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Models for thin viscous sheets

Published online by Cambridge University Press:  26 September 2008

P. D. Howell
Mathematical Institute, 24–29 St Giles', Oxford, UK


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.

Research Article
Copyright © Cambridge University Press 1996

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