Skip to main content Accessibility help

Edge behaviour in the glass sheet redraw process

  • D. O’Kiely (a1), C. J. W. Breward (a1), I. M. Griffiths (a1), P. D. Howell (a1) and U. Lange (a2)...


Thin glass sheets may be manufactured using a two-part process in which a sheet is first cast and then subsequently reheated and drawn to a required thickness. The latter redrawing process typically results in a sheet with non-uniform thickness and with smaller width than the cast glass block. Experiments suggest that the loss of width can be minimized and the non-uniformities can be essentially confined to thickening at the sheet edges if the heater zone through which the glass is drawn is made very short. We present a three-dimensional mathematical model for the redraw process and consider the limits in which (i) the heater zone is short compared with the sheet width, and (ii) the sheet thickness is small compared with both of these length scales. We show that, in the majority of the sheet, the properties vary only in the direction of drawing and the sheet motion is one-dimensional, with two-dimensional behaviour and the corresponding thick edges confined to boundary layers at the sheet extremities. We present numerical solutions to this boundary-layer problem and demonstrate good agreement with experiment, as well as with numerical solutions to the full three-dimensional problem. We show that the final thickness at the sheet edge scales with the inverse square root of the draw ratio, and explore the effect of tapering of the ends to identify a shape for the initial preform that results in a uniform rectangular final product.


Corresponding author

Email address for correspondence:


Hide All
Ansys Inc. Polyflow, 2013 Release 15.0.
Beaulne, M. & Mitsoulis, E. 1999 Numerical simulation of the film casting process. Int. Polym. Proc. 14 (3), 261275.
Buellesfeld, F., Lange, U., Biertuempfel, R., Pudlo, L. & Jung, H.2014 Method for production of glass components. US Patent 20,140,342,120.
Debbaut, B., Marchal, J. M. & Crochet, M. J. 1995 Viscoelastic effects in film casting. In Theoretical, Experimental, and Numerical Contributions to the Mechanics of Fluids and Solids, pp. 679698. Springer.
Dewynne, J., Ockendon, J. R. & Wilmott, P. 1989 On a mathematical model for fiber tapering. SIAM J. Appl. Maths 49 (4), 983990.
Dobroth, T. & Erwin, L. 1986 Causes of edge beads in cast films. Polym. Engng Sci. 26 (7), 462467.
Filippov, A. & Zheng, Z. 2010 Dynamics and shape instability of thin viscous sheets. Phys. Fluids 22 (2), 023601.
Fortin, M. 1981 Old and new finite elements for incompressible flows. Intl J. Numer. Meth. Fluids 1 (4), 347364.
Griffiths, I. M. & Howell, P. D. 2008 Mathematical modelling of non-axisymmetric capillary tube drawing. J. Fluid Mech. 605, 181206.
d’Halewyu, S., Agassant, J. F. & Demay, Y. 1990 Numerical simulation of the cast film process. Polym. Engng Sci. 30 (6), 335340.
Howell, P. D.1994 Extensional thin layer flows. PhD thesis, University of Oxford.
Howell, P. D. 1996 Models for thin viscous sheets. Eur. J. Appl. Maths 7 (4), 321343.
Logg, A. & Wells, G. N. 2010 DOLFIN: automated finite element computing. ACM Trans. Math. Softw. 37 (2), 20:1–20:28.
Logg, A., Wells, G. N. & Hake, J. 2012 DOLFIN: A C++/Python finite element library. In Automated Solution of Differential Equations by the Finite Element Method, pp. 173225. Springer.
Matovich, M. A. & Pearson, J. R. A. 1969 Spinning a molten threadline. Steady-state isothermal viscous flows. Ind. Engng Chem. Fundam. 8 (3), 512520.
Modest, M. F. 2013 Radiative Heat Transfer. Academic.
Pearson, J. R. A. & Matovich, M. A. 1969 Spinning a molten threadline. Stability. Ind. Engng Chem. Fundam. 8 (4), 605609.
Scheid, B., Quiligotti, S., Tran, B., Gy, R. & Stone, H. A. 2009 On the (de)stabilization of draw resonance due to cooling. J. Fluid Mech. 636, 155176.
Shah, Y. T. & Pearson, J. R. A. 1972 On the stability of nonisothermal fiber spinning. Ind. Engng Chem. Fundam. 11 (2), 145149.
Silagy, D., Demay, Y. & Agassant, J. F. 1999 Numerical simulation of the film casting process. Intl J. Numer. Meth. Fluids 30 (1), 118.
Smith, S. & Stolle, D. 2000 Nonisothermal two-dimensional film casting of a viscous polymer. Polym. Engng Sci. 40 (8), 18701877.
Taroni, M., Breward, C. J. W., Cummings, L. J. & Griffiths, I. M. 2012 Asymptotic solutions of glass temperature profiles during steady optical fibre drawing. J. Engng Maths 80, 120.
Trouton, F. T. 1906 On the coefficient of viscous traction and its relation to that of viscosity. Proc. R. Soc. Lond. A 77 (519), 426440.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Edge behaviour in the glass sheet redraw process

  • D. O’Kiely (a1), C. J. W. Breward (a1), I. M. Griffiths (a1), P. D. Howell (a1) and U. Lange (a2)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed