Finite element simulations of thin films flowing down planes or cylinders

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.