Suppressing van der Waals driven rupture through shear

Abstract

An ultra-thin viscous film on a substrate is susceptible to rupture instabilities driven by van der Waals attractions. When a unidirectional ‘wind’ shear τ is applied to the free surface, the rupture instability in two dimensions is suppressed when τ exceeds a critical value τc and is replaced by a permanent finite-amplitude structure, an intermolecular-capillary wave, that travels at approximately the speed of the surface. For small amplitudes, the wave is governed by the Kuramoto–Sivashinsky equation. If three-dimensional disturbances are allowed, the shear is decoupled from disturbances perpendicular to the flow, and line rupture would occur. In this case, replacing the unidirectional shear with a shear whose direction rotates with angular speed, , suppresses the rupture if τ ≳ 2τc. For the most dangerous wavenumber, τc ≈ 10−2 dyn cm−2 at ≈ 1 rad s−1 for a film with physical properties similar to water at a thickness of 100 nm.