Free surface flows in industry

Applied mathematicians have long sourced problems from industrial processes. The relationship between mathematics and industry is mutually beneficial. Mathematical models provide industry with invaluable insights into the fundamental physical processes at play in a system and give mathematicians the opportunity to apply known techniques to new problems. In this thesis, two independent problems originating in industrial processes are studied, with a common feature of a fluid free surface. The first problem concerns the manufacture of contact lenses. Contact lenses are produced by placing a fluid between two moulds and squeezing the fluid outwards to form the shape of the lens. The manufacturers reported an issue with the process, finding that at times the fluid moves outwards asymmetrically, resulting in partially formed lenses. The system is modelled using the thin flim equations and the results are analysed to find the optimal operating setup to reduce asymmetrical flow. The second problem comes from the production of stout beer. Stout beer is made with a mixture of nitrogen and carbon dioxide gases to create a creamy long-lasting head. Nitrogen gas is much less soluble in water than carbon dioxide, causing the bubbles it forms to be small and stable. Stout beers require initiation by mechanical methods. Previous work has suggested that cellulose bres may be used to initiate stout beer but a better understanding of the fundamental science behind bubble nucleation by cellulose fibres is needed. In this work, a gas pocket in a cellulose fibre is modelled to estimate the parameters governing disjoining pressure and to determine the mechanism for bubble detachment.