title: 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 μf,c: when the friction coefficient μfis below μf,c, particles' rearrangements are dominated by sliding, otherwise they are dominated by rolling. Because of this reason, both ϕ(μf) and Z(μf) change sharply across μf,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.
authors.affiliation: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China. lishuiqing@tsinghua.edu.cn.
authors.forename: Wenwei
authors.initials: W
authors.lastname: Liu
authors.affiliation: Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan.
authors.forename: Yuliang
authors.initials: Y
authors.lastname: Jin
authors.affiliation: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China. lishuiqing@tsinghua.edu.cn.
authors.forename: Sheng
authors.initials: S
authors.lastname: Chen
authors.affiliation: Levich Institute and Physics Department, City College of New York, New York 10031, USA.
authors.forename: Hernán A
authors.initials: HA
authors.lastname: Makse
authors.affiliation: Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China. lishuiqing@tsinghua.edu.cn.
authors.forename: Shuiqing
authors.initials: S
authors.lastname: Li