The Mathematical Institute, University of Oxford, Eprints Archive

The surface-tension-driven evolution of a two-dimensional annular viscous tube

Griffiths, I. M. and Howell, P. D. (2007) The surface-tension-driven evolution of a two-dimensional annular viscous tube. Journal of Fluid Mechanics . ISSN 0022-1120 (In Press)

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Abstract

We consider the evolution of an annular two-dimensional region occupied by viscous fluid driven by surface tension and applied pressure at the free surfaces. We assume that the thickness of the domain is small compared with its circumference so that it may be described as a thin viscous sheet whose ends are joined to form a closed loop. Analytical and numerical solutions of the resulting model are obtained and we show that it is well posed whether run forwards or backwards in time. This enables us to determine, in many cases explicitly, which initial shapes will evolve into a desired final shape. We also show how the application of an internal pressure may be used to control the evolution. This work is motivated by the production of non-axisymmetric capillary tubing via the Vello process. Molten glass is fed through a die and drawn off vertically, while the shape of the cross-section evolves under surface tension and any applied pressure as it flows downstream. Here the goal is to determine the die shape required to achieve a given desired final shape, typically square or rectangular. We conclude by discussing the role of our two-dimensional model in describing the three-dimensional tube-drawing process.

Item Type:Article
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:653
Deposited By:Richard Booth
Deposited On:14 Sep 2007
Last Modified:20 Jul 2009 14:23

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