Equation of state for random sphere packings with arbitrary adhesion and friction

Abstract

We systematically generate a large set of random micro-particle packings over a wide range of adhesion and friction by means of adhesive contact dynamics simulation. The ensemble of generated packings covers a range of volume fractions ϕ from 0.135 ± 0.007 to 0.639 ± 0.004, and of coordination numbers Z from 2.11 ± 0.03 to 6.40 ± 0.06. We determine ϕ and Z at four limits (random close packing, random loose packing, adhesive close packing, and adhesive loose packing), and find a universal equation of state ϕ(Z) to describe packings with arbitrary adhesion and friction. From a mechanical equilibrium analysis, we determine the critical friction coefficient μ_f,c: when the friction coefficient μ_f is below μ_f,c, particles' rearrangements are dominated by sliding, otherwise they are dominated by rolling. Because of this reason, both ϕ(μ_f) and Z(μ_f) change sharply across μ_f,c. Finally, we generalize the Maxwell counting argument to micro-particle packings, and show that the loosest packing, i.e., adhesive loose packing, satisfies the isostatic condition at Z = 2.