Adhesive Loose Packings Research Articles

Ultraslow Settling Kinetics of Frictional Cohesive Powders.

Using discrete element method simulations, we show that the settling of frictional cohesive grains under ramped-pressure compression exhibits strong history dependence and slow dynamics that are not present for grains that lack either cohesion or friction. Systems prepared by beginning with a dilute state and then ramping the pressure to a small positive value P_{final} over a time τ_{ramp} settle at packing fractions given by an inverse-logarithmic rate law, ϕ_{settled}(τ_{ramp})=ϕ_{settled}(∞)+A/[1+Bln(1+τ_{ramp}/τ_{slow})]. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that τ_{slow} is set by the slow dynamics of structural void stabilization rather than the faster dynamics of bulk densification. We formulate a kinetic free-void-volume theory that predicts this ϕ_{settled}(τ_{ramp}), with ϕ_{settled}(∞)=ϕ_{ALP} and A=ϕ_{settled}(0)-ϕ_{ALP}, where ϕ_{ALP}≡.135 is the "adhesive loose packing" fraction found by Liu etal. [Equation of state for random sphere packings with arbitrary adhesion and friction, Soft Matter 13, 421 (2017)SMOABF1744-683X10.1039/C6SM02216B].

X-ray nanotomography of dry colloidal packings

Random packings are crucial in understanding arrangement and geometry of particles. Random packings of dry small particles may be subject to adhesion or friction, as expected theoretically and numerically. We explore experimentally random packings of dry colloids with X-ray nanotomography that directly provides three-dimensional structural and geometric information of dry colloidal packings. We find that dry colloidal packings, as characterized by contact number and packing density, are quite consistent with adhesive loose packings that significantly deviate from random loose packings for hard spheres. This study may offer direct evidence for adhesive loose packings comprising dry small particles, as proven by X-ray nanotomography.

Random adhesive loose packings of micron-sized particles under a uniform flow field

The effects of hydrodynamic interactions on random adhesive loose packings of monodisperse spherical micro-particles are investigated via a two-way coupled CFD-DEM approach. It is found out that the packing fraction and coordination number do not follow the regression of the adhesion number, which was proposed recently to well characterize the bulk properties of adhesive packings. Based on the balance between particle adhesion and fluid drag force, we propose a modified fluid adhesion number, Adf, which successfully normalizes the packing fraction and coordination number. Besides, the pressure drop through the packed bed shows a critical behavior, which validates the jamming threshold of fine powders, but occurs at a fixed packing fraction of ϕ ≈ 0.22 under the present protocol. The normalized permeability of the packed bed for different parameters is analyzed, which is in good agreement with the derivation of Kozeny-Carman equation.

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

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 μf is 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.

Effects of hydrodynamic interaction on random adhesive loose packings of micron-sized particles

Random loose packings of monodisperse spherical micron-sized particles under a uniform flow field are investigated via an adhesive discrete-element method with the two-way coupling between the particles and the fluid. Characterized by a dimensionless adhesion parameter, the packing fraction follows the similar law to that without fluid, but results in larger values due to the hydrodynamic compression. The total pressure drop through the packed bed shows a critical behaviour at the packing fraction of ϕ ≈ 0.22 in the present study. The normalized permeability of the packed bed for different parameters increases with the increase of porosities and is also in consistent with the Kozeny-Carman equation.

Computer simulation of random loose packings of micro-particles in presence of adhesion and friction

With a 3D discrete-element method specially developed with adhesive contact mechanics, random loose packings of uniform spherical micron-sized particles are fully investigated. Characterized by a dimensionless adhesion parameter Ad proposed in the previous work, four packing regimes are identified: random close packing (RCP) regime with Ad<0.01; random loose packing (RLP) regime with 0.01<Ad<1; adhesion regime with 1<Ad<20 and an asymptotic limit regime with Ad>20. The evolution of the radial distribution function with respect to Ad is analyzed and divided into three stages. Force distribution of these adhesive loose packings follows P(f)~fθ for small forces and P(f)~e−βf for big forces, respectively, which shares a similar form with that in packings without adhesion but results in distinct exponents of θ=0.879, β=0.839 for normal forces. A local mechanical equilibrium analysis demonstrates that adhesion enhances both sliding and rolling resistance so that the fairly loose packing structures of adhesive particles can still be mechanically stable.

Effect of long-range repulsive Coulomb interactions on packing structure of adhesive particles.

The packing of charged micron-sized particles is investigated using discrete element simulations based on adhesive contact dynamic model. The formation process and the final obtained structures of ballistic packings are studied to show the effect of interparticle Coulomb force. It is found that increasing the charge on particles causes a remarkable decrease of the packing volume fraction ϕ and the average coordination number 〈Z〉, indicating a looser and chainlike structure. Force-scaling analysis shows that the long-range Coulomb interaction changes packing structures through its influence on particle inertia before they are bonded into the force networks. Once contact networks are formed, the expansion effect caused by repulsive Coulomb forces are dominated by short-range adhesion. Based on abundant results from simulations, a dimensionless adhesion parameter Ad*, which combines the effects of the particle inertia, the short-range adhesion and the long-range Coulomb interaction, is proposed and successfully scales the packing results for micron-sized particles within the latest derived adhesive loose packing (ALP) regime. The structural properties of our packings follow well the recent theoretical prediction which is described by an ensemble approach based on a coarse-grained volume function, indicating some kind of universality in the low packing density regime of the phase diagram regardless of adhesion or particle charge. Based on the comprehensive consideration of the complicated inter-particle interactions, our findings provide insight into the roles of short-range adhesion and repulsive Coulomb force during packing formation and should be useful for further design of packings.

Adhesive loose packings of small dry particles.

We explore adhesive loose packings of small dry spherical particles of micrometer size using 3D discrete-element simulations with adhesive contact mechanics and statistical ensemble theory. A dimensionless adhesion parameter (Ad) successfully combines the effects of particle velocities, sizes and the work of adhesion, identifying a universal regime of adhesive packings for Ad > 1. The structural properties of the packings in this regime are well described by an ensemble approach based on a coarse-grained volume function that includes the correlation between bulk and contact spheres. Our theoretical and numerical results predict: (i) an equation of state for adhesive loose packings that appear as a continuation from the frictionless random close packing (RCP) point in the jamming phase diagram and (ii) the existence of an asymptotic adhesive loose packing point at a coordination number Z = 2 and a packing fraction ϕ = 1/2(3). Our results highlight that adhesion leads to a universal packing regime at packing fractions much smaller than the random loose packing (RLP), which can be described within a statistical mechanical framework. We present a general phase diagram of jammed matter comprising frictionless, frictional, adhesive as well as non-spherical particles, providing a classification of packings in terms of their continuation from the spherical frictionless RCP.