Journal of Fluid Mechanics

Papers

Suppressing van der Waals driven rupture through shear

M. J. DAVISa1, M. B. GRATTONa1 c1 and S. H. DAVISa1

a1 Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA

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.

(Received January 29 2010)

(Revised June 09 2010)

(Accepted June 09 2010)

(Online publication August 18 2010)

Key words:

  • oating;
  • instability;
  • lubrication theory

Correspondence:

c1 Email address for correspondence: m-gratton@northwestern.edu

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