Models for thin viscous sheets
- 1 August 1996
- journal article
- research article
- Published by Cambridge University Press (CUP) in European Journal of Applied Mathematics
- Vol. 7 (4) , 321-343
- https://doi.org/10.1017/s0956792500002400
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.Keywords
This publication has 17 references indexed in Scilit:
- Onset of folding in plane liquid filmsJournal of Fluid Mechanics, 1996
- Pressure-driven flow of a thin viscous sheetJournal of Fluid Mechanics, 1995
- Dynamics of a Lamella in a Capillary TubeSIAM Journal on Applied Mathematics, 1995
- SLENDER VISCOUS FIBRES WITH INERTIA AND GRAVITYThe Quarterly Journal of Mechanics and Applied Mathematics, 1994
- Universal pinching of 3D axisymmetric free-surface flowPhysical Review Letters, 1993
- A systematic derivation of the leading-order equations for extensional flows in slender geometriesJournal of Fluid Mechanics, 1992
- Buckling instabilities in layers of viscous liquid subjected to shearingJournal of Fluid Mechanics, 1988
- The buckling and stretching of a viscidaJournal of Fluid Mechanics, 1975
- The flow of a tubular film Part 2. Interpretation of the model and discussion of solutionsJournal of Fluid Mechanics, 1970
- The flow of a tubular film. Part 1. Formal mathematical representationJournal of Fluid Mechanics, 1970