Unified size-density and size-topology relations in random packings of dry adhesive polydisperse spheres.

We study the size-density and size-topology relations in random packings of dry adhesive polydisperse microspheres with Gaussian and lognormal size distributions through a geometric tessellation. We find that the dependence of the neighbor number on the centric particle size is always quasilinear, regardless of the size distribution, size span, or interparticle adhesion. The average local packing fraction as a function of normalized particle size for different size variances is well regressed on the same profile, which increases to larger values as the relative strength of adhesion decreases. The variations of the local coordination number with the particle size converge onto a single curve for all adhesive particles, but gradually transfer to another branch for nonadhesive particles. Such adhesion-induced size-density and size-topology relations are interpreted theoretically with a modified geometrical "granocentric" model, where the model parameters are dependent on a single dimensionless adhesion number. Our findings, together with the modified theory, provide a more unified perspective on the substantial geometry of amorphous polydisperse systems, especially those with fairly loose structures.