Jamming transition in emulsions and granular materials

Abstract

We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find that the construction history parametrized by the compression rate during the preparation protocol has a strong effect on the micromechanical properties of granular materials but not on emulsions. This leads the granular system to jam at different volume fractions depending on the histories. Isostaticity is found in the packings close to the jamming transition in emulsions and in granular materials at slow compression rates and infinite friction. Heterogeneity of interparticle forces increases as the packings approach the jamming transition which is demonstrated by the exponential tail in force distributions and the small values of the participation number measuring spatial localization of the forces. However, no signatures of the jamming transition are observed in structural properties, like the radial distribution functions and the distributions of contacts.

The jamming scenario—an introduction and outlook

“…In the presence of static friction, therefore, the properties of a packing are very history dependent, as the tangential forces are not only dependent on the configuration, but also on how the configuration was made -see e.g. [78][79][80][81].…”

Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

“…These barriers can be understood as follows: so far we have treated the case of hard spheres considered as soft spheres (interacting via soft-potential such as Hertz-Mindlin forces) in the limit of vanishing deformation or infinite shear modulus. Indeed, the way to consider forces in granular materials is by considering the small tiny deformation at the contact points and a given force law [32]. In a sense, deformable particles are needed when discussing realistic jammed states especially when considering the problem of sound propagation and elastic behavior [65,66].…”

“…Consider a set of spherical particles interacting via normal and tangential contact forces. These can be the standard Hertz and Mindlin/Coulomb forces of contact mechanics [35,36,32], respectively, see Section 7.1. We set N : number of particles, N n : number of unknown normal forces, N t : number of unknown tangential forces, E f : number of force balance equations, E t : number of torque balance equations, Z = 2M/N : average coordination number of the packing, where M is the total number of contacts, f 1 (µ): undetermined function of the friction coefficient µ such that 1 − f 1 (µ) is the fraction of spheres that can rotate freely (f 1 (0) = 0 and f 1 (∞) = 1), and f 2 (µ): undetermined function of µ indicating the ratio of contacts satisfying F t < µF n , which satisfies f 2 (0) = 0 and f 2 (∞) = 1.…”

“…(b) Critical phenomena of deformable particle: jamming is seen as a critical point at which observables such as pressure, coordination number and elastic moduli behave as power-law near the critical volume fraction, φ c , [26,27,29,31,32,30,28,33,34]. The jammed state is modelled as granular media composed of soft particles, typically Hertz-Mindlin [32,35,36] grains under external pressure and emulsions compressed under osmotic pressure [37], as they approach the jamming transition from the solid phase above the critical density: φ → φ + c .…”

“…The jammed state is modelled as granular media composed of soft particles, typically Hertz-Mindlin [32,35,36] grains under external pressure and emulsions compressed under osmotic pressure [37], as they approach the jamming transition from the solid phase above the critical density: φ → φ + c . (c) Hard-sphere glasses: In parallel to studies in the field of jamming there exists a community attempting to understand the packing problem approaching jamming from the liquid phase [38,39,40], that is, φ → φ − c .…”