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, $\widehat{\omega}$, suppresses the rupture if $\tau \gtrsim 2{\tau}_{c}$. For the most dangerous wavenumber, ${\tau}_{c}\approx {10}^{-2}$ dyn cm${}^{-2}$ at $\widehat{\omega}\approx 1$ 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) |