The dewetting of a thin film sandwiched between a solid substrate and an unbounded liquid bath

We report the dynamics of a thin liquid film of viscosity μ sandwiched between a solid substrate and an unbounded liquid bath of viscosity λμ. In the limit of negligible inertia, the flow depends on two non-dimensional parameters, namely λ and a dimensionless measure of the relative strengths of capillarity and van der Waals forces. We first analyse the linear temporal stability revealing that when the viscosity of the outer bath is much larger than that of the film, λ>>1, the most amplified wavenumber decreases as  k_m∼λ^-1/3, indicating that very slender dewetting structures are expected when λ becomes large. We then march in time the complete Stokes equations to investigate the spatial structure of the flow close to rupture revealing that, for λ<∞, the flow becomes self-similar with the minimum film thickness scaling as  h_min=K(λ) τ^1/3 when τ→0, being τ the time remaining before rupture. The presence of an outer liquid bath affects the self-similar structure obtained by Moreno-Boza et al. 2020 through the prefactor of the film thinning law, K(λ), and the opening angle of the self-similar film shape, θ(λ). For negligible film viscosity, λ→∞, the near-rupture flow is shown to be also self-similar but non-universal, in that the initial conditions dictate the final film shape close to rupture.