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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 $\tau$ is applied to the free surface, the rupture instability in two dimensions is suppressed when $\tau$ exceeds a critical value ${\tau }_{c}$ 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, $\stackrel{^}{\omega }$, suppresses the rupture if $\tau \gtrsim 2{\tau }_{c}$. For the most dangerous wavenumber, ${\tau }_{c}\approx {10}^{-2}$ dyn cm${}^{-2}$ at $\stackrel{^}{\omega }\approx 1$ rad s${}^{-1}$ for a film with physical properties similar to water at a thickness of 100 nm.
##### MSC:
 76E17 Interfacial stability and instability (fluid dynamics) 76A20 Thin fluid films (fluid mechanics)
##### Keywords:
oating; instability; lubrication theory