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

Wenwei Liu; Yuliang Jin; Sheng Chen; Hernán A Makse; Shuiqing Li

doi:10.1039/c6sm02216b

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

Soft Matter. 2017 Jan 4;13(2):421-427. doi: 10.1039/c6sm02216b.

Authors

Wenwei Liu¹, Yuliang Jin², Sheng Chen¹, Hernán A Makse³, Shuiqing Li¹

Affiliations

¹ Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China. [email protected].
² Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan.
³ Levich Institute and Physics Department, City College of New York, New York 10031, USA.

PMID: 27942690
DOI: 10.1039/c6sm02216b

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.