The coordination number of granular cylinders

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(in progress)

Soft Matter Keywords

Coordination Number,

Summary

In a granular material, the average coordination number <math>\langle z\rangle</math> is defined as the average number of touching neighbors per particle. For hard spheres, <math>\langle z\rangle</math> has been well-studied and is widely-agreed upon. This is paper discusses <math>\langle z\rangle</math> for cylindrical grains. Using constraint equations, the authors prove the following equations:

Grain Type <math>\langle z\rangle</math>
10
Multiplication table
× 1 2 3
1 1 2 3
2 2 4 6
3 3 6 9
4 4 8 12
5 5 10 15

First, the authors prove that frictionless cylinder grains have <math>\langle z\rangle = 10</math>, which comes right out of constraint equations.

Relevance to Soft Matter

References

J. Blouwolff and S. Fraden. "The coordination number of granular cylinders." Europhys. Letters, 76 (6), pp. 1095-1101 (2006).