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# Mathematicians Reinvent The Beer Widget

Paper could replace the plastic widgets that give canned beers a better head, according to a new mathematical analysis
March 4, 2011

Many a beer drinker will have puzzled over the following: why, when a can of beer is opened, do carbon dioxide bubbles form so slowly. Why not all at once?

The study of bubble formation in carbonated drinks is a relatively new science. In fact, it is only ten years since scientists settled this matter. One group calculated from first principles the rate at which carbon dioxide leaks from solution into a bubble. The answer is slowly. What’s more, it cannot start start without some sort of nucleation site.

Then, another group discovered that the primary sources of nucleation are pockets of gas trapped in cellulose fibres in the drink. The news was greeted by the sound of clinking glasses the world over. Problem solved, right?.

Not quite. While most beers and lagers are pressurised with carbon dioxide, some stouts, dark beers such as Guinness, are pressurised by a mixture of carbon dioxide and nitrogen.

They do this because nitrogen forms smaller bubbles giving the drink a smoother, creamier mouth feel. But it also changes the bubble dynamics significantly. The question is why.

Today, William Lee a mathematician at the University of Limerick in Ireland and a few pals extend the theory of bubble formation to include nitrogen in the mix. Sure enough, nitrogen leaks out of solution more slowly ensuring that its bubbles are smaller. No surprise there.

But Lee and co’s formulation of the problem leads to an interesting idea–the possibility of an entirely new type of widget.

If you’re not familiar with widgets, here’s some background. One problem with nitrogen-pressurised stouts sold in cans is that opening the can, depressurising the beer and pouring it into a glass does not create enough bubbles to form a head.

In the 70s, 80s and 90s, a crack team of scientists at Guinness solved this problem with a device that has come to be known as a widget. In its current form, a widget is a hollow ball with a small hole in it filled with nitrogen and carbon dioxide under pressure.

Opening the can causes the gas to jet out into the stout, creating many millions of bubbles at a much faster rate than usual. These bubbles then rise to the top forming a head. This great invention (some say the greatest) allows drinkers to enjoy so-called ‘draught Guinness’ at home, out of can.

Lee and co studied the problem by creating a mathematical model of a small nitrogen/carbon dioxide bubble trapped in a cellulose fibre and working out how quickly it would grow.

And in a brave move for mathematicians, they have even confirmed their numerical results by watching real bubbles forming in the cellulose fibres in coffee filter paper. “A single ﬁbre produces one bubble every 1.28 seconds,” they say.

That doesn’t sound like enough to make any difference to a can of stout, which requires some 10^8 bubbles to form a head. But if a drink takes 30 seconds to pour, Lee and co calculate that this would require 4.3x10^6 fibres, about as many as you get in a sheet of coffee filter paper about 3cm square.

So their idea is to replace the beloved widget with a credit-card sized sheet of paper. I’m guessing beer drinkers won’t mind if the new approach keeps the price of a pint down. Time for some serious testing.

Ref: arxiv.org/abs/1103.0508: Bubble Nucleation In Stout Beers

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Illustration by Rose Wong

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