Gallery: Voronoi Cells
Update (October 2008): the software used to create the this image is now available as an open source library – see the Voro++ website.
In a typical static random packing of spheres, the particles occupy around 60% to 65% of the volume. During flow, this packing fraction can decrease by several percent, and the nature of this decrease can provide valuable insight into the random-packing dynamics.
Ideally we would like to look at these density fluctuations on a scale of several particle diameters. However, due to the discreteness of the problem, getting an accurate local measurement of density is difficult, and naive methods of counting up the number of particles in a small region can have errors larger than the scale of interest.
We therefore make use of Voronoi cells. For each particle in a granular packing, we can define a cell around it which consists of all the space which is closer to that particle than any other. Voronoi cells take the form of irregular polyhedra, the sides of which are the planes which are perpendicular bisectors between a particle and its neighbors. Dividing a cell volume by the sphere volume gives an accurate measurement of local packing fraction at a scale of a single particle.
The above image shows an example output from our Voronoi algorithm, for a small section of a packing which is eight particle diameters thick.
