The Mathematical Institute, University of Oxford, Eprints Archive

Models for thin viscous sheets

Howell, P. D. (1996) Models for thin viscous sheets. European Journal of Applied Mathematics, 7 . pp. 321-343.

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Abstract

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 generalised to give new models for fully three-dimensional sheets.

Item Type:Article
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:106
Deposited By:Peter Howell
Deposited On:04 Aug 2004
Last Modified:20 Jul 2009 14:18

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