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Electrohydrodynamic deformation of liquid film underneath a topographical template

Published online by Cambridge University Press:  16 May 2025

Tingting Zhang Open the ORCID record for Tingting Zhang [Opens in a new window] ,
Fenhong Song Open the ORCID record for Fenhong Song [Opens in a new window] ,
Ben Q. Li ,
Feng Xu Open the ORCID record for Feng Xu [Opens in a new window]  and
Qingzhen Yang Open the ORCID record for Qingzhen Yang [Opens in a new window]
Tingting Zhang
Affiliation:
College of Mechanical & Electrical Engineering, Shaanxi University of Science and Technology, Xi’an, Shaanxi 710021, PR China
Fenhong Song
Affiliation:
School of Energy and Power Engineering, Northeast Electric Power University, Jilin, Jilin 132012, PR China
Ben Q. Li
Affiliation:
Department of Mechanical Engineering, University of Michigan-Dearborn, Dearborn, MI 48128, USA
Feng Xu*
Affiliation:
The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
Qingzhen Yang*
Affiliation:
The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China Research Institute of Xi’an Jiaotong University, Hangzhou, Zhejiang 311215, PR China
*
Corresponding authors: Qingzhen Yang, qzyang@mail.xjtu.edu.cn; Feng Xu, fengxu@mail.xjtu.edu.cn
Corresponding authors: Qingzhen Yang, qzyang@mail.xjtu.edu.cn; Feng Xu, fengxu@mail.xjtu.edu.cn
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Abstract

Deformation occurs in a thin liquid film when it is subjected to a non-uniform electric field, which is referred to as the electrohydrodynamic patterning. Due to the development of a non-uniform electrical force along the surface, the film would evolve into microstructures/nanostructures. In this work, a linear and a nonlinear model are proposed to thoroughly investigate the steady state (i.e. equilibrium state) of the electrohydrodynamic deformation of thin liquid film. It is found that the deformation is closely dependent on the electric Bond number BoE. Interestingly, when BoE is larger than a critical value, the film would be deformed remarkably and get in contact with the top template. To model the ‘contact’ between the liquid film and the solid template, the disjoining pressure is incorporated into the numerical model. From the nonlinear numerical model, a hysteresis deformation is revealed, i.e. the film may have different equilibrium states depending on whether the voltage is increased or decreased. To analyse the stability of these multiple equilibrium states, the Lyapunov functional is employed to characterise the system’s free energy. According to the Lyapunov functional analysis, at most three equilibrium states can be formed. Among them, one is stable, another is metastable and the third one is unstable. Finally, the model is extended to study the three-dimensional deformation of the electrohydrodynamic patterning.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Interfacial Flows (free surface): Thin films Drops and Bubbles: Electrohydrodynamic effects

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , A46
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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