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Vol. LXI, No. 19
Wednesday, May 9, 2007
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Got Froth? Institute Math Prof May Help Settle Beer Question

Linda Arntzenius

It's not the sort of public reaction normally expected for a scientific article, but a joint paper by mathematician Robert D. MacPherson and physicist David J. Srolovitz has sparked a good deal of comment in the British press after its recent publication in the scientific journal Nature.

The article's findings bear on the question of why the froth on a pint of stout, like Guinness for example, lingers while that on a regular pint dissipates.

The BBC quickly picked up the story and it's been the subject of blogs by academics and beer lovers alike.

According to Nature, the research may lead to the "development of predictive models for capillarity-driven microstructure evolution in a wide range of industrial and commercial processing scenarios such as the heat treatment of metals, or even controlling the 'head' on a pint of beer."

And Brits take beer seriously.


Titled "The von Neumann relation generalized to coarsening of three-dimensional microstructures," the paper concerns cellular structures such as those found in nature as well as in manmade metal and ceramic materials, which are composed of many small crystalline grains separated by boundaries that change according to temperature and manufacturing processes.

Beer foam comprises networks of gas-filled bubbles separated by liquid. It's a microstructure with complex interfaces.

Over time, the bubbles merge and the foam settles and eventually disappears in a process known as "coarsening."

The research shows that bubble walls move as a result of surface tension — the same property that supports an insect on pond water — and the speed at which they move is related to the curvature of the bubbles.

According to Prof. Srolovitz, what happens in beer is the small bubbles shrink and the big bubbles grow and eventually pop as their walls get thinner and thinner. "On Earth, there's gravity and the liquid that's within the walls tends to drain out back into the beer."

The new findings predict the evolution of every single bubble in beer froth as well as in other polycrystalline materials. "The theory tells you how the size of every single bubble will evolve in time," said Prof. Srolovitz in a BBC interview.

According to Prof. MacPherson, who has made major contributions to the fields of algebraic geometry, geometry-topology, differential geometry, and singularity theory, "Mathematical invariants that have beautiful properties are mathematically natural, and mathematically natural concepts have the amazing tendency to come up in real world applications."

The formula may lead to a host of improved materials and the key to its discovery was applying a concept from the discipline of "pure math" to a problem in the "real world."


The discovery is the result of an unusual collaboration. While attending Prof. Srolovitz's graduate course in materials science at Princeton University, Prof. MacPherson was reminded of a two-dimensional grain growth formula devised by John von Neumann.

One of the Institute's first professors, von Neumann came up with the formula explaining the growth rate of cellular structures in two dimensions as a function of the number of sides per grain in 1952.

Prof. MacPherson has extended the 50-year-old math to apply in three, four, five, and six dimensions.

"I thought materials science would be a good source of new mathematical problems," said the Institute mathematician who believes there may be other unsolved problems in materials science that could yield to already existing mathematics as well as other problems that would require the development of new mathematics.

Now that, he said, would be even more interesting.


The media "hoopla" has tickled both scientists. "'Mathematician studies beer' seems to be like 'man bites dog' in making newspapers and bloggers notice a story," said Prof. MacPherson, who warns that the scientists' findings don't provide the last word on the matter of the head on a pint of beer.

"Beer froth is the product of several processes, and our formula applies to only one of them," he pointed out.

Because of all the publicity, however, the scientists did hear from one beer scientist who revealed the secret of the famous stout's fine head: Guinness uses nitrogen to make its bubbles.

Although the consensus in the British press seems to be that the matter is now settled, one blogger begs to differ. Responding quickly to the April 26 Nature article, the blogger called Beervatar was skeptical. He said: "Pfft! The reason is because stout has higher levels of sticky proteins in it, so the bubbles last longer…"

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