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General exotic capillary tubes

Published online by Cambridge University Press:  17 December 2019

Fei Zhang Open the ORCID record for Fei Zhang [Opens in a new window]  and
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window]
Fei Zhang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Xinping Zhou*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The general exotic capillary tube is a non-uniform capillary tube which permits an entire continuum of equilibrium menisci if applying a pressure $p=-\unicode[STIX]{x1D700}z$ at the tube inlet. The shapes of general exotic capillary tubes under positive and negative loads are determined mathematically. Lowering the pressure at the tube inlet slightly from the value $p=-\unicode[STIX]{x1D700}z$ causes the tube to completely drain out, while raising the pressure slightly forces the tube to fill up, which implies that the general exotic capillary tube is sensitive to pressure. The general exotic capillary tube is also related to meniscus stability. It is found that the boundary parameters $\unicode[STIX]{x1D712}_{1}$ of general exotic cylinders with arbitrary contact angle are equal to the critical values $\unicode[STIX]{x1D712}_{1}^{\ast }$ for determining the meniscus stability. Then, a convenient alternative to solving the Jacobi equation for determining $\unicode[STIX]{x1D712}_{1}^{\ast }$ is proposed based on the ‘exotic’ property.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A1
Copyright
© 2019 Cambridge University Press

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