Monolayer flow on a thin film

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Abstract
Two-dimensional flow of a surface-active monolayer on a thin viscous film is considered. Simplifications of negligible gravity and pressure forces are made. Interfacial properties are described by simple model equations of state. Solutions are obtained for when the monolayer is scraped along the interface by a barrier and a steady state exists where surface advection is balanced by surface diffusion. Surface velocity, film thickness and spreading rate dependence on surface diffusivity are examined.