Dr Simon Cox
Reader in Applied Mathematics
Specialist Subjects: Foams (structure, drainage and rheology), cellular patterns, yield stress fluids, pressure impulse theory, wave breaking
My research interests involve the study of foam, an example of soft condensed matter. I am interested in modelling structural and dynamic properties of collections of bubbles to be able to predict their response in various applications.
For example, every time you drink a pint, take a bath, or wash up your dishes, you are hoping that the foam will increase your enjoyment and/or the effectiveness of the process. How does the size of the bubbles affect their lifetime? When you eat bread or chocolate mousse, you want it to be formed from lots of small bubbles rather than one large one (as you sometimes see in a loaf of bread). How do you control the bubble size or get the foam into the mould?
Industrially, metallic foams are made in method similar to the baking of bread. Liquid foams are used in the petroleum industry to push oil out of the porous rocks in which it is found. In the mining industry, metal ores are separated from rock by bubbling the mixture through foam, a process known as froth flotation.
Modelling Foams
There are therefore many reasons why it is worthwhile to develop an understanding of the behaviour of foams under various conditions. First, one needs to understand their structure, either in 2D or in 3D. Then, there are a number of dynamic phenomena.
In trying to progress to understand how foams respond, I separate these phenomena into four processes:
- Drainage - the motion of liquid through the foam, usually due to gravity. It is therefore the network of liquid channels between the bubbles, coloured green in the picture below, that are important. I am involved in a project that aims to understand how the liquid moves through a foam which is in a microgravity environment - it generally wants to redistribute itself evenly.
- Rheology - the flow of the whole foam in response to an applied force. I use Brakke's Surface Evolver to perform simulations of flowing foams in which details about each bubble are available (in contrast to a continuum model). I aim to answer questions about how a foam moves past an obstacle, for example when insulation foam has to flow past the handle mount when filling a fridge door, or in a variety of industrial processes in which foam is transported. In the image below, bubbles move past a ball, coloured grey, from left to right, with colour representing their pressure. The wake affects the force that the foam exerts on the ball, which in turn relates to the force that must be applied to push the foam along. I also want to understand what role the viscosity of the foam plays.
- Coarsening - the change in structure due to gas diffusion across the soap films. This leads, in general, to large bubbles (with many faces) growing at the expense of small bubbles. In this context, I use the Surface Evolver to investigate the structure of clusters of bubbles, or foams in containers, that are aging in this way. The software gives all the information necessary to determine the growth-rate of a bubble, and allows me to simulate the evolution of the foam in time.
- Collapse/Coalescence - the bursting of soap films, when they get very thin, or dirty, leads to two bubbles coalescing. If this continues, the whole foam collapses. Sometimes one wishes to be able to collapse a foam quickly, when it is an undesired product of a process. At other times, severe coalescence is detrimental. What remains to be understood is how to relate the coalescence characteristics of a single soap film in controlled conditions to the behaviour of a similar film immersed in a flowing or draining foam.
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BSc (Warwick), PhD (East Anglia)
Mathematics and Physics
Aberystwyth University
Tel: 01970 622764 Fax: 01970 622826 Email: sxc@aber.ac.uk
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