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Suppressing van der Waals driven rupture through shear. (English) Zbl 1205.76115
Summary: 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 τ c 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, ω ^, suppresses the rupture if τ2τ c . For the most dangerous wavenumber, τ c 10 -2 dyn cm -2 at ω ^1 rad s -1 for a film with physical properties similar to water at a thickness of 100 nm.
MSC:
76E17Interfacial stability and instability (fluid dynamics)
76A20Thin fluid films (fluid mechanics)