Article: Finite element simulations of thin films flowing down planes or cylinders Journal: Progress in Computational Fluid Dynamics, An International Journal (PCFD) 2021 Vol.21 No.3 pp.161 - 169 Abstract: This paper considers contact line dynamics for liquid films flowing down planes or cylinders. Finite element modelling are introduced based on the open-source finite element software Freefem++. Using the reduced model of thin liquid films, the weak form of the partial differential equations are derived for finite element simulations. Both two-dimensional flow and three-dimensional flow of thin films are numerically simulated and the surface instability is analysed. The results obtained in this paper show good agreement with the results from the previous investigation. Results show that travelling wave phenomena is found in the time evolution while a unperturbed initial contact line is given. If given a small perturbed initial contact line, pattern of viscous fingers appears. The radius of the cylinder plays an important role in the flow pattern, and the number of fingers is approximately linearly with the radius of the cylinder. The proposed method and calculation code are useful for gaining better insight into the thin liquid film problems. Inderscience Publishers - linking academia, business and industry through research

Title: Finite element simulations of thin films flowing down planes or cylinders

Authors: Chicheng Ma; Wei Wang; Mingyu Shao; Zonghe Guo

Addresses: Department of Mechanics, School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, 255000, China ' School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, 255000, China ' School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, 255000, China ' School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, 255000, China

Abstract: This paper considers contact line dynamics for liquid films flowing down planes or cylinders. Finite element modelling are introduced based on the open-source finite element software Freefem++. Using the reduced model of thin liquid films, the weak form of the partial differential equations are derived for finite element simulations. Both two-dimensional flow and three-dimensional flow of thin films are numerically simulated and the surface instability is analysed. The results obtained in this paper show good agreement with the results from the previous investigation. Results show that travelling wave phenomena is found in the time evolution while a unperturbed initial contact line is given. If given a small perturbed initial contact line, pattern of viscous fingers appears. The radius of the cylinder plays an important role in the flow pattern, and the number of fingers is approximately linearly with the radius of the cylinder. The proposed method and calculation code are useful for gaining better insight into the thin liquid film problems.

Keywords: numerical simulation; cylinder; falling film; finite element method; Freefem++.

DOI: 10.1504/PCFD.2021.115132

Progress in Computational Fluid Dynamics, An International Journal, 2021 Vol.21 No.3, pp.161 - 169

Received: 25 Jul 2019
Accepted: 07 Jul 2020
Published online: 19 May 2021 *

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Title: Finite element simulations of thin films flowing down planes or cylinders

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