is demonstrated in this paper, the concept of this method is equally applicable to free surface flow in the vicinity of a contact line where the capillary force dominates the flow.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 6

A schematic description for the geometry method

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Figure 5

Variation of the Reynolds numbers for cases a, b, and c

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Figure 4

The average friction factor cf as a function of t for cases a, b, and c

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Figure 3

Comparison of the predicted capillary rise h¯(t) with the existing experiment for cases a, b, and c

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Figure 2

The average friction factor cf as a function of ξ for Eq. 1

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Figure 1

The coordinate system and geometrical variables appearing in the problem

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Figure 7

Influence of the time step on the hcl(t) results for case a

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Figure 8

The resulting hcl(t) functions based on various θD models

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Figure 9

Evolution of the free surface shape based on Hoffman-Kistler’s model (12) for cases a, b, c, d, e, and f

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Figure 10

The “correct” dynamic contact angle for cases a, b, and c

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