Proving a pint

The BBC News website today reports a further contribution to that perennially popular topic, the mathematics of food and drink. Specifically, a group of researchers from the University of Limerick have produced a study that claims to settle the question of why the bubbles in a freshly-poured pint of Guinness travel downwards rather than rising — as we’d expect them to do, given that they’re less dense than the surrounding fluid.

This is a question to which more than one answer has been proposed over the last ten years or so. An early explanation, which has been refined since, was that the bubbles themselves continue moving upward but the waves of bubble density propagate downwards, in the same sort of way that traffic jams travel backwards along roads. Later experiments at Stanford University suggested that individual bubbles do indeed travel downward, at least at the outsides of the glass where they can be seen. The explanation that was offered for this relies on the presence of a large-scale circulation, with bubbles rising preferentially in the middle of the glass, dragging the liquid with them, and a return flow carrying a few bubbles back down the outsides. However, it’s not clear why bubbles should consistently rise in the middle and sink at the outside — the explanations in terms of drag or surface tension don’t seem to answer this entirely.

The Stanford group found that the shape of the glass was not important. In contrast, the recent work from Limerick, which used a computer fluid dynamics (CFD) model of bubbly flow as well as a few experiments, suggests that the shape of the glass is crucial. (We can probably expect a few enjoyable stushies in conferences until this gets settled one way or another!) The Limerick researchers found that if the glass has the classic shape and widens towards the top, bubbles will rise away from the sides leaving a layer of bubble-poor fluid at the edges. This layer then sinks under its own weight, driving the circulation. When the glass is turned upside down, the CFD results suggest that the circulation does indeed reverse.

This mechanism is similar to a well-known process in the sedimentation of dense particles, known as the Boycott effect. In its simplest form, this is the effect by which particles settle quicker in a tilted test-tube and drive a flow of clear liquid at the top — first discovered in the 1920s as a useful trick for separating blood samples. There is also a process called “intrinsic convection” which doesn’t require the walls of the container to be tilted. This occurs becayse the region of fluid near the wall is relatively poor in particles or bubbles because they can’t fit within a particle (or bubble) radius of the wall: the resulting density difference can be enough to drive rising or sinking relative to the interior of the container.

So, does any of this actually matter? The answer as far as Guinness is concerned is: probably not — not many people will buy an extra pint just because it exhibits interesting fluid dynamics! However, there are parallels to be drawn with some much more important flow problems. In all sorts of chemical engineering processes, it’s necessary to separate small solid particles or small gaseous bubbles from a surrounding fluid, or to keep them from separating for as long as possible, and so it’s necessary to understand the flow processes involved. (A particularly vivid example occurs in the oil and gas industry: it’s common to produce oil and natural gas from the same well, and controlling how much they separate as they travel down kilometres of pipe to the production platform can make a big difference to the wear and tear on the machinery.)

My favourite parallel, though, comes from volcanology. Magma — molten rock — typically contains a lot of dissolved gases such as water vapour. At high pressures within a magma chamber these gases remain dissolved, but when an eruption starts the pressure drops, and as the magma travels up the volcanic conduit the pressure drops still further — like opening a well-shaken bottle of fizzy juice. If the gas escapes quickly enough (which depends on the rock chemistry and the time taken for magma to make its way up the conduit), it may separate entirely so the magma emerges as relatively thick, gloopy lava. If the gas and rock don’t separate entirely, they can emerge as a mixture of hot gas and fragmented rock (ash), giving a classic Plinian eruption column or pyroclastic flows. (I think the analogy between magma and Guinness was first drawn in this paper by Michael Manga of the University of California, Berkeley; some experimental footage on his website illustrates these behaviours.) For those who monitor volcanoes with an eye to public safety, the distinction between these eruption types is absolutely crucial.

So, if you’re a Guinness drinker, take a good look at the next pint that’s poured for you. The brewers may no longer be allowed to claim that “Guinness Is Good For You”[1], but it might do something for your appreciation of physics even if it doesn’t do much for your liver…


[1] Utterly irrelevant cultural footnote: this famous slogan used by Guinness from the late 1920s is said — with some plausibility — to have been written by Dorothy L. Sayers, better known as an essayist, translator of Dante and perhaps the greatest of the “golden era” English detective novelists. She’s also credited with the Guinness toucan, but this is less plausible.

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One Response to Proving a pint

  1. strathmaths says:

    Update: it turns out that our own Prof. Sean McKee was external examiner for the thesis on which this paper was based. So there’s even a Strathclyde connection…

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