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Interface coupling effect and multi-mode Faraday instabilities in a three-layer fluid system

Published online by Cambridge University Press:  01 March 2024

Yi-Fei Huang ,
Rong-Lin Zhuo ,
Juan-Cheng Yang Open the ORCID record for Juan-Cheng Yang [Opens in a new window]  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Yi-Fei Huang
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
Rong-Lin Zhuo
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China
Juan-Cheng Yang*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
†Email addresses for correspondence: yangjc@xjtu.edu.cn, mjni@ucas.ac.cn
†Email addresses for correspondence: yangjc@xjtu.edu.cn, mjni@ucas.ac.cn
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Abstract

We investigate the Faraday instabilities of a three-layer fluid system in a cylindrical container containing low-viscosity liquid metal, sodium hydroxide solution and air by establishing the Mathieu equations with considering the viscous model derived by Labrador et al. (J. Phys.: Conf. Ser., vol. 2090, 2021, 012088). The Floquet analysis, asymptotic analysis, direct numerical simulation and experimental method are adopted in the present study. We obtain the dispersion relations and critical oscillation amplitudes of zigzag and varicose modes from the analysis of the Mathieu equations, which agree well with the experimental result. Furthermore, considering the coupling strength of two interfaces, besides zigzag and varicose modes, we find a beating instability mode that contains two primary frequencies, with its average frequency equalling half of the external excitation frequency in the strongly coupled system. In the weakly coupled system, the $A$-interface instability, $B$-interface instability and $A$&$B$-interface instability are defined. Finally, we obtain a critical wavenumber $k_c$ that can determine the transition from zigzag or varicose modes to the corresponding $A$-interface or $B$-interface instability.

JFM classification

Waves/Free-surface Flows: Faraday waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 982 , 10 March 2024 , A8
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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