Math whizzes recalculate beer-foaming equation

Just in time for St. Patty's, mathematicians from Ireland figure out how to put a better, cheaper head on your Guinness.

Pay attention students; here's yet another reason to do your advanced math homework. Mathematicians have conducted a new analysis that could have a profound impact on future St. Patrick's Days--by building a better beer widget.

If you've enjoyed a Guinness or one of several other stout beers from a can in the last few years, you've probably encountered a beer widget. It's the hollow plastic ball that's left rattling around in the can or bottle after all the thick, creamy goodness has been poured out; it's also largely responsible for the foamy head on that just-poured brew.

William Lee, a university mathematician from Limerick in Ireland (disclosure: also the ancestral home of this writer) has set out to improve one of the most treasured modern inventions of pub-goers, and his findings seem to indicate a way to create a more efficient, less expensive widget. Drinkers rejoice!

But before getting to the toasting and celebrating, a little background on the fluid dynamics of stout beers. A tall can of Guinness has nitrogen added to keep it pressurized, rather than just the carbon dioxide found in most other canned beers. This is because nitrogen produces smaller bubbles, creating that distinctively smooth, creamy stout foam.

The downside of nitrogen is that just cracking open and pouring the can doesn't create enough bubbles for a truly satisfying head. Enter the widget--the hollow ball is filled with nitrogen that shoots out into the stout when the can is cracked, creating millions of bubbles and giving a little turbo-boost to the foam creation process. Problem solved, right? Sure, but there's always a way to build a better widget.

Enter Lee's research (PDF), conducted with a few colleagues from the Department of Mathematics and Statistics at the University of Limerick.

The team looked at an alternate means of boosting stout foaming action--essentially, the idea involves harnessing the gas pockets trapped within cellulose fibers as points for bubbles to grow and release within the beer when cracked and poured. Using a mathematical model, Lee and company figured out just how much cellulose fiber would be needed to create enough bubbles for a head that could compete with a draught pour at a local pub. As stated in the team's final report, titled "Bubble Nucleation In Stout Beers" and submitted to the journal Physical Review E, but not published there yet:

The total area that must be occupied by fibres is 8.3 x 10-4 m2 equivalent to a square with edge length 2.9 cm."

Translation: Add a credit-card size piece of paper to a can of Guinness, or perhaps coat the inside of the can with a layer of paper-like fibers, and you've just built a much simpler widget that could take a few cents of the price off that can of stout.

The current plastic widgets aren't expensive, but their production and the time-intensive process of extracting potentially beer-souring oxygen from them does add a minimal cost for Guinness lovers everywhere.

There is a bit of a catch, though. The cellulose fiber method--which has yet to make its way to any watering holes that we know of--doesn't add the single quick jolt of bubble production that the widget does.

That means that ensuring a sufficient head from a paper-based widget will require a slow pour from the can, probably about 30 seconds from full to empty (more info on beverage-pouring essentials here). But as true Guinness fans know, half the pleasure is in the anticipation.

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