Griffiths, I. M. and Howell, P. D. (2007) Mathematical modelling of nonaxisymmetric capillary tube drawing. Journal of Fluid Mechanics . ISSN 00221120 (Submitted)

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Abstract
This paper concerns the manufacture of nonaxisymmetric capillary tubing via the Velloprocess, in which molten glass is fed through a die and drawn off vertically. The shapeof the crosssection 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 crosssection evolves like a twodimensional Stokes flow when expressed in suitably scaled Lagrangian coordinates. This allows us to use a previously derived model for the surface tensiondriven evolution of a thin twodimensional 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 nonisothermal 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:  29 May 2015 18:26 
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