Browsing by Author "Naire, S."
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Item A 2+1 Dimensional Insoluble Surfactant Model for a Vertical Draining Free Film(Department of Mathematical Sciences, 2002-05-09) Naire, S.; Braun, Richard J.; Snow, S.A.A 2 + 1 dimensional mathematical model is constructed to study the evolution of a vertically-oriented thin, free liquid film draining under gravity when there is an insoluble surfactant, with finite surface viscosity, on its free surface. Lubrication theory for this free film results in four coupled nonlinear partial differential equations (PDEs) describing the free surface shape, the surface velocities and the surfacant transport, at leading order. Numerical experiments are performed to understand the stability of the system to perturbations across the film. In the limit of large surface viscosities, the evolution of the free surface is that of a rigid film. In addition, these large surface viscosities act as stabilizing factors due to their energy dissipating effect. An instability is seen for the mobile case; this is caused by a competition between gravity and the Marangoni effect. The behavior observed from this model qualitatively matches some structures observed in draining film experimentsItem Hydrodynamics of Bounded Vertical Film with Nonlinear Surface Properties(Department of Mathematical Sciences, 2001) Heidari, A.H.; Braun, Richard J.; Hirsa, A. H.; Snow, S.A.; Naire, S.The drainage of a thin liquid film with an insoluble monolayer down a vertical wall is studied. Lubrication theory is used to develop a model where the film is pinned at the top with a given thickness and the film drains into a bath at the bottom. A nonlinear equation of state is used for the surface tension and the surface viscosity is a nonlinear function of the surfactant concentration; these are appropriate for some aqueous systems. The three partial differential equations are solved via discretization in space and then solving the resulting differential algebraic system. Results are described for a wide range of parameters, and the conditions under which the free surface is immobilized are discussed.