Random close packing revisited: How many ways can we pack frictionless disks?

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in 2d using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2d and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability $P(\phi)$ for obtaining a collectively jammed state at a particular packing fraction $\phi$ into two composite functions: 1) the density of CJ packing fractions $\rho(\phi)$, which only depends on geometry and 2) the frequency distribution $\beta(\phi)$, which depends on the particular algorithm used to create them. We find that the function $\rho(\phi)$ is sharply peaked and that $\beta(\phi)$ depends exponentially on $\phi$. We predict that in the infinite system-size limit the behavior of $P(\phi)$ in these systems is controlled by the density of CJ packing fractions--not the frequency distribution. These results suggest that the location of the peak in $P(\phi)$ when $N \to \infty$ can be used as a protocol-independent definition of random close packing.Comment: 9 pages, 14 figure

The jamming transition and new percolation universality classes in particulate systems with attraction

We numerically study the jamming transition in particulate systems with attraction by investigating their mechanical response at zero temperature. We find three regimes of mechanical behavior separated by two critical transitions--connectivity and rigidity percolation. The transitions belong to different universality classes than their lattice counterparts, due to force balance constraints. We also find that these transitions are unchanged at low temperatures and resemble gelation transitions in experiments on colloidal and silica gels.Comment: 4 pages, 2 figures, 2 table

Motion of a rod-like particle between parallel walls with application to suspension rheology

We study the dynamics of elongated axisymmetric particles undergoing shear flow between two parallel planar walls, under creeping-flow conditions. Particles are modeled as linear chains of touching spheres and it is assumed that walls are separated by a distance comparable to particle length. The hydrodynamic interactions of the chains with the walls are evaluated using our Cartesian-representation algorithm Bhattacharya et al., Physica A 356, 294–340 2005b . We find that when particles are far from both walls in a weakly confined system, their trajectories are qualitatively similar to Jeffery orbits in unbounded space. In particular, the periods of the orbits and the evolution of the azimuthal angle in the flow-gradient plane are nearly independent of the initial orientation of the particle. For stronger confinements, however, i.e., when the particle is close to one or both walls a significant dependence of the angular evolution on the initial particle configuration is observed. The phases of particle trajectories in a confined dilute suspension subject to a sudden onset of shear flow are thus slowly randomized due to unequal trajectory periods, even in the absence of interparticle hydrodynamic interactions. Therefore, stress oscillations associated with initially coherent particle motions decay with time. The effect of near contact particle-wall interactions on the suspension behavior is also discussed

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap $h_0$ between the large particle and the wall is assumed to be comparable to the diameter $2a$ of the smaller particles so there is a length-scale separation between the gap width $h_0$ and the radius of the large particle $b<<h_0$. We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations $h_0$, the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For $h_0<<a$, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.Comment: 11 pages, 5 figure

A percolation model for slow dynamics in glass-forming materials

We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq \beta \leq 1$ and the functional dependence of the structural relaxation time $\tau_\alpha$ and exponent $\beta$ on temperature, density, and wave number.Comment: 4 pages, 1 figur