Arrangement of discs in 2d binary assemblies

We study arrangements of the two species of discs in binary assemblies at an intermediate scale. Small discs rearrange along large ones in clusters whose mass and compactness are analyzed with the tools of percolation. The assemblies are generated analogically on an air table or numerically from RSA or Powell algorithms. At a given packing fraction, an infinite cluster of small discs exists above a critical composition; a phenomenological expression for this threshold is proposed. Like in usual percolation problems, the number of inner links in a cluster is a linear function of its mass, with a slope depending both on the packing fraction, the composition of the mixture and the building procedure. An approximate expression is derived for it.