Having solving all the world’s problems, Irish mathematicians now explain why Guinness bubbles sink

Simulations of the elongated vortices in (left) a pint glass, where bubbles sink near the glass wall, and (right) an anti-pint glass, where bubbles rise near the wall. Image credit: E. S. Benilov, et al.

From Phys.org

— Why do the bubbles in a glass of stout beer such as Guinness sink while the beer is settling, even though the bubbles are lighter than the surrounding liquid? That’s been a puzzling question until now, as a team of mathematicians from the University of Limerick has shown that the sinking bubbles result from the shape of a pint glass, which narrows downwards and causes a circulation pattern that drives both fluid and bubbles downwards at the wall of the glass. So it’s not just the bubbles themselves that are sinking (in fact, they’re still trying to rise), but the entire fluid is sinking and pulling the bubbles down with it.

As mathematicians Eugene Benilov, Cathal Cummins and William Lee explain in their paper at arXiv.org, stout beers such as Guinness foam due to a combination of carbon dioxide and nitrogen bubbles, while other beers foam due only to carbon dioxide bubbles. The nitrogen results in a less bitter taste, a creamy long-lasting head, and smaller bubbles that sink while the beer is settling.

The researchers here are not the first to examine the problem of sinking bubbles in stout beers. During the past decade, experiments have shown that the phenomenon of sinking bubbles is real and not an optical illusion, and simulations have demonstrated the existence of a downward flow near the wall of the glass and an implied upward flow in the middle. But this is the first time that researchers have shown that the mechanism of this circulation pattern depends on the shape of the glass.

To analyze the effect of different glass shapes, the mathematicians modeled Guinness beer containing randomly distributed bubbles in both a pint glass and an anti-pint glass (i.e., an upside-down pint). An elongated swirling vortex forms in both glasses, but in the anti-pint glass the vortex rotates in the opposite direction, causing an upward flow of fluid and bubbles near the wall of the glass.

The researchers explain that the difference arises from the way the sloping glass walls affect the surrounding bubble density. Once a drink is poured, bubbles start to rise. In the typical pint glass, the bubbles move away from the upward and outward sloping wall as they rise, resulting in a much denser region of fluid next to the wall, with fewer bubbles. Because this region is less buoyant, it sinks under its own gravity. Although the nearby bubbles are still trying to rise, the velocity of the downward flow exceeds the upward velocity of the bubbles, so the bubbles that are close enough to the wall get pulled down by the surrounding liquid.

The opposite effect happens in an anti-pint glass, where bubbles tend to clump more near the oppositely sloped wall as they rise. The increase in bubbles results in a less dense region next to the wall, and fluid near the wall moves upwards.

While this explanation seems to accurately describe observations, the researchers noted that they are still uncertain of the specific mechanism responsible for reducing the bubble density near the wall for the pint geometry and increasing it for the anti-pint one.

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