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Mathematical modelling of thermocapillary patterning in thin liquid film: an equilibrium study

Published online by Cambridge University Press:  26 May 2021

Qingzhen Yang Open the ORCID record for Qingzhen Yang [Opens in a new window] ,
Ben Q. Li ,
Xuemeng Lv ,
Fenhong Song ,
Yankui Liu Open the ORCID record for Yankui Liu [Opens in a new window]  and
Feng Xu Open the ORCID record for Feng Xu [Opens in a new window]
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, Shaanxi710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an, Shaanxi710049, PR China Micro-/Nano-technology Research Center, State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi710049, PR China Research Institute of Xi'an Jiaotong University, Hangzhou, Zhejiang311215, PR China
Ben Q. Li
Affiliation:
Department of Mechanical Engineering, University of Michigan-Dearborn, Dearborn, MI48128, USA
Xuemeng Lv
Affiliation:
The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, Shaanxi710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an, Shaanxi710049, PR China
Fenhong Song
Affiliation:
School of Energy and Power Engineering, Northeast Electric Power University, Jilin, Jilin132012, PR China
Yankui Liu
Affiliation:
School of Energy and Power Engineering, Northeast Electric Power University, Jilin, Jilin132012, PR China
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, Shaanxi710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an, Shaanxi710049, PR China
*
† Email address for correspondence: fengxu@mail.xjtu.edu.cn
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Abstract

Thermocapillary patterning, namely, the formation of micro/nano patterns in a liquid film by surface deformation induced by an imposed thermal gradient, has enjoyed widespread applications in engineering. In this paper, we present the development of analytical and numerical models and model analyses to predict the equilibrium states of a deformed liquid polymer film under the action of thermocapillary forces. The deformation is found to be dependent on a non-dimensional parameter $\Im \equiv Ma \, Ca$, with Ma denoting the Marangoni number and Ca the capillary number. Model analyses show that a hysteresis phenomenon is associated with the thermocapillary deformation of the film with increasing and then decreasing $\Im$. When $\Im$ is increased above a critical value ${\Im _{c,1}}$, significant deformation occurs in the film until the polymer touches the top solid template. Then, if $\Im$ is allowed to decrease, the polymer film would not detach from the template until $\Im$ is decreased below another critical value ${\Im _{c,2}}$ (usually ${\Im _{c,2}} < {\Im _{c,1}}$). With $\Im \in [{\Im _{c,2}},\;{\Im _{c,1}}]$, there exist multiple (three at the maximum) equilibrium states. The Lyapunov energy analysis of these states reveals that one equilibrium state is stable, another is metastable and the third one is unstable.

JFM classification

Convection: Marangoni convection Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A29
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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