DPhil in the use of asymptotic techniques in modelling glass manufacture

Glass processing typically involves the flow of a viscous liquid, whose viscosity is a strong function of temperature, in a thin domain. We are particularly interested in modelling situations where the geometry is complicated and unknown in advance and/or where the process may be subject to instabilities. In this project, we will focus on the drawing of thin glass sheets to make screens for TVs, tablets and smartphones. It is known that regions of compression can cause these sheets to buckle, resulting in local ripples in the final product. However, there is currently no good complete theory of viscous sheet buckling that explains how the amplitude of the disturbance saturates, due to weakly nonlinear effects, or how the ripples become "frozen in" as the glass cools. Within the project there is also the potential to tackle relevant and pertinent industrial problems on the modelling of glass manufacture should such problems arise within the course of study.

The novelty of the research is as a result of there not yet being a fully known theory of viscous sheet buckling - which will explore during the course of the study. It also comes from utilizing techniques from applied mathematics on a selection of new problems relevant to the industry, where if solved, the quality and efficiency of manufacture will be improved.

While coming under the mathematical sciences theme, this project will specifically fall under the EPSRC research areas of: continuum mechanics, fluid dynamics and aerodynamics, manufacturing the future theme and mathematical analysis. It falls under the area of continuum mechanics because the viscosity of glass is heavily dependent on temperature, so can exhibit both solid and fluid behaviour. As glass behaves as a viscous liquid in the manufacturing process, the research is linked to fluid dynamics and aerodynamics. Because the project aims to improve the ability of the industry to manufacture glass, due to the focus on understanding the instabilities in the process and so helping to limit the defects of the procedure, the research also falls under the manufacturing the future theme. The project also falls under the mathematical analysis area of research because asymptotic techniques will be used to exploit the fact that the geometries studies will often be thin. Techniques in ordinary and partial differential equations will also be used when analysing the resulting equations. Numerical simulations and models will then be used to capture the behaviour of the systems if explicit solutions are not tractable from the analysis.