Measuring grain size fractions of bidisperse granular materials using X-ray radiography

The mechanical properties of granular materials such as sand, snow and rice are inherently tied to the size of the constituent particles. When a system is composed of particles of various sizes, it is common for these particles to segregate by size when disturbed. There is therefore a need to measure the particle size distribution within granular media as it evolves over time. However, there are very few experimental techniques available which can measure the particle sizes in situ without disturbing the medium. Here we present a technique to determine the volume fractions of the grain sizes in bidisperse granular materials with the aid of dynamic X-ray radiography. As a result of the penetration of the X-rays into the medium, radiography minimises the effect of walls and boundaries on experimental measurements, which typically dominate optical measurements. The technique proposed here is based on using Fourier transforms of X-ray radiographs to extract local measurements evolving over time that can be related to the particle size distribution. For the case of bidisperse granular media, with two distinct particle sizes, we show that this technique can measure the relative concentration of the two species, which we determine via a heuristic calibration parameter. We validate this technique by comparing discrete element simulations of mixtures of known concentration with experimental measurements derived from X-ray radiography of glass beads. In the future, this technique could be used to measure the grain size distribution in systems of bidisperse dense granular media where the concentration of particles is not known a priori. Additionally, the technique can be used to analyse granular segregation as it evolves dynamically.