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Stability and hysteresis of Faraday waves in Hele-Shaw cells

Published online by Cambridge University Press:  24 May 2019

Jing Li ,
Xiaochen Li  and
Shijun Liao Open the ORCID record for Shijun Liao [Opens in a new window]
Jing Li
Affiliation:
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Xiaochen Li
Affiliation:
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, PR China
Shijun Liao*
Affiliation:
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China State Key Laboratory of Plateau Ecology and Agriculture, Xining 810018, PR China School of Hydraulic and Electric Engineering, Qinghai University, Xining 810018, PR China
*
†Email address for correspondence: sjliao@sjtu.edu.cn
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Abstract

The instability of Faraday waves in Hele-Shaw cells is investigated experimentally and theoretically. A novel hydrodynamic model involving capillary action is proposed to capture the variation of the dynamic contact line between two close walls of narrow containers. The amplitude equations are derived from the gap-averaged model. By means of Lyapunov’s first method, a good prediction of the onset threshold of forcing acceleration is obtained, which shows the model’s validity for addressing the stability problem for Faraday waves in Hele-Shaw cells. It is found that the effect of the dynamic contact line is much greater than that of Poiseuille assumption of velocity profile for the cases under investigation. A new dispersion relation is obtained, which agrees well with experimental data. However, we highly recommend the conventional dispersion relation for gravity–capillary waves, which can generally meet common needs. Surface tension is found to be a key factor of interface flows in Hele-Shaw cells. According to our experimental observations, a liquid film is found on the front wall of the Hele-Shaw cell when the wave is falling. As a property of the friction coefficient from molecular kinetics, wet and dry plates show different wetting procedures. Unlike some authors of previous publications, we attribute the hysteresis to the out-of-plane interface shape rather than to detuning, i.e. the difference between natural frequency and response frequency.

JFM classification

Waves/Free-surface Flows: Faraday waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 694 - 716
Copyright
© 2019 Cambridge University Press 

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