Contact numbers in packings of frictional cylinders

The mechanical stability of a granular system depends on the average number of contacts Z between its particles. For most particle shapes, predicting Z as a function of the average volume fraction ϕ is complicated by the spatial correlations between simultaneously contacting particles. However, in the dilute packings formed by cylinders with large aspect ratios α (length of the cylinder divided by its diameter) the individual contacts can be expected to become uncorrelated. Philipse (Langmuir 12, 1127 (1996)) derived from this idea the Random Contact Model (RCM) which predicts ZRCM = 2αϕ. Here we compare ZRCM with X-ray tomography measurements of Z(α, ϕ) in cylinder packings with α = of 14.1, 21.1, and 28.2. We find the measured Z to be smaller than 0.85 ZRCM. Using a Voronoi tessellation we then analyze Z as a function of ϕ on the level of individual particles where the linear relationship does not hold up.