Suppressing van der Waals driven rupture through shear

M. J. Davis, M. B. Gratton, S. H. Davis

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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 is applied to the free surface, the rupture instability in two dimensions is suppressed when exceeds a critical value 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, suppresses the rupture if 2c. For the most dangerous wavenumber, c 102 dyn cm 2 at 1 rad s1 for a film with physical properties similar to water at a thickness of 100 nm.

Original languageEnglish (US)
Pages (from-to)522-529
Number of pages8
JournalJournal of fluid Mechanics
Volume661
DOIs
StatePublished - Oct 25 2010

Keywords

  • coating
  • instability
  • lubrication theory

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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