High-Precision MRI Reconstruction Algorithm for 3D Sphere Packings

Packings of granular materials are complex systems consisting of large sets of particles interacting via contact forces. Their internal structure is interesting for several theoretical and practical reasons, especially when the model system consists in a large amount (up to 10⁵) of identical spheres. We herein present a method to process three-dimensional water density maps recorded in wet granular packings of mm-size spheres by magnetic resonance imaging (MRI). Packings of spheres with highly mono-dispersed diameter are considered and the implementation of an ad hoc reconstruction algorithm tailored for this feature allows for the determination of the position of each single sphere with an unprecedented precision (with respect to the scale of the system) while ensuring that all spheres are identified and no non-existing sphere is introduced in the reconstructed packing. The reconstruction of a 0.5 L sample containing about 2 × 10⁴ spheres is presented to demonstrate the robustness of the method.