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Publications [#9802] of Thomas P. Witelski
search www.ams.org.Papers Published
- D. Vaynblat, J. R. Lister and Thomas P. Witelski, Rupture of Thin Viscous Films by van der Waals Forces: Evolution and Self-similarity,
Physics of Fluids 13, 5 (2001) 1130-1140.
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(last updated on 2001/04/12)
Abstract: Van der Waals driven rupture of a freely suspended
thin viscous sheet is examined using a long-wavelength
model. Dimensional
analysis shows the possibility of first-type similarity
solutions in which
the dominant physical balance is between inertia,
extensional viscous
stresses and the van der Waals disjoining pressure, while
surface tension is
negligible. For both line rupture and point rupture the film
thickness decreases
like $(\ts-t)^{1/3}$ and the lateral lengthscale like
$(\ts-t)^{1/2}$, where
$\ts-t$ is the time remaining until rupture. In each
geometry these scalings
are confirmed by numerical simulations of the time-dependent
behaviour, and a
discrete family of similarity solutions is found. The
`lowest-order' mode in
the family is the one selected by the time-dependent
dynamics.
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