Geometrical properties of disordered packings of hard disks

Abstract

We present experimental and theoretical results for geometrical properties of 2D packings of disks. We were mainly interested in the study of mixtures with disk size distribution which are of more practical interest than equal disks. Average geometrical properties, such as packing fraction or coordination number do not depend on the composition of the mixture, contrary to what would be expected from 3D experiments. We show the existence of a local order in the relative positions of grains with different sizes ; this local order may modify the physical properties of the packing. An approximate theoretical expression for the packing fraction c of 2D close packings is given. It implies the knowledge of the average area of quadrilaterals of the network drawn from the real contacts only. For equal disk disordered packings, it yields the limit c = π2/12∼ 0.822