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Equilibria and stabilities of a confined floating cylinder

Published online by Cambridge University Press:  03 January 2023

Wanqiu Zhang Open the ORCID record for Wanqiu Zhang [Opens in a new window]  and
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window]
Wanqiu Zhang
Affiliation:
School of Mechanical Science and Engineering, 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 State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, PR China
*
†Email address for correspondence: xpzhou08@hust.edu.cn
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Abstract

A two-dimensional system with a floating cylinder confined between two parallel vertical stationary plates partially immersed in an infinite liquid bath in a downward gravity field is considered. The equilibrium states of the system are investigated using the Young–Laplace equation in two dimensions. According to the symmetry of menisci at both sides of the cylinder, the equilibrium states are classified into three types: the equilibria of fully symmetric menisci, the equilibria of partially symmetric menisci and the equilibria of asymmetric menisci. The study is then extended to investigate the stabilities of the confined cylinder with bifurcation theory. Results show that there can be at most two stable regions in the bifurcation diagram. For different plates’ contact angles, there are five representative types of bifurcation behaviours for either the case of one stable region or the case of two stable regions. In comparison with the case of an unconfined cylinder, the confinement by two hydrophobic plates with a small spacing can assist the stable interfacial floatation of the confined cylinder with a large weight.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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