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We report a theoretical and numerical investigation of the linear andnonlinear dynamics of a thin liquid film of viscosity $\mu$ sandwiched betweena solid substrate and an unbounded liquid bath of viscosity $\lambda \mu$. Inthe limit of negligible inertia, the flow depends on two non-dimensionalparameters, namely $\lambda$ and a dimensionless measure of the relativestrengths of the stabilizing surface tension force and the destabilizing vander Waals force between the substrate and the film. We first analyze the linearstability of the film, providing an analytical dispersion relation. When theviscosity of the outer bath is much larger than that of the film, $\lambda \gg1$, the most amplified wavenumber decreases as $k_{\textrm{m}} \sim\lambda^{-1/3}$, indicating that very slender dewetting structures are expectedwhen $\lambda$ becomes large. We then perform fully nonlinear simulations ofthe complete Stokes equations to investigate the spatial structure of the flowclose to rupture revealing that the flow becomes self-similar with the minimumfilm thickness scaling as $h_{min} = K(\lambda) \tau^{1/3}$ when $\tau \to 0$,where $\tau$ is the time remaining before the singularity. It is demonstratedthat the presence of an outer liquid bath affects the self-similar structurethrough the prefactor of the film thinning law, $K(\lambda)$, and the openingangle of the self-similar film shape, which is shown to decrease with$\lambda$.

The influence of an outer bath on the dewetting of an ultrathin liquid film