Modeling and analysis of a two-phase thin film model with insoluble surfactant

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• 作者：Gabriele Bruell ^{bruell@ifam.uni-hannover.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Thin liquid film ; Surfactant spreading ; Lubrication approximation ; Degenerated parabolic equations
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：27
• 期：Complete
• 页码：124-145
• 全文大小：721 K

文摘

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.