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Irish Mathematicians Solve The Guinness Sinking Bubble Problem

Bubbles sink in Guinness because of the peculiar geometry of pint glasses, say a dedicated group of researchers at the University of Limerick

One of the more intriguing conundrums in fluid dynamics is the puzzling behaviour of bubbles in Guinness, the famous Irish stout. 

As many drinkers will attest, the bubbles in Guinness appear to sink as the drink settles and the head forms. How can this be, given that bubbles are less dense than the surrounding fluid and so should rise?

Over the last ten years or so, physicists have begun to pick this problem apart. Most recently they’ve shown that it is not the bubbles that sink but the liquid, which circulates in a way that is downwards near the glass walls and upwards in the interior.  As long as the downward flow of the liquid is faster than the upward motion of the bubbles, they will appear to sink. 

But that still leaves a puzzle: why does the liquid circulate in this way?

Today, a dedicated team of Irish mathematicians reveal the answer. Eugene Benilov, Cathal Cummins and William Lee at the University of Limerick say the final piece in this puzzle is the shape of the glass, which has a crucial influence over the circulatory patterns in the liquid.

To understand how, first remember that the motion of every bubble exerts a drag on the liquid around it. Now imagine what would happen if there were a region of liquid containing fewer bubbles near the wall of a pint glass and consequently a region of higher bubble density near the middle of the glass. 

Benilov and co say that the drag will be higher in the region where the bubble density is higher, in other words near the centre of the glass. This creates an imbalance that sets up a circulation pattern in which the liquid flows upwards in the centre of the glass and downwards near the walls.  

That’s exactly as observed in a pint of Guinness. But what causes the region of low bubble density near the glass walls in the first place? 

Benilov and co imagine that to start with, the bubbles are distributed evenly throughout the liquid. In a perfect cylinder, they would simply rise together. The bubbles in each volume of liquid are steadily replenished from below.  

But imagine a container that is narrower at the bottom and wider at the top so that the walls rise at an angle, as in a pint glass. In this case, the simple act of bubbles rising creates a region of low bubble density next to the angled wall because the bubbles are not being steadily replenished below. 

By contrast, the bubble density is higher in the middle of the glass because the bubbles are replenished from below. 

That would set up exactly the circulation pattern that is observed, say Benilov and co.

This effect is well known in sedimentation theory as the Boycott effect. “It was first observed in test tubes containing red blood cells when it was discovered that sedimentation times could be significantly reduced by inclining the test tubes,” say Benilov and co.

These guys have even created a computer model of bubble behaviour in Guinness which confirms their thinking. 

The icing on the cake, however, is that there is a simple experiment that can easily confirm the theory. 

Experiments are not usually the domain of mathematicians. But Benlivo and co demonstrate valour beyond the call of mathematical duty by actually performing the experiment in which they bravely pour Guinness into a cylinder. “If the container is tilted, bubbles will be observed to move upwards near its upper surface and downwards near its lower surface,” they say. 

They have even created a video of this experiment which you can download here (avi).

Of course, the essence of experimental science is repeatability. Many readers will not be content with mere visual evidence from a video but insist on repeating this experiment on their own terms, perhaps in a hostelry of their own choosing. Quite right.

But if you choose this route, remember that this work is not entirely whimsical. “Understanding these types of bubbly flows is important for a number of applications, such as manufacturing champagne glasses engraved with nucleation sites, and widget and similar technologies for promoting foaming in stouts,” say Benilov and co.

Guinness drinkers (and servers) will also be aware of another problem that plagues them–the time it takes for a pint of Guinness to settle, which is significantly longer than with most ales and lagers. 

Could this work allow pint glasses to be redesigned in a way that encourages stouts to settle more quickly? 

We’ll be following future developments closely.

Ref: arxiv.org/abs/1205.5233: Why Do Bubbles In Guinness Sink?

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