Foam takes on real shape

Physicists and mathematicians research spatially complex structures

What shape is a typical cell in foam? Knowing the answer to this question is very useful in creating parts that must be as light and, at the same time, as stable as possible. Mathematics and physics can provide a solid basis for these sorts of complex structures before engineering researchers get down to work. The new research group “Geometry and Physics of Spatial Random Systems” (GPSRS) provides a link between the two disciplines. Set up by the DFG (German Research Foundation) at the Institute for Theoretical Physics at the Friedrich Alexander University of Erlangen Nuremberg (FAU) and the Karlsruhe Institute for Technology, it has a budget of 1.5 million euros for a total of six projects over the first three-year grant period. The money will be shared between the two institutions: half will go to physicists at Erlangen and the other half to mathematicians in Karlsruhe and Aarhus (Denmark).

Three of the approved projects are based in Prof. Dr. Klaus Mecke’s department, which he heads with his colleague Dr. Gerd Schröder Turk. This cooperation with mathematicians from the Karlsruhe Institute for Technology (spokesperson: Prof. Dr. Günter Last) will be supported by the Danish Centre for Excellence for Stochastic Geometry and Bio imaging in Aarhus (director: Prof. Dr. Eva Vedel Jensen), providing additional Danish financing. The project’s financing may be extended by a further three years after the end of the initial grant period.

The research group is entitled “Geometry and Physics of Spatial Random Systems”. This covers materials such as foam, granulate and liquid crystals. In order to better understand materials with such complex structures and to be able to describe their properties and reactions under specific conditions, further development of spatial stochastics and integral geometry methods and models is planned. This, however, requires physics and geometry to work hand in hand. Fortunately, Erlangen has a long tradition in just this and it is the central focus of the Institute for Theoretical Physics.

At Erlangen, statistical physics is tasked with ascertaining the essential relationships between the geometrical and physical properties of condensed materials. Help is drawn from the methods used in field theory, density functional theory and percolation theory. The latter, for example, describes the “seepage” of water through porous materials and the influence of the shape of complex associated pore space on the amount of water that flows through. This can be seen in a process that takes place in millions of kitchens every day: making filtered coffee. Astonishingly, the thermodynamic behaviour of liquids in pores and channels (see photo) depends on just a few geometrical wall sizes and not on the details of complex pore shapes. The density and microscopic structure of liquids, and other substances with similar physical characteristics, can be calculated using density functional theory. What takes place at the micro and nano levels is fundamentally linked to the shape of the parts. Elongated particles, for example, can form liquid crystal structures that are used in technology – in flat screen TV’s (LCD) for instance. Bringing geometry and physics together is essential to understanding this phenomenon.

Thanks to this academic basis, it will be possible to find answers to important but as of yet unsolved technological questions, such as: Why can elliptically shaped grains be more tightly packed into a space than spherical shaped ones? How can movement through porous materials be controlled by means of the shape and alignment of pores? Clarification of the cell structure of foam also falls under this research. In this way, the most complex, supposedly most opaque basic mathematical and physical research makes it easier to tackle very practical problems.

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