The transition from lubrication flow to extensional flow in the overflow fusion process

Journal article

We derive a mathematical model for the overflow fusion glass manufacturing process. In the limit of zero wedge angle, the model leads to a canonical fluid mechanics problem in which, under the effects of gravity and surface tension, a free-surface viscous flow transitions from lubrication flow to extensional flow. We explore the leading-order behaviour of this problem in the limit of small capillary number, and find that there are four distinct regions where different physical effects control the flow. We obtain leading-order governing equations and determine the solution in each region using asymptotic matching. The downstream behaviour reveals appropriate far-field conditions to impose on the full problem, resulting in a simple governing equation for the film thickness that holds at leading order across the entire domain.

Authors: Hart, O; Breward, C; Howell, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Journal of Fluid Mechanics
• Volume: 1021
• Article number: A52
• Publication date: 2025-10-23
• Acceptance date: 2025-09-22
• DOI: 10.1017/jfm.2025.10761
• EISSN: 1469-7645
• ISSN: 0022-1120
• Language: English
• Keywords: lubrication theory; thin films