Modelling the spreading and draining of viscous films

摘要: The focus of the work in this thesis is to gain new insight into fluid behaviour observed a float glass furnace by means simplified mathematical models. In particular, models explore dynamics films foam, known as logs, that spread across surface pool molten glass. model employed throughout two dimensional Navier-Stokes equations, limit zero Reynolds number, together with appropriate conditions at moving boundaries. Throughout thesis, slender geometry exploited using asymptotic techniques simplify introductory chapter, motivating manufacturing process described, then and modelling assumptions are used introduced. first technical chapter for spreading viscous on deep considered. Although neglects effects drainage it enables analytical progress be made. As such, gained how logs interact one another they underlying pool. Analytic expressions evolution single film, an infinite array obtained. addition, some comments general configuration next draining film flat simplistic, interaction via pool, does allow initial ideas explored. systematically reduced nonlinear diffusion PDE. subsequent analysis applicable broad family PDEs, hence presented generality. Solutions PDEs under consideration exhibit interesting which front compactly supported solution changes its direction propagation. To phenomenon, advances (due gravity driven spreading) recedes drainage) examined. solutions local time propagation obtained their implications discussed. final from previous chapters drawn together. A considered incorporates both drainage, allows It shown can singular integro-differential equation (SIDE). special case, steady state SIDE combination numerical techniques. complement chapters, advancing receding fronts also results summarised, practical implementation not only gives rise number novel results, but provides understanding industrial