The formula explains how the tiny bubbles that make up foam grow — an explanation that could lead to the development of products such as metal shrink wrap.

The possibilities include "the heat treatment of metals or even controlling (the) head on a pint of beer," Robert MacPherson of Princeton University in New Jersey and David Srolovitz of Yeshiva University in New York report in the journal Nature.

Foam is made up of many tiny bubbles that scientists think of as cells with boundaries. The new formula calculates how these microstructures grow.

These tiny structures or grains are abundant in nature, making up the foam on a beach or the pebble in your shoe. They also can be found in man-made materials such as ceramics or metals.

"What the theory does is it tells you how the size of every single bubble will evolve in time," Srolovitz said in a telephone interview.

David Kinderlehrer, a mathematician at Carnegie Mellon University in Pittsburgh, said the finding will help materials scientists concoct a number of newfangled materials by rearranging the grains in various materials using computer simulation.

"It tells you how an individual grain grows by itself until something happens to it. That is very important for understanding how to process material," Kinderlehrer said in a telephone interview.

In metal, that means striking the right balance.

"The strength of a metal depends on grain size. As you make smaller and smaller grains, the metal gets stronger and stronger but it also gets more brittle," Srolovitz said.

"For a particular application you want the grain size that represents a compromise between as strong as you can get and as brittle as you can live with," Srolovitz said.

Kinderlehrer said new materials now under study are batteries that do not corrode and shrink-wrap metals that could be used to repair nuclear power plants — without shutting them down.

"A lot of things we can only imagine," said Kinderlehrer, who wrote a commentary accompanying the study.

Julie Steenhuysen