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The stability of a thin liquid film bounded by two free surfaces is examinedin the presence of insoluble surface active agents. The surface active agentsnot only cause gradients in surface tension, but could also render surfaceviscosity to be significant, and variable, as a function of theirconcentration. A set of three coupled nonlinear evolution equations are derivedfor the film height, concentration of surface active agents, and the horizontalliquid velocity which governs the dynamics of the free film. Suitablephenomenological models for variation of surface tension and surface viscositywith the concentration of surface active agents are incorporated in theinterfacial stress boundary condition. Linear stability analysis reveals theeffect of various non-dimensional parameters, specifically the retarding natureof surface viscosity and Marangoni effects on film rupture. An analysis of the`jamming' limit of surfactant concentration reveals that $\Gamma_0^{(nl)}<3\mathbb{D}/M$ is a sufficient criteria for instability of the system, where$\Gamma_0^{(nl)}$ is a normalized initial surface particle concentration,$\mathbb{D}$ is the disjoining pressure number and $\textit{M}$ is theMarangoni number. Nonlinear simulations suggest film profiles at rupture arealso qualitatively different from those reported in earlier studies, revealingthat free films in the jamming limit are remarkably stable and their freesurfaces behave like immobile interfaces. Furthermore, self-similar exponentsextracted from our nonlinear simulations are used to explain topologicaldifferences between zero and constant surface viscosity in the vicinity ofrupture.

On the role of variable surface viscosity in free viscous films