Systematic onset of periodic patterns in random disk packings

May 7, 2018, University of Erlangen-Nuremberg

Physicists at Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) have proven that random packings of disks of the same size between parallel walls always form a periodic structure, regardless of the width of the container. The results, which should help scientists to better understand the packing properties of microparticles, have now been published in the renowned journal Physical Review Letters.

People have wondered which patterns should be used to pack objects at the highest density in containers for several centuries now. As early as 1611, Johannes Kepler suggested that no arrangement of spheres of the same size had a greater density than offset layers in hexagonal lattices. While packings of spheres randomly poured into a box have a mean density of around 65 percent, a density of around 74 percent can be achieved with the periodic of hexagonal packing. Kepler's theory was finally proven in 2014 by using complex computer simulations.

In conjunction with colleagues from Brazil and the USA, physicists at FAU have now discovered that when spheres are poured randomly into a container, they always form a periodic structure. They were able to confirm this with two-dimensional experiments. In a series of computer simulations, the researchers poured up to 10 million disks of the same size from various positions into an open rectangular container. The researchers were astonished to find that a periodic structure formed during every single one of the simulations. "In our case, periodic means that there are equivalents for each particle that are repeated at the same position on the x-axis at regular intervals," explains Prof. Dr. Thorsten Pöschel from the Institute for Multiscale Simulation of Particulate Systems at FAU. The of disks and voids that forms continues upwards in a uniform fashion with an average of four contacts per .

However, these periodic patterns do not form immediately. Initially, there is a disordered phase that is mainly characterised by larger spaces or by clusters of disks that have more or less than four contacts. Although the fill level at which the disks form a can vary greatly between containers of the same width, this average level increases when the distance between the walls of the container increases. Or, to put it another way, the wider the channel, the more layers have to be poured in until the disks form periodic patterns. This is because there are more ways for the disks to arrange themselves in disordered positions at the beginning of the filling process, and this continues upward in significantly more layers than in narrow containers. But regardless of the width of the , the researchers were able to demonstrate that the probability that a channel is not yet periodic decreases exponentially with increasing fill level.

The findings should help to increase the understanding of packing properties of monodisperse and polydisperse microparticles. Packing particles as densely as possible is the key to several practical applications, for example, for minimising material porosity during 3-D printing processes and other methods of additive manufacturing, thus increasing the strength of new materials.

The results of the project have now been published in Physical Review Letters, titled "Systematic Onset of Periodic Patterns in Random Disk Packings."

Explore further: How particles pack in a confined space

More information: Nikola Topic et al, Systematic Onset of Periodic Patterns in Random Disk Packings, Physical Review Letters (2018). DOI: 10.1103/PhysRevLett.120.148002

Related Stories

How particles pack in a confined space

February 10, 2016

(Phys.org)—Many biological systems involve dense packing of a large amount of material or particles in a confined space. For example, eukaryotes' nuclei hold about two meters of DNA that is tightly wound into chromosomes. ...

Modeling Jupiter and Saturn's possible origins

March 5, 2013

New theoretical modeling by Carnegie's Alan Boss provides clues to how the gas giant planets in our solar system—Jupiter and Saturn—might have formed and evolved. His work was published recently by the Astrophysical Journal.

Recommended for you

Neutron stars may hold an answer to neutron puzzle on Earth

August 15, 2018

According to University of Illinois physicist Douglas H. Beck, "Neutrons play some unusual roles in our world. Free neutrons decay in about 900 s but, bound in nuclei, they are stable and make up somewhat more than half the ...

When mixing granular matter, order among disorder

August 14, 2018

Mixing liquids is easy, or at least scientifically understood: a drop of food coloring will eventually mix into a cup of water through diffusion, and a dollop of cream can be mixed into coffee with a spoon through what is ...

0 comments

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.