Soot, Comet Ice, And Medical Powders All Have This Number In Common

A new universal packing density for things made of small, rigid particles

If you were to pack a bowl with billiard balls—I know, nobody does this in real life—you would find the balls filled the bowl to a density of 74 percent. If you were to pack a pool with bowling balls—really nobody does this in real life—the balls would fill the pool to a density of… 74 percent.

This is because 74 percent is the maximum density to which perfect spheres fill a space. It doesn’t matter what size the spheres are. And abstract as this idea is, there is one “real life” application where the number shows up. In their mathematical models for predicting climate change, environmental scientists usually assume soot aggregates in the atmosphere in a densities of 74 percent. Soot is a major contributor to global warming, so it plays an important role in climate models.

In a new series of measurements, however, a team of researchers has discovered soot packs at a density of 36 percent, not 74 percent. Not only that, but a wide variety of real life things, including materials in comets, also pack to a density of 36 percent. Thirty-six percent might be a universal density for stuff that’s made of small, rigid particles… which is includes more things than you might think.

Thirty-six percent might be a universal density.

To test their figure, the researchers made soot in their lab at the U.S. National Institute of Standards and Technology. They also recruited one college student and one high school student to perform a series of simple tests. The students glued plastic spheres together in aggregations that mimic the aggregations soot particles form in the air. Instead of filling a space evenly, the way billiard balls do, things like bits of soot tend to clump together in lacy-looking, fractal patterns. Then, different forces—ranging from the forces between molecules to the effects of gravity—pack the lacy stuff into rough spheres. So yes, two students spent their summer internship at NIST sticking plastic balls together in these funny lumpy spheres, then filling bowls and graduated cylinders with the spheres, then measuring the density at which the spheres packed. Science thanks you, students of the world.

Like the lab-made soot, the student-made plastic-ball aggregations packed at a density of 36 percent, the researchers found. When the scientists checked published scientific literature, they found numbers similar to 36 percent in several areas. Silicon dioxide used in ceramics fills at roughly that density, as do pharmaceutical powders whose grains tend to clump together. NASA’s measurements for 20 comets estimate that they have a density ranging from 20 percent to 40 percent.

The NIST researchers published their work this week in the Proceedings of the National Academies of Sciences. They listed their students among the study authors.