Rupture of thin free films of Newtonian fluids is analyzed when the sheets' two free surfaces are covered with insoluble surfactant and surface rheological effects are important. The analysis relies on a long-wavelength model composed of a system of one-dimensional evolution equations for film thickness $h(z,t)$, lateral velocity $v(z,t)$, and surfactant concentration $\mathrm{\Gamma }(z,t)$ ($z$: lateral coordinate, $t$: time). As the dynamics near the space-time singularity in sheet rupture is asymptotically self-similar when surfactants are convected away from the rupture point, the partial differential equations are also reduced to a set of ordinary differential equations in similarity space. For both highly viscous fluids in the Stokes limit and moderately viscous fluids, it is shown that the dominant balance involves van der Waals pressure and bulk viscous as well as surface viscous stresses while surface tension pressure and Marangoni stress are negligible. In the Stokes limit, self-similarity is of the second kind and $h\sim \mathrm{\Gamma }\sim {\tau }^{1/3}, z\sim {\tau }^{{\alpha }_z}$, and $v\sim {\tau }^{{\alpha }_z-1}$ where $\tau$ is time remaining until rupture and ${\alpha }_z$ is the lateral scaling exponent. Although ${\alpha }_z$ cannot be determined by dimensional arguments, it is shown to equal 0.249. For moderately viscous fluids, inertia also enters the picture and self-similarity is of the first kind ($h\sim \mathrm{\Gamma }\sim {\tau }^{1/3}, z\sim {\tau }^{1/2}$, and $v\sim {\tau }^{-1/2}$). Scalings determined from theory are confirmed by numerical solution of the evolution equations. Closed-form expressions for the sheet's thinning rate, which have heretofore been lacking, are also reported.

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• Instability of free-surface flows
• Interfacial flows
• Thin fluid films
• Ultrathin films