SpherePack1D

Project Information

About this project:

This is the SpherePack1D project ("spherepack1d")

The program spherepack1d is a command-line tool, which estimates the maximum random close packing fraction of hard spheres with a distribution of diameters, based upon an algorithm in J. Chem. Phys. 131, 244104 (2009). It was registered in Jul 29, 2011.

Background information

There are a number of contexts in science and engineering when a system consists, at least approximately, of a collection of spherical objects. For example, emulsions typically consist of spherical droplets of one liquid in another, while many granular materials (sand, various powders) may also have roughly spherical grains. Under these circumstances, the maximum packing fraction is a key parameter which can help to estimate system properties. For example, in suspensions of hard particles, it determines the point where the viscosity becomes very high (or, in principle, diverges), whicle for emulsions, it sets the boundary between liquid-like and soft-solid-like behaviour.

For a collection of equal sized spheres, it is known that the maximum packing fraction is around 64% (i.e. a volume fraction of around 0.64). However, if the spheres are of different sizes then no one knows the answer in general.

The approach that has been taken in the past is to simulate a large number of spheres jiggling around in a box, and gradually compress the box until everything jams up. This is conceptually straightforward, but requires a fair amount of coding to set up the simulation, and then it might take several hours to run in order to obtain a high quality estimate for the packing fraction. The computational difficulty becomes rapidly greater as the width of the distribution of sphere sizes becomes broader.

More recently, a simple one-dimensional algorithm for predicting the answer has been published, which (when compared to the full-scale packing simulations) appears to be very accurate while being many times faster.. The algorithm, is decribed in the Journal of Chemical Physics, volume 131, article number 244104, from 2009. However, I recognize that not everyone is inclined to spend an hour or two turning that algorithm into runnable code. Hence this project.

Running the program

The program is available as source code in c, which on a Unix-like system with a GNU toolchain can be compiled using the instruction

gcc -lm spherepack1d.c -o spherepack1d

On Windows systems, you will either need to find a compiler, or download a free program like Cygwin which provides a Unix-like environment in its own right.

You should then run the program from the command line. It takes a number of command line options, but to begin with, I would recommend running it with the -h option:

./spherepack1d -h

which will print out a help screen with instructions on how to use the program more generally.

Good luck, and please let me know if there are any bugs or other issues. If it turns out to be a useful piece of code, I would love to see it packaged and distribued with some of the Linux distributions. If you have any knowledge about that area and would like to help, please get in touch.

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