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In this paper we consider a two-phase thin film consisting of two immiscibleviscous fluids endowed with a layer of insoluble surfactant on the surface ofthe upper fluid. The governing equations for the two film heights and thesurfactant concentration are derived using a lubrication approximation. Takinggravitational forces into account but neglecting capillary effects, theresulting system of evolution equations is parabolic, strongly coupled, ofsecond order and degenerated in the equations for the two film heights.Incorporating on the contrary capillary forces and neglecting the effects ofgravitation, the system of evolution equations is parabolic, degenerated and offourth order for the film heights, strongly coupled to a second order transportequation for the surfactant concentration. Local well-posedness and asymptoticstability are shown for both systems.

Modeling and Analysis of a Two-Phase Thin Film Model with Insoluble Surfactant