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On the nonlinear behaviour of the Rayleigh–Taylor instability with a tangential electric field for inviscid and perfect dielectric fluids

Published online by Cambridge University Press:  09 March 2023

Wenxuan Guo ,
Qiang Zhang Open the ORCID record for Qiang Zhang [Opens in a new window]  and
Dongdong He Open the ORCID record for Dongdong He [Opens in a new window]
Wenxuan Guo
Affiliation:
Research Center of Mathematics, Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai 519087, PR China
Qiang Zhang*
Affiliation:
Research Center of Mathematics, Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai 519087, PR China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, PR China
Dongdong He
Affiliation:
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, PR China
*
†Email address for correspondence: mazq@uic.edu.cn
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Abstract

Fluid interfacial instability induced by gravity or external acceleration, known as the Rayleigh–Taylor instability, plays an important role in both scientific research and industrial application. How to control this instability is challenging. Researchers have been actively exploring the suppression method of applying electric fields parallel to dielectric fluid interfaces. The instability is characterized by the penetration of fingers at the interface. The velocities at the finger tips are the most important quantities since they characterize how fast the penetration occurs. The dynamics of the fingers is nonlinear. We present a nonlinear perturbation procedure for determining the amplitude and velocity of fingers at a Rayleigh–Taylor unstable interface between two incompressible, inviscid, immiscible and perfectly dielectric fluids in the presence of a horizontal electric field in two dimensions. The analytic formulas are displayed explicitly up to the third order of the initial disturbance. The comparison with the data from numerical simulations based on the vortex sheet method shows the theoretical formulas can capture well the nonlinear behaviour of the fingers. It is known that the interplay between the electric field and the fluids can lead to the suppression of interfacial instability. We further analyse the electrical force along the interface and show how this force leads to the instability suppression in our setting. It has been reported numerically in the literature that switching the electric permittivities of the fluids leads to quantitative differences in finger velocity. We show theoretically this phenomenon can only be explained by the nonlinear behaviour of the system.

JFM classification

Interfacial Flows (free surface): Fingering instability MHD and Electrohydrodynamics: Electrokinetic flows Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 958 , 10 March 2023 , A36
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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