The mathematics of Guinness and falling stout bubbles

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The mathematics of Guinness and falling stout bubbles

Who would have guessed that the Irish would put their best minds to work on stout bubbles? Irish scientists have figured out the mystery of why bubbles in stout beer sink, and it may just come down to the shape of the glass.

Simulations suggest an upward flow at the glass’s centre and a downward flow at its edges in which the liquid carried the bubbles down with it.

But the reasons behind this flow pattern remained a mystery.

Now a study on the Arxiv server reports simulations and experiments showing the standard glass’ shape is responsible.

Many stout beers contain nitrogen as well as the carbon dioxide that is present in all beers.

Because nitrogen is less likely to dissolve in liquid, that results in smaller and longer-lasting bubbles.

But it is the sinking bubble that has confounded physicists and mathematicians alike for decades.

Like many such “fluid dynamics” problems, getting to the heart of the matter is no easy task; only recently was it proved they actually sink rather than being the result of an optical illusion.

Now the University of Limerick’s William Lee, Eugene Benilov and Cathal Cummins have discovered the simple answer to the problem - and a test that can be carried out by consumers as well.

The team has been generally interested in the formation of bubbles in liquids.

“One of the things we found was it’s actually very easy to see bubbles forming in stout beer rather than in, say, champagne where the bubble formation process is much more violent,” Dr Lee told BBC News.

But as has happened to a generation of like-minded scientists before them, the question of falling bubbles became their focus.

The team had the idea - borne out by calculations carried out by Mr Cummins - that the relative density of bubbles and the surrounding liquid could be behind the phenomenon.

“If you imagine your pint is full of bubbles, then the bubbles will start to rise,” Dr Lee said.

But the bubbles in a standard pint glass find themselves in a different environment as they rise straight up.

“Because of the sloping wall of the pint, the bubbles are moving away from the wall, which means you’re getting a much denser region next to the wall,” Dr Lee explained.

“That is going to sink under its own gravity, because it’s less buoyant, and that sinking fluid will pull the bubbles down.”

The bubbles, that is, are “trying” to rise, but the circulation that creates drives fluid down at the wall of the glass.

“You’ll see sinking bubbles not because the bubbles themselves are sinking, but because the fluid is and it’s pulling them down with it.”