Modeling and analysis of a two-phase thin film model with insoluble surfactant |
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| Institution: | 1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, PR China;2. Department of Mathematics, Shanghai University, Shanghai, 200444, PR China;1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2. Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China;1. Department of Mathematics and Statistics, McGill University, Montreal, H3A 2K6, Canada;2. Department of Mathematics, Champlain College St.-Lambert, Quebec, J4P 3P2, Canada;3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;1. Materials Genome Institute, Shanghai University, Shanghai 200444, China;2. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, China;3. Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | In this paper we consider a two-phase thin film consisting of two immiscible viscous fluids endowed with a layer of insoluble surfactant on the surface of the upper fluid. The governing equations for the two film heights and the surfactant concentration are derived using a lubrication approximation. Taking gravitational forces into account but neglecting capillary effects, the resulting system of evolution equations is parabolic, strongly coupled, of second order and degenerated in the equations for the two film heights. Incorporating on the contrary capillary forces and neglecting the effects of gravitation, the system of evolution equations is parabolic, degenerated and of fourth-order for the film heights, strongly coupled to a second-order transport equation for the surfactant concentration. Local well-posedness and asymptotic stability are shown for both systems. |
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| Keywords: | Thin liquid film Surfactant spreading Lubrication approximation Degenerated parabolic equations |
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