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Effects of surface tension on a floating body in two dimensions

Published online by Cambridge University Press:  23 May 2018

Fei Zhang Open the ORCID record for Fei Zhang [Opens in a new window] ,
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window]  and
Chengwei Zhu
Fei Zhang
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Xinping Zhou*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, PR China
Chengwei Zhu
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China
*
†Email address for correspondence: [email protected]
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Abstract

A model for calculating the force profile and the moment profile of a floating body in two dimensions with an arbitrary cross-section is proposed. Three types of cross-sections with different contact angles and densities are calculated by using the model to determine the vertical and rotational equilibria and their stabilities. Results show that the model can be applied to convex floating bodies with finitely many sharp edges. The study is then extended to investigate the surface tension effects on the vertical and rotational stabilities by varying the following parameters: the radii of curvature of the solid surface at the contact lines and the size of floating body. In general, the smaller the radii of curvature the better the vertical and rotational stabilities. However, for the contact angle $\unicode[STIX]{x1D703}=0$ (or $\unicode[STIX]{x1D703}=\unicode[STIX]{x03C0}$) the radii of curvature have no effect on the vertical stability of the floating body. By varying the size of the floating body, it is found that the vertical and rotational stabilities of mesoscale floating bodies vary continuously between the stabilities of the macroscale and microscale floating bodies with other parameters remaining unchanged.

JFM classification

Interfacial Flows (free surface): Capillary flows Mathematical Foundations: Mathematical Foundations Mathematical Foundations: Variational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 489 - 519
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Copyright
© 2018 Cambridge University Press 

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Zhang et al. supplementary movie 1

The vertical displacement of the selected shape.

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Zhang et al. supplementary movie 2

The rotational displacement of the selected shape.

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Video 2.3 MB