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Permanent link (DOI): https://doi.org/10.7939/R35Q4S06K

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Buckling of a thin, viscous film in an axisymmetric geometry. Open Access

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Author or creator
Bhattacharya, S.
Craster, R. V.
Flynn, M.R.
Additional contributors
Subject/Keyword
Surface tension
Fluid equations
Viscosity
Buckling
Shear rate dependent viscosity
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
By adapting the Föppl-von Kàrmàn equation, which describes the deformation of a thin elastic membrane, we present an analysis of the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution, obtained using spectral techniques, yields the most unstable azimuthal wave-number, m ⋆. Contrary to the discussion of Slim et al. [J. Fluid Mech.694, 5–28 (Year: 2012)]10.1017/jfm.2011.437, it is argued that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart, i.e., at the onset of instability, m ⋆ is indefinitely large. Away from this point, however, a comparison with analogue experimental results is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of m ⋆, the phase speed and the wave amplitude; note that no prediction concerning the latter two quantities can be made using the present theory. Experiments reveal a limited range of angular velocities wherein waves of either small or large amplitude may be excited. Transition from one to the other regime does not appear to be associated with a notable change in m ⋆.
Date created
2013
DOI
doi:10.7939/R35Q4S06K
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© 2013 S. Bhattacharya et al. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
Citation for previous publication
Bhattacharya, S., Craster, R., and Flynn, M. (2013). Buckling of a thin, viscous film in an axisymmetric geometry.. Phys. Fluids, 25(), 043102.
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