Two Mathematical Problems Related to Drawing of Glass Sheets
[A] Dripping of Viscous Fluids
One way to make large glass sheets is with the overflow fusion process . “Overflow” of viscous fluids and “dripping”  are general phenomena. Recent work by Lin and Kondic  covers the stability of thin films flowing down inverted substrates, with a particular assumption of the flow at the leading edge. In other cases of physical interest , the flow at the leading edge is different with a “tank tread type motion” and particles on the free surface end up on the wall. Lava can flow in a similar way 
The proposed problems:
(1) What are the non-dimensional parameters that predict leading edge ‘dripping’ of a viscous fluid on an inverted substrate with a “tank-tread” type leading edge flow?
(2) Can we analyze the problem if the leading edge is not straight (i.e. slightly wavy)?
[B] Deformation of Thin Viscous Sheets
Howell has presented ,  a rigorous derivation of the equations governing the stretching of thin viscous sheets. Further work in this area has been done by Filippov & Zheng  in an application to the drawing of thin glass sheets for TFT LCD displays.
Sheets as large as 2880x3130x0.70mm  are formed in manufacturing.
The proposed problems:
(1) When can bending stresses be neglected? Edge effects: How close to the edge can bending stresses be neglected? How important are these relative to capillary forces near the edge?
(2) If there is a viscosity gradient through the thickness (for example a small thermal gradient) how should that affect the evolution of the shape and Howell’s conjecture  about isometric shapes?
 Lin, H-J., and Chang, W-K., “Design of a sheet forming apparatus for overflow fusion process by numerical simulation”, J. Non-Crystalline Sol. (2007) Vol. 353 pp.2817-2825.
 Wilson, S.D.R, “The slow dripping of a viscous fluid”, J. Fluid Mech. (1988) Vol. 190 pp.561-570.
 Lin, T., and Kondic, L, “Thin films flowing down inverted substrates”, submitted to Phys. Fluids, pre-print available at
 Radler, J., Strey, H., and Sackmann, E., “Phenomology and Kinetics of Lipid Bilayer Spreading on Hydrophilic Surfaces”, Langmuir (1995) Vol. 11. pp.4539-4548.
 Osiptsov, A.A., “Three-Dimensional Isothermal Lava Flows over a Non-Axisymmetric Conical Surface”, Fluid Dynamics (2006) Vol. 41 No. 2
 Howell, P.D., “Models for thin viscous sheets”, Eur. J. Appl. Math. (1996) Vol. 7 pp.321-343.
 Howell, P.D., “Extensional thin layer flows”, Ph.D. thesis, Univ. Oxford 1994.
 Filippov, A., and Zheng, Z., “Dynamics and shape instability of thin viscous sheets”, Phys. Fluids (2010) Vol. 22, p. 023601
 “Corning Gives Tour of New LCD Glass Substrate Facility”, Ceramic Industry 3/18/2010