Attractive emulsion droplets probe the phase diagram of jammed granular matter

Abstract

It remains an open question whether statistical mechanics approaches apply to random packings of athermal particles. Although a jamming phase diagram has recently been proposed for hard spheres with varying friction, here we use a frictionless emulsion system in the presence of depletion forces to sample the available phase space of packing configurations. Using confocal microscopy, we access their packing microstructure and test the theoretical assumptions. As a function of attraction, our packing protocol under gravity leads to well-defined jammed structures in which global density initially increases above random close packing and subsequently decreases monotonically. Microscopically, the fluctuations in parameters describing each particle, such as the coordination number, number of neighbors, and local packing fraction, are for all attractions in excellent agreement with a local stochastic model, indicating that long-range correlations are not important. Furthermore, the distributions of local cell volumes can be collapsed onto a universal curve using the predicted k-gamma distribution, in which the shape parameter k is fixed by the polydispersity while the effect of attraction is captured by rescaling the average cell volume. Within the Edwards statistical mechanics framework, this result measures the decrease in compactivity with global density, which represents a direct experimental test of a jamming phase diagram in athermal systems. The success of these theoretical tools in describing yet another class of materials gives support to the much-debated statistical physics of jammed granular matter.T he random packing of particles is a problem of great practical and theoretical importance with applications to systems as diverse as granular materials, emulsions, and colloids. How athermal particles pack is affected by many parameters, including the packing protocol, the shape and roughness of the particles, as well as their polydispersity. Nevertheless, experiments and numerical simulations have suggested the existence of reproducible disordered packing structures, which can be achieved by sedimenting and shaking monodisperse (1, 2) and polydisperse (3) spheres, ellipsoids (4), and tetrahedra (5). For frictional particles, there emerges a reversible packing density curve from random loose packing (RLP) to random close packing (RCP) as a function of the applied tapping protocol (6). The dependence of density of jammed states on the friction coefficient has led to an equation of state and a prediction of a jamming phase diagram to describe the behavior of these systems in numerical simulations (7). Moreover, experiments on compressible two-dimensional packings of photoelastic beads (8) and foams (9) have probed configurations at different packing densities by applying an external load. The reproducibility of all these jammed states for a given set of experimental conditions suggests that a statistical mechanics framework may apply to these inherently out-of-equilibrium systems (10-12). Other studies have argued...

Jammed elastic shells – a 3D experimental soft frictionless granular system

“…However, introduction of attractive forces between droplets was found to greatly affect the contact number distribution, shiing the peak or hZi to a value below the isostatic value for repulsive frictionless spheres in 3D (hZi ¼ 6). 21 The particles with fewer than 4 contacts in the lowest volume fraction samples, for 4 < 0.726, represent the rattlers present in the system, which completely vanish at higher compression. The fraction of rattlers at all volume fractions is shown in Table 1.…”

“…Compressed emulsions and foams are the two most widely studied experimental so frictionless systems to date, of which studies on compressed emulsions were performed in 3D. [15][16][17][18][19][20][21][22][23][24] These latter studies have produced a detailed characterization of jammed packings of spherical particles. There are not many other so particles available today to study the nature of jammed matter experimentally.…”

The glass and jamming transitions in dense granular matter

“…It is not clear a priori that one can safely neglect them. Still, careful experiments with photoelastic grains [12], emulsions [16,17] and foams [18] have demonstrated the relevance of point J to describe their mechanical properties.…”

Elasticity and glassy dynamics of dense emulsions

“…In stable emulsions neighbouring particles do not interpenetrate, in contrast to soft polymer spheres [5,6]. The interaction potential is known and can be tuned from soft to hard, repulsive to attractive and if required emulsions can be optically index matched or contrast enhanced, density matched and fluorescently labeled [3,7,8,9,10,11,12].…”