The role of inertia in the rupture of ultrathin liquid films

Abstract

Theory and numerical simulations of the Navier-Stokes equations are used to unravel the influence of inertia on the dewetting dynamics of an ultrathin film of Newtonian liquid deposited on a solid substrate. A classification of the self-similar film thinning regimes at finite Ohnesorge numbers is provided, unifying previous findings. We reveal that, for Ohnesorge numbers smaller than one, the structure of the rupture singularity close to the molecular scales is controlled by a balance between liquid inertia and van der Waals forces, leading to a self-similar asymptotic regime with hmin ∞ τ2/5 as τ → 0, where hmin is the minimum film thickness and τ is the time remaining before rupture. The flow exhibits a three-region structure comprising an irrotational core delimited by a pair of boundary layers at the wall and at the free surface. A potential-flow description of the irrotational core is provided, which is matched with the vortical layers, allowing us to present a complete parameter-free asymptotic description of inertia-dominated film rupture.