The Mathematical Institute, University of Oxford, Eprints Archive

Mathematical modelling of non-axisymmetric capillary tube drawing

Griffiths, I. M. and Howell, P. D. (2007) Mathematical modelling of non-axisymmetric capillary tube drawing. Journal of Fluid Mechanics . ISSN 0022-1120 (Submitted)

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Abstract

This paper concerns the manufacture of non-axisymmetric capillary tubing via the Velloprocess, in which molten glass is fed through a die and drawn off vertically. The shapeof the cross-section evolves under surface tension as it flows downstream. The aim is to achieve a given desired final shape, typically square or rectangular, and our goal is to determine the required die shape. We use the result that, provided the tube is slowly varying in the axial direction, each cross-section evolves like a two-dimensional Stokes flow when expressed in suitably scaled Lagrangian coordinates. This allows us to use a previously derived model for the surface- tension-driven evolution of a thin two-dimensional viscous tube. We thus obtain, and solve analytically, equations governing the axial velocity, thickness and circumference of the tube, as well as its shape. The model is extended to include non-isothermal effects.

Item Type:Article
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:654
Deposited By:Richard Booth
Deposited On:14 Sep 2007
Last Modified:20 Jul 2009 14:23

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