Physicists determine density limit for randomly packed spherical materials

Jun 02, 2008

The problem of how many identical-sized spheres can be randomly packed into a container has challenged mathematicians for centuries. A team of physicists at The City College of New York (CCNY) has come up with a solution that could have implications for everything from processing granular materials to shipping fruit.

Writing in the May 29 edition of Nature, they demonstrate that random packing of hard, i.e. non-crushable, spheres in three dimensions cannot exceed a density limit of 63.4 percent of the volume. This upper limit is a consequence of a completely "jammed" state that occurs when the materials are at their lowest energy levels, i.e. as close to inert as possible.

"Theoretically, the jammed state would be achieved by lowering the temperature of the spheres to approach absolute zero, since this would cause them to contract," explained Dr. Hernán Makse, CCNY Associate Professor of Physics and principal investigator. "In real life, however, it is attained by shaking the materials."

The findings have potential applications for the manufacture of pharmaceuticals and cosmetics, where powders have to be mixed to a homogenous consistency, he said. Currently, manufacturers must rely on empirical data, i.e. trial and error, to establish their formulas. Professor Makse said his goal is to develop a theory of powders that could enable manufacturers to more efficiently develop new products.

Source: City College of New York

Explore further: Fluctuation X-ray scattering

add to favorites email to friend print save as pdf

Related Stories

Privacy is dead, Davos hears

Jan 22, 2015

Imagine a world where mosquito-sized robots fly around stealing samples of your DNA. Or where a department store knows from your buying habits that you're pregnant even before your family does.

Computer model enables design of complex DNA shapes

Dec 03, 2014

MIT biological engineers have created a new computer model that allows them to design the most complex three-dimensional DNA shapes ever produced, including rings, bowls, and geometric structures such as icosahedrons that ...

Recommended for you

Fluctuation X-ray scattering

4 hours ago

In biology, materials science and the energy sciences, structural information provides important insights into the understanding of matter. The link between a structure and its properties can suggest new ...

Hydrodynamics approaches to granular matter

6 hours ago

Sand, rocks, grains, salt or sugar are what physicists call granular media. A better understanding of granular media is important - particularly when mixed with water and air, as it forms the foundations of houses and off-shore ...

Behind the dogmas of good old hydrodynamics

8 hours ago

A new theory, which gives insights into the transport of liquid flowing along the surface under an applied electric field, was developed by a group of Russian scientists lead by Olga Vinogradova who is a ...

User comments : 2

Adjust slider to filter visible comments by rank

Display comments: newest first

JKF
4 / 5 (2) Jun 02, 2008
The density limit of spheres is 64.95 percent.

Do your math!
h0dges
4 / 5 (2) Jun 02, 2008
The density limit of spheres is 64.95 percent.

Do your math!

Actually for FCC packing (the highest close-packing possible), the density limit is 74.048%

Do your math!

Anyway the article is about random packing, not perfect close-packing, completely different issue which has to involve complex statistics.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.