The answer in black and white

ON MARCH 17th, St Patrick's day, countless pints of Irish stout will be poured in pubs and homes around the world. As they sup their beer, revellers might do well to give a nod to the technology that makes possible the creamy head which sits atop it—for unlike the natural head on an ale or a lager, the head on stout is a work of art.

To make it foam, draught stout is forced through a special plate. Bottled and canned versions require the intervention of a tiny beer-widget. This is a hollow plastic sphere that, upon the container being opened, releases a jet of gas into the beer. When introduced, the widget was the subject of an incredibly irritating advertising campaign, apparently conceived by marketing types who were terrified their customers might be put off by such an elegant piece of technology.

The widget's days, though, may be numbered, for a crack group of mathematicians from the University of Limerick, led by William Lee, has modelled bubble formation in stout beers in detail. Their work suggests that lining the rims of cans and bottles with a material similar to an ordinary coffee filter would be a simpler, cheaper alternative to the widget. The team's calculations show that a copious number of bubbles would form from air trapped inside the hollow fibres making up this lining. They have just submitted their work for publication in Physical Review E and are hoping that industry will soon begin testing their proposal.

Most beers are pressurised with carbon dioxide. Stouts, though, use a mixture of that gas and four times its volume of nitrogen. This makes the beer less acidic, and also produces smaller, creamier bubbles. But nitrogen is less soluble than carbon dioxide. Hence the need for the widget. And the widget adds to the container's cost, so brewers of stout would be delighted to find a way to get rid of it.

In that spirit representatives of Diageo, which owns Guinness, one of the most widely sold brands of stout, approached Dr Lee in 2009. They wondered if he might be able to construct a mathematical model of the formation and growth of bubbles in stout. Dr Lee was happy to oblige. And once he had produced the model, he started thinking more about the problem. He wondered why the normal mechanism of bubbling in beers and sparkling wines does not appear to work in stouts.

Conventional wisdom used to hold that once the pressure inside a bottle or can has been released by opening it, the bubbles in a fizzy drink, whether alcoholic or not, are seeded by pockets of air trapped in scratches and imperfections on the surface of the glass being drunk from. Over the past decade, however, scientific scrutiny has revealed that most bubbles actually form on fibres of cellulose that have either fallen into the glass from the air or been left behind when it was dried with a towel. These fibres, which are generally hollow, trap a small amount of air in their interiors.

To see what is going on in stouts, Dr Lee and his team wrote down the equations governing the physics of the dissolved gases and fibres. They found that molecules of nitrogen and carbon dioxide are able to diffuse from the liquid through the walls of the fibres into the air pockets trapped inside them, causing those pockets of air to expand. If a pocket reaches the end of a fibre, it breaks off as a bubble.

The problem, as far as stouts are concerned, is that the low concentration of dissolved nitrogen means the process works at only a 15th of the rate seen in ales and lagers. But Dr Lee has an answer to that: more cellulose. He and his team spiked their beer with extra fibres from a cut-up coffee filter and watched the bubbles form under a microscope. By crunching the numbers from these observations, they calculate that lining a can of stout with nine square centimetres of fibres should form a head as good as that produced by a widget. If their method works on an industrial scale it will have two benefits. Stout will be cheaper. And those irritating adverts proclaiming that you do not need to know how a widget works in order to enjoy its benefits will disappear for ever.