When you pour yourself a nice pint of Guinness, there’s only one thing running through your mind, right? As the brew settles, why do the bubbles sink down instead of rising up?! Okay, so the “Guinness cascade” may not have been your primary concern, but the gravity-defying bubbles did intrigue a few mathematicians at the University of Limerick, who explored how the shape of the Guinness glass affected the flow of bubbles

in an article they posted at the pre-print arXiv.

Credit: Alexander & Zare

The Guinness cascade is not a new phenomenon, and a basic

explanation already exists

. All things being equal, the bubbles of gas in a liquid like soda or beer rise because gravity exerts more force on the denser liquid around them. But it turns out that where the bubbles are in the glass makes a big difference in their behavior. The bubbles near the walls of a container stick to the glass, which drags on them and slows their upward motion. The bubbles in the center of the cup, in contrast, can rise unimpeded. As they move, they exert a slight drag force on the surrounding liquid. This motion forms a column that circulates the beer in the center of the glass upward, while forcing the beer---and the bubbles---along the wall to sink down. In fact, this effect happens in other liquids as well, but in a glass of Guinness, the cream-colored bubbles stand out particularly clearly against the dark drink. http://youtu.be/kEEbE3vbGw8 But the Irish mathematicians chose to tackle the problem from a new perspective: How does the shape of the glass affect the Guinness cascade? To find out, they created a mathematical model of the bubbles’ flow in a traditional pint glass, whose walls slope out from a smaller bottom to a wider mouth, and in the so-called “anti-pint” glass, with walls that slope in from the bottom to the smaller opening. (Note: do not touch a pint to an anti-pint or they will annihilate

and send rays of beer flying away from the collision in opposite directions. We're almost sure of it.)

Rising bubbles' positions with respect to the wall of a pint (left) and anti-pint glass.

There were some key differences between the two mathematical models. More bubbles clustered along the walls of the anti-pint glass than along the walls of the traditional pint. To understand why, the researchers considered the bubbles' motion immediately after the beer is poured into the glass, before the Guinness cascade effect kicks in. The walls of the pint glass slant outward, so as the bubbles rise, they move away from the walls (see panel a in the figure to the right). The walls of the anti-pint glass slant in, so when the bubbles rise, they wind up running into the walls (panel b). As you'll recall, bubbles can drag liquid along with them when they move. This means that when there are lots of bubbles in the center of a glass, as in the pint glass, there is also more drag force in the center, creating that central column that pushes down the liquid at the edges, which in turn creates the Guinness cascade effect. But in the anti-pint glass, the researchers’ simulation indicated that the higher bubble density at the edges would give the central column less drag force, and allow the bubbles near the wall to flow up. According to the model, pouring Guinness into an anti-pint should negate the sinking-bubbles effect. Now, all that remains is to confirm this conclusion with an experiment. Perhaps one in an Irish pub rather than a lab…

Image via benjaminasmith / Flickr