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The study of the rheology, or flow, of foams aims to understand how a foam moves when pushed or squeezed. The motivations for wanting to understand the properties of foam are widespread and diverse. Foams are common in oil extraction and industrial cleaning. They are also used in the process which separates metal ores, such as lead and zinc, from the rock in which they are found. Closer to home, an understanding of flowing foams helps to extinguish fires more efficiently, to generate the perfect pint of beer, and to get a chocolate mousse into its pot. Foams also have peculiar and remarkable properties: they fall half-way between the familiar extremes of liquid and solid. When only a small force is applied to it, a foam behaves as a solid, and bounces back to its original shape. If the force is larger, or applied more quickly, then a foam moves like a liquid. They therefore generate a rich range of behaviours. Apart from their industrial uses, where an understanding of foam rheology can help to make processes more efficient and cost-effective, anyone who has looked closely at a foam in their bath can tell you that it has a beautiful, easily visible, structure. This structure is very well-defined, and that allows us to analyse the flow behaviour of a foam more easily than that of many other complex fluids. At this workshop, we want to improve the agreement between what is seen in real-life experiments and the mathematical models that researchers are designing to show that they can predict what a foam will do in any given set of circumstances. The most effective way of doing these experiments is to squeeze the foam between two glass plates so that every bubble can be seen as it moves around. This two-dimensional foam is also a simpler thing to theorize about, allowing us to isolate and study new phenomena. In contrast to most existing models, which treat the foam as having no small-scale structure but only particular macroscopic properties, we aim to include the particular structure of foam in our models. It is this structure, after all, that gives the foam its properties. The research will build on the traditional quasi-static model of foam flow, in which the foam is taken to move through a series of equilibrium states in which its surface energy is minimized. The most promising candidate to succeed this model is the Viscous Froth Model, originally developed in Dublin with the help of the PI. In this Viscous Froth Model, which is being further developed jointly in Aberystwyth, the University of Manchester and Dublin, the drag force of the foam against the sides of the container is included, leading to an equation that describes the motion of each bubble in the foam. Solutions to this equation exist for various special cases, and in certain limits; however, for a large foam with many bubbles, new computational techniques are now being investigated to allow its efficient solution. Preliminary results give good qualitative agreement with experiment; we seek to make this agreement quantitative. We therefore intend to work more closely with experiments being performed around the world (in particular, the universities of Grenoble and Rennes in France, and the University of Indiana in the US).
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