Glass Manufacturing
OCIAM enjoys a long-standing and fruitful
relationship with
Pilkington plc,
one of the world's largest glass manufacturers.
We work on the mathematical modelling of many different aspects of
glass processing, of which the following are of greatest current interest.
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Brittle fracture
A current hot topic is the study of the rapid propagation and
bifurcation of cracks through a piece of glass when it is struck by a
hard object.
Melting sand to make glass
All glass originates from sand which is heated upto 1500 degrees in
a furnace before it flows out
to make into windows, TV screens, optical fibres, etc. The mechanics and heat flow in the
furnace pose mathematical challenges akin to those encountered in, say, magma dynamics
within the earth. But in glass manufacture, minute imperfactions are all important
and high precision modelling is vital. With concerning vthe melting of the sand and through
the hydrodynamics of the molten glass.
Capillary tube drawing
How do we make square test tubes and capillary tubing?
To produce regular capillary tubing requires vthe drawing of molten glass through a `doughnut'
shaped die, and drawn off. However, if we begin with a square cross-sectional die, then the effects of
surface tension during the tube drawing process will cause the profile to evolve towards a more circular profile.
The full question we wish to answer is: given any final tube cross-section, what is the die shape required to
produce this?
This work is motivated by our links with Scott Glass in Mainz, Germany.
Window glass cooling
In the final stages of window glass manufacture in a float glass factory
(where the liquid glass from the furnace solidifies as it floats on a thin layer of molten tin)
the glass needs ot be cooled by about 100 degrees by passing it under a cold water jet. The hydrodynamics
of this jet are such that it leads to a completely novel class of boundary layer problems in viscous flow,
wherein water in the jet can flow both upstream and downstream at any particular spot on the glass.
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Selected references
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J. N. Dewynne, J. R. Ockendon & P. Wilmott,
1989 On a mathematical model for fiber tapering,
SIAM J. Appl. Math. 49, 983-990.
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B. W. van de Fliert, P. D. Howell & J. R. Ockendon,
1995 Pressure-driven flow of a thin viscous sheet,
J. Fluid Mech. 292, 359-376.
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P. D. Howell,
1996 Models for thin viscous sheets,
Euro. Jnl Appl. Maths 7, 321-343.
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L. J. Cummings & P. D. Howell,
1999 On the evolution of nonaxisymmetric viscous fibres with surface
tension, inertia and gravity,
J. Fluid Mech. 389, 361-389.
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D. Salazar & R. Westbrook,
2002 Inverse Problems of Mixed Type in Linear Plate Theory,
in preparation.
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People working in this area within OCIAM
are
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