  We study the 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 neighbour
number on the centric particle size is always quasilinear, independent of the
size distribution, the 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 grows to larger values
as the relative strength of adhesion decreases. As for the local coordination
number-particle size profiles, they converge onto a single curve for all the
adhesive particles, but will gradually transfer to another branch for
non-adhesive particles. Such adhesion induced size-topology relations are
interpreted theoretically by a modified geometrical "granocentric" model, where
the model parameters are dependent on a 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.
