Profs ponder disappearing beer foam

Hey there, time traveller!
This article was published 26/04/2007 (7011 days ago), so information in it may no longer be current.

DRAWING on 50 years of math theory and a few nights at the pub, a couple of American professors has found the formula describing why the foam doesn’t last after you pour a beer.

Any drinker knows the tiny, foamy bubbles turn into bigger bubbles, and pretty soon there are no bubbles at the top of the glass at all.

Describing why that happens takes a formula with four Greek letters, four English ones, a couple of sets of brackets (one inside the other), and numbers piled three storeys high on top of each other.

Nature, a hotshot science journal, today carries this beer-math study called The von Neumann relation generalized to coarsening of three-dimensional microstructures.

Nature adds a subtitle for people whose math is shaky: “How to pull the perfect pint.”

David Srolovitz, dean of Yeshiva University in New York, is pleased with the beer angle in his study, even though he just threw it in as an afterthought. Everybody’s paying attention to the discovery he made with co-author Bob MacPherson of the Institute for Advanced Study in Princeton, N.J., Albert Einstein’s old school.

Besides, it let him do some field testing.

The roots of their theory go back a couple of generations, to early studies on how bubbles form.

Many materials are made of a lot of grain-sized crystals stuck together. Molten metals generally harden into this form. So do ceramics.

As these grains form, they’re changing from many tiny ones to fewer, larger ones, exactly like soap bubbles or beer foam.

Metal mills and ceramic factories have to make the grain-sized crystals just the right size. Too small, and the material will be brittle. Too big, and it’s less brittle but weak.

Back in 1952, a Princeton math genius named John von Neumann worked out the formula that describes this action in two dimensions. (He just came up with it during discussion at a conference, “seeing” the answer all of a sudden.)

Since then, people working with industrial materials — metals, ceramics, even the shock-absorbing foam in a hockey helmet — have tried tweaking the von Neumann numbers into something that more or less works in three dimensions.

The new formula for three dimensions, Srolovitz says, “gives you an exact result for how every individual bubble in the whole array of bubbles will evolve in time.” (There’s still some work left to do, figuring out how the average bubble will behave.)

Beer, meanwhile, behaves like the molten metal in the steel mill, going through a transition from tiny bubbles to larger ones under the influence of surface tension.

Srolovitz says a field trip to the pub can help with basic concepts.

“You have to get an idea of the basic geometry,” he explains.

“I would say it’s the kind of thing anybody could just sort of stare at, if you’ve had four or five beers and you’re more likely to be in staring mode. It’s really fascinating to watch.”

— CanWest News Service