European Journal of Applied Mathematics

Research Article

Models for thin viscous sheets

P. D. Howella1

a1 Mathematical Institute, 24–29 St Giles', Oxford, UK

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

(Received December 18 1994)

(Revised September 01 1995)