31 May 2018
IMA Journal of Applied Mathematics
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 dimensions of the heater zone used for the latter ‘redraw’ process determine the relative change in the width and thickness of the sheet. When a product with the same cross-sectional aspect ratio as the original sheet is desired, the heater zone through which the sheet is drawn must be long compared with the sheet width. However, deviations from the original aspect ratio due to the finite length of the heater zone can be significant, and the final product is typically thick at the edge compared to the centre. We present a model for redraw of a thin glass sheet and consider the limit in which the heater zone is long compared with the sheet width. We show that the deviations in aspect ratio and thickness depend linearly on the ratio of sheet width to heater zone length and arise due to boundary layers at the sheet ends where the fluid flow adjusts to satisfy imposed boundary conditions. The behaviour inside the boundary layers can be reduced to a canonical problem that is independent of process parameters, and we thus calculate the final thickness and width of the redrawn sheet.
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