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  • European Journal of Applied Mathematics, Volume 7, Issue 4
  • August 1996, pp. 321-343

Models for thin viscous sheets

  • P. D. Howell (a1)
  • DOI:
  • Published online: 01 September 2008

Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalized to give new models for fully three-dimensional sheets.

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J. N. Dewynne , J. R. Ockendon & P. Wilmott (1989) On a mathematical model for fiber tapering. SIAM J. Appl. Math. 49, 983990.

J. N. Dewynne , P. D. Howell & P. Wilmott (1994) Slender viscous fibres with inertia and gravity. Quart. J. Mech. Appl. Math. 47, 541555.

J. Eggers (1993) Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71, 34583460.

M. P. Ida & M. J. Miksis (1995) Dynamics of a lamella in a capillary tube. SIAM J. Appl. Math. 55, 2357.

W. W. Schultz & S. H. Davis (1982) One-dimensional liquid fibers. J. Rheology 26, 331345.

L. Ting & J. B. Keller (1990) Slender jets and sheets with surface tension. SIAM J. Appl. Math. 50, 15331546.

P. Wilmott (1989) The stretching of a thin viscous inclusion and the drawing of glass sheets. Phys. Fluids A1, 10981103.

A. L. Yarin , P. Gospodinov & V. I. Roussinov (1994) Stability loss and sensitivity in hollow-fiber drawing. Phys. Fluids 6, 14541463.

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European Journal of Applied Mathematics
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